Given small computational resources how navigation was implemented ( Not Samples of old guidance software)How did the Apollo computers evaluate transcendental functions like sine, arctangent, log?How did the Apollo guidance computer handle parity bit errors?How did the Apollo guidance computer handle the Earth-Moon system's rotation around the Sun?Samples of old guidance software using computational resources on Earth implementing navigation in spaceHow often, if ever, was “software” updated in the shuttle orbiter?

opening Illustrator template file (.ait) for editing results in untitled.ai

Right way to say that I disagree with a design but will implement it despite my objections

The falling broom handle

Implementing simplified Jaipur board game

Is 2FA via mobile phone still a good idea when phones are the most exposed device?

Should I correct a mistake on an arXiv manuscript, that I found while refereeing it?

Order of the products of two order-2 elements in a finite group

draw table with tikz matrix line shift a little bit

Left a meeting without apparent reason. What to do?

Does no-one standing against the speaker of the house in UK lead to the local electorate being disenfranchised?

Was this “caterpillar” strategy a good way to advance my pawns?

I can be found near gentle green hills and stony mountains

Moving parentheses vertically

Who originated the dangerous avocado-pitting technique?

Find intersecting polygon within a layer

Can Shadow Pokémon be Shiny in Pokémon Go?

180W Laptop charged with 45W charger, is it dead?

Can I swap out this 20A breaker for a 15A breaker?

How would a young girl/boy (about 14) who never gets old survive in the 16th century?

Help resolve territory acquisition design difference of opinion in MMO RTS

Is it likely that my lack of post-secondary education is holding my resume back?

Why don't my appliances work when my tester shows voltage at the outlets?

How is warfare affected when armor has (temporarily) outpaced guns? How can guns compete?

Differences between vehicles used on the Moon and the ones used on Mars



Given small computational resources how navigation was implemented ( Not Samples of old guidance software)


How did the Apollo computers evaluate transcendental functions like sine, arctangent, log?How did the Apollo guidance computer handle parity bit errors?How did the Apollo guidance computer handle the Earth-Moon system's rotation around the Sun?Samples of old guidance software using computational resources on Earth implementing navigation in spaceHow often, if ever, was “software” updated in the shuttle orbiter?






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty
margin-bottom:0;

.everyonelovesstackoverflowposition:absolute;height:1px;width:1px;opacity:0;top:0;left:0;pointer-events:none;








16














$begingroup$


Update : What I really wanted to know was how spacecraft navigation ( not guidance ) computers worked, given small computational resources. I have asked in another question and edit this question to limit answers to examples of old guidance software source code, For those interested in samples of old guidance software please refer to Samples of old guidance software ( not with small computational resources implement navigation in space) instead. Leaving the original ( incorrect question below as it was in order to not make the responses look irrelevant).



In an article I came across the something like "X used hardware programme for Venus mission with 65Kb (not sure if this number is correct?) memory".



I am a software developer and with all the resources available today I cannot fathom where one could even start such an endeavour.



Is there an archive (museum) of old/antique software that was written (hard or soft ) for interplanetary missions? if something at a higher level than assembly or the equivalent in today's Java/Pascal/C# etc. programming languages with no consideration for memory and disk usage then that would be even better.



From what little I understood it seems a task equivalent to construction of Pyramids with primitive tools. Are there any simulation or tools to get a today's simpleton programmer a glimpse and appreciation of what those giants did.










share|improve this question












$endgroup$










  • 1




    $begingroup$
    not an answer, but links in answers to the following questions might be helpful: How did the Apollo computers evaluate transcendental functions like sine, arctangent, log? as well as How did the Apollo guidance computer handle parity bit errors? and also How did the Apollo guidance computer handle the Earth-Moon system's rotation around the Sun?
    $endgroup$
    – uhoh
    Oct 14 at 10:27






  • 1




    $begingroup$
    The relationship is both 'space probes' and ICBMs need to leave earth first. - "Samples of old guidance software" for a Saturn-V... you will not find.
    $endgroup$
    – Mazura
    Oct 14 at 23:13






  • 3




    $begingroup$
    @Arjang, orbital-transfer software might not be suitable for ICBMs, but I'm pretty sure the Apollo re-entry guidance software is.
    $endgroup$
    – Mark
    Oct 15 at 6:44






  • 3




    $begingroup$
    Even something simple like notepad has a whole host of OS compatibility layers, the gui and other libraries it's built on... It's written in a fairly high level language, targeted to the fairly complex x86 platform and has a surprising amount of functionality. When you get down to assembly and optimising for size, you can do incredible things - e.g. theverge.com/2012/5/14/3014698/assembly-4k-demoscene-fractals
    $endgroup$
    – Baldrickk
    Oct 15 at 10:31






  • 7




    $begingroup$
    As a programmer I strongly encourage you to try microcontroller programming. An Arduino is a great introduction. The basic model has 1k of RAM. You'd be amazed at how much you can achieve with 1k of RAM. People have written everything from quadcopter (drone) controllers, radio-control receivers, walking robot controllers to airplane autopilot guidance/navigation software all in 1k of RAM. I started microcontroller programming with the PIC16F84 which has 68 bytes (yes, bytes, not kilobytes) of RAM and I implemented a lot of projects with it.
    $endgroup$
    – slebetman
    Oct 16 at 4:26


















16














$begingroup$


Update : What I really wanted to know was how spacecraft navigation ( not guidance ) computers worked, given small computational resources. I have asked in another question and edit this question to limit answers to examples of old guidance software source code, For those interested in samples of old guidance software please refer to Samples of old guidance software ( not with small computational resources implement navigation in space) instead. Leaving the original ( incorrect question below as it was in order to not make the responses look irrelevant).



In an article I came across the something like "X used hardware programme for Venus mission with 65Kb (not sure if this number is correct?) memory".



I am a software developer and with all the resources available today I cannot fathom where one could even start such an endeavour.



Is there an archive (museum) of old/antique software that was written (hard or soft ) for interplanetary missions? if something at a higher level than assembly or the equivalent in today's Java/Pascal/C# etc. programming languages with no consideration for memory and disk usage then that would be even better.



From what little I understood it seems a task equivalent to construction of Pyramids with primitive tools. Are there any simulation or tools to get a today's simpleton programmer a glimpse and appreciation of what those giants did.










share|improve this question












$endgroup$










  • 1




    $begingroup$
    not an answer, but links in answers to the following questions might be helpful: How did the Apollo computers evaluate transcendental functions like sine, arctangent, log? as well as How did the Apollo guidance computer handle parity bit errors? and also How did the Apollo guidance computer handle the Earth-Moon system's rotation around the Sun?
    $endgroup$
    – uhoh
    Oct 14 at 10:27






  • 1




    $begingroup$
    The relationship is both 'space probes' and ICBMs need to leave earth first. - "Samples of old guidance software" for a Saturn-V... you will not find.
    $endgroup$
    – Mazura
    Oct 14 at 23:13






  • 3




    $begingroup$
    @Arjang, orbital-transfer software might not be suitable for ICBMs, but I'm pretty sure the Apollo re-entry guidance software is.
    $endgroup$
    – Mark
    Oct 15 at 6:44






  • 3




    $begingroup$
    Even something simple like notepad has a whole host of OS compatibility layers, the gui and other libraries it's built on... It's written in a fairly high level language, targeted to the fairly complex x86 platform and has a surprising amount of functionality. When you get down to assembly and optimising for size, you can do incredible things - e.g. theverge.com/2012/5/14/3014698/assembly-4k-demoscene-fractals
    $endgroup$
    – Baldrickk
    Oct 15 at 10:31






  • 7




    $begingroup$
    As a programmer I strongly encourage you to try microcontroller programming. An Arduino is a great introduction. The basic model has 1k of RAM. You'd be amazed at how much you can achieve with 1k of RAM. People have written everything from quadcopter (drone) controllers, radio-control receivers, walking robot controllers to airplane autopilot guidance/navigation software all in 1k of RAM. I started microcontroller programming with the PIC16F84 which has 68 bytes (yes, bytes, not kilobytes) of RAM and I implemented a lot of projects with it.
    $endgroup$
    – slebetman
    Oct 16 at 4:26














16












16








16


2



$begingroup$


Update : What I really wanted to know was how spacecraft navigation ( not guidance ) computers worked, given small computational resources. I have asked in another question and edit this question to limit answers to examples of old guidance software source code, For those interested in samples of old guidance software please refer to Samples of old guidance software ( not with small computational resources implement navigation in space) instead. Leaving the original ( incorrect question below as it was in order to not make the responses look irrelevant).



In an article I came across the something like "X used hardware programme for Venus mission with 65Kb (not sure if this number is correct?) memory".



I am a software developer and with all the resources available today I cannot fathom where one could even start such an endeavour.



Is there an archive (museum) of old/antique software that was written (hard or soft ) for interplanetary missions? if something at a higher level than assembly or the equivalent in today's Java/Pascal/C# etc. programming languages with no consideration for memory and disk usage then that would be even better.



From what little I understood it seems a task equivalent to construction of Pyramids with primitive tools. Are there any simulation or tools to get a today's simpleton programmer a glimpse and appreciation of what those giants did.










share|improve this question












$endgroup$




Update : What I really wanted to know was how spacecraft navigation ( not guidance ) computers worked, given small computational resources. I have asked in another question and edit this question to limit answers to examples of old guidance software source code, For those interested in samples of old guidance software please refer to Samples of old guidance software ( not with small computational resources implement navigation in space) instead. Leaving the original ( incorrect question below as it was in order to not make the responses look irrelevant).



In an article I came across the something like "X used hardware programme for Venus mission with 65Kb (not sure if this number is correct?) memory".



I am a software developer and with all the resources available today I cannot fathom where one could even start such an endeavour.



Is there an archive (museum) of old/antique software that was written (hard or soft ) for interplanetary missions? if something at a higher level than assembly or the equivalent in today's Java/Pascal/C# etc. programming languages with no consideration for memory and disk usage then that would be even better.



From what little I understood it seems a task equivalent to construction of Pyramids with primitive tools. Are there any simulation or tools to get a today's simpleton programmer a glimpse and appreciation of what those giants did.







navigation software






share|improve this question
















share|improve this question













share|improve this question




share|improve this question








edited Oct 15 at 21:03







Arjang

















asked Oct 14 at 10:13









ArjangArjang

1881 silver badge7 bronze badges




1881 silver badge7 bronze badges










  • 1




    $begingroup$
    not an answer, but links in answers to the following questions might be helpful: How did the Apollo computers evaluate transcendental functions like sine, arctangent, log? as well as How did the Apollo guidance computer handle parity bit errors? and also How did the Apollo guidance computer handle the Earth-Moon system's rotation around the Sun?
    $endgroup$
    – uhoh
    Oct 14 at 10:27






  • 1




    $begingroup$
    The relationship is both 'space probes' and ICBMs need to leave earth first. - "Samples of old guidance software" for a Saturn-V... you will not find.
    $endgroup$
    – Mazura
    Oct 14 at 23:13






  • 3




    $begingroup$
    @Arjang, orbital-transfer software might not be suitable for ICBMs, but I'm pretty sure the Apollo re-entry guidance software is.
    $endgroup$
    – Mark
    Oct 15 at 6:44






  • 3




    $begingroup$
    Even something simple like notepad has a whole host of OS compatibility layers, the gui and other libraries it's built on... It's written in a fairly high level language, targeted to the fairly complex x86 platform and has a surprising amount of functionality. When you get down to assembly and optimising for size, you can do incredible things - e.g. theverge.com/2012/5/14/3014698/assembly-4k-demoscene-fractals
    $endgroup$
    – Baldrickk
    Oct 15 at 10:31






  • 7




    $begingroup$
    As a programmer I strongly encourage you to try microcontroller programming. An Arduino is a great introduction. The basic model has 1k of RAM. You'd be amazed at how much you can achieve with 1k of RAM. People have written everything from quadcopter (drone) controllers, radio-control receivers, walking robot controllers to airplane autopilot guidance/navigation software all in 1k of RAM. I started microcontroller programming with the PIC16F84 which has 68 bytes (yes, bytes, not kilobytes) of RAM and I implemented a lot of projects with it.
    $endgroup$
    – slebetman
    Oct 16 at 4:26













  • 1




    $begingroup$
    not an answer, but links in answers to the following questions might be helpful: How did the Apollo computers evaluate transcendental functions like sine, arctangent, log? as well as How did the Apollo guidance computer handle parity bit errors? and also How did the Apollo guidance computer handle the Earth-Moon system's rotation around the Sun?
    $endgroup$
    – uhoh
    Oct 14 at 10:27






  • 1




    $begingroup$
    The relationship is both 'space probes' and ICBMs need to leave earth first. - "Samples of old guidance software" for a Saturn-V... you will not find.
    $endgroup$
    – Mazura
    Oct 14 at 23:13






  • 3




    $begingroup$
    @Arjang, orbital-transfer software might not be suitable for ICBMs, but I'm pretty sure the Apollo re-entry guidance software is.
    $endgroup$
    – Mark
    Oct 15 at 6:44






  • 3




    $begingroup$
    Even something simple like notepad has a whole host of OS compatibility layers, the gui and other libraries it's built on... It's written in a fairly high level language, targeted to the fairly complex x86 platform and has a surprising amount of functionality. When you get down to assembly and optimising for size, you can do incredible things - e.g. theverge.com/2012/5/14/3014698/assembly-4k-demoscene-fractals
    $endgroup$
    – Baldrickk
    Oct 15 at 10:31






  • 7




    $begingroup$
    As a programmer I strongly encourage you to try microcontroller programming. An Arduino is a great introduction. The basic model has 1k of RAM. You'd be amazed at how much you can achieve with 1k of RAM. People have written everything from quadcopter (drone) controllers, radio-control receivers, walking robot controllers to airplane autopilot guidance/navigation software all in 1k of RAM. I started microcontroller programming with the PIC16F84 which has 68 bytes (yes, bytes, not kilobytes) of RAM and I implemented a lot of projects with it.
    $endgroup$
    – slebetman
    Oct 16 at 4:26








1




1




$begingroup$
not an answer, but links in answers to the following questions might be helpful: How did the Apollo computers evaluate transcendental functions like sine, arctangent, log? as well as How did the Apollo guidance computer handle parity bit errors? and also How did the Apollo guidance computer handle the Earth-Moon system's rotation around the Sun?
$endgroup$
– uhoh
Oct 14 at 10:27




$begingroup$
not an answer, but links in answers to the following questions might be helpful: How did the Apollo computers evaluate transcendental functions like sine, arctangent, log? as well as How did the Apollo guidance computer handle parity bit errors? and also How did the Apollo guidance computer handle the Earth-Moon system's rotation around the Sun?
$endgroup$
– uhoh
Oct 14 at 10:27




1




1




$begingroup$
The relationship is both 'space probes' and ICBMs need to leave earth first. - "Samples of old guidance software" for a Saturn-V... you will not find.
$endgroup$
– Mazura
Oct 14 at 23:13




$begingroup$
The relationship is both 'space probes' and ICBMs need to leave earth first. - "Samples of old guidance software" for a Saturn-V... you will not find.
$endgroup$
– Mazura
Oct 14 at 23:13




3




3




$begingroup$
@Arjang, orbital-transfer software might not be suitable for ICBMs, but I'm pretty sure the Apollo re-entry guidance software is.
$endgroup$
– Mark
Oct 15 at 6:44




$begingroup$
@Arjang, orbital-transfer software might not be suitable for ICBMs, but I'm pretty sure the Apollo re-entry guidance software is.
$endgroup$
– Mark
Oct 15 at 6:44




3




3




$begingroup$
Even something simple like notepad has a whole host of OS compatibility layers, the gui and other libraries it's built on... It's written in a fairly high level language, targeted to the fairly complex x86 platform and has a surprising amount of functionality. When you get down to assembly and optimising for size, you can do incredible things - e.g. theverge.com/2012/5/14/3014698/assembly-4k-demoscene-fractals
$endgroup$
– Baldrickk
Oct 15 at 10:31




$begingroup$
Even something simple like notepad has a whole host of OS compatibility layers, the gui and other libraries it's built on... It's written in a fairly high level language, targeted to the fairly complex x86 platform and has a surprising amount of functionality. When you get down to assembly and optimising for size, you can do incredible things - e.g. theverge.com/2012/5/14/3014698/assembly-4k-demoscene-fractals
$endgroup$
– Baldrickk
Oct 15 at 10:31




7




7




$begingroup$
As a programmer I strongly encourage you to try microcontroller programming. An Arduino is a great introduction. The basic model has 1k of RAM. You'd be amazed at how much you can achieve with 1k of RAM. People have written everything from quadcopter (drone) controllers, radio-control receivers, walking robot controllers to airplane autopilot guidance/navigation software all in 1k of RAM. I started microcontroller programming with the PIC16F84 which has 68 bytes (yes, bytes, not kilobytes) of RAM and I implemented a lot of projects with it.
$endgroup$
– slebetman
Oct 16 at 4:26





$begingroup$
As a programmer I strongly encourage you to try microcontroller programming. An Arduino is a great introduction. The basic model has 1k of RAM. You'd be amazed at how much you can achieve with 1k of RAM. People have written everything from quadcopter (drone) controllers, radio-control receivers, walking robot controllers to airplane autopilot guidance/navigation software all in 1k of RAM. I started microcontroller programming with the PIC16F84 which has 68 bytes (yes, bytes, not kilobytes) of RAM and I implemented a lot of projects with it.
$endgroup$
– slebetman
Oct 16 at 4:26











3 Answers
3






active

oldest

votes


















19
















$begingroup$

In many of the early probes, up until close to Apollo there were not true computers on space probes. All computing was done on earth and the onboard electronics was known as a sequencer, for Pioneer 10 it had 222 possible commands 5 of which could be readied. Early Venus probes sent data by mechanically switching different sensors to modulate a CW transmitter in turn and sorting it all apart on earth.



This also applied to much of the Apollo launch process, where the hardware in the launch platform did not run true software but a sequence (from here) of 'wait, activate this, wait, measure that and if out of bounds hold else continue'.



Along with the AGC code link by Ludo you can look at the abort controller as a smaller scale example of how things were done (fixed loop of known steps and timing).



Even today it is very rare to send code to a space craft that does not boil down to a sequence of very specific instructions to be run in order. Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code.



In general terms code was made to fit the same way people program for microcontrollers today:



Not having any form of user interface in code (Apollo DSKY was largely hardware)



Using approximation or integer math over floating point (lots of things are possible where pi = 3) or precompute constants on earth and upload when required (say gravity or engine performance)



Custom designing supporting hardware like star trackers to be preloaded with constants from earth and to output pre formatted and bound checked for the next processing step.
In fact, bounds check only once, where data is sourced and ensure no following step can overflow it.



Design algorithms to work in register(s) rather than memory locations (which makes horrible source since you do not have variables) but means you can avoid lots of moving values in and out of memory.



Avoid general problems for the specific, for space craft this was all about navigation, reporting sensor/instrument states and pointing. All of these could have carefully crafted code that worked well over a specific range of inputs (Though see).



Trust your data (in security sense) (though nature can still get you)






share|improve this answer










$endgroup$










  • 2




    $begingroup$
    "Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code." Well, Mars Pathfinder (from the 90s) had a real-time operating system (VxWorks) with sufficent complexity of task schedule that it could run into a priority inversion problem. Complex, Complex.
    $endgroup$
    – David Tonhofer
    Oct 16 at 6:06



















21
















$begingroup$

(originally answered to "Samples of old guidance software")



The first that comes to mind is the Github repository of the Apollo 11 Guidance Computer (AGC). The repository has both Command Module and Lunar Module software, but note that it is transcribed from hardcopies, so it might not be fully complete (yet). You can find a simulator of the AGC on the Virtual AGC website (there's a ton of other references there also).






share|improve this answer












$endgroup$






















    10
















    $begingroup$


    I am a software developer and with all the resources available today I cannot fathom where one could even start such an endeavour.




    There are plenty of computer-based systems to this day that have to live with such limitations. There are plenty of embedded systems where 2^16 (65536) bytes of memory remains a luxury. After all, on machines that use 16 bit memory addresses (plenty of which still exist and are plenty of which are still manufactured to this day), there's no point in having over 65636 bytes of memory. And just as there's no problem with a computer with 64 bit addresses having less than 18+ exabytes of memory, there's no problem with a computer that uses 16 bit addresses having less than 2^16 bytes of memory.



    There are many ways to start with such an endeavor. The number one rule is to eschew the use of an operating system. Many (most?) embedded systems are bare machines. There's no OS, and there's only one program running, ever. Your microwave oven has a computer operating as an embedded system, and it has no operating system. If your car was manufactured in the last 25+ years, it has lots of embedded systems running in it. If your car is anywhere close to modern, it has several dozens of microcontrollers that collectively run several million lines of code.



    Many of the microcontrollers in a modern car are not subject to the 64K (2^16, or 65536) address limit. Back in the day, that was a very common limit, and it inherently limited the size of memory. But it did not limit storage. The problem of having disk size exceed address limitations was solved in the 1950s and 1960s. A common solution was to use memory overlays. This technique, one I'm glad to have (mostly) forgotten about, remains common to this day in embedded systems programming.



    Another widely used technique was and is to have the embedded machine follow a Harvard architecture as opposed to a von Neumann architecture. There is no distinction between code and data in a Von Neumann machine. Code and data are very different things in a Harvard architecture machine, possibly with different word sizes. Your laptop or desktop machine most likely is a von Neumann architecture machine, at least on the surface. Deep under the hood it looks more like a Harvard machine, with separate caches for code and data.






    share|improve this answer










    $endgroup$














    • $begingroup$
      Yes, I should have said application developer on PCs with (almost) unlimited amounts of everything, forgot about the embedded systems and all their challenges for a extremely limited memory and storage. Shouldn't be throwing around "I am a software developer" so lightly.
      $endgroup$
      – Arjang
      Oct 15 at 21:08






    • 1




      $begingroup$
      When I was a physics student the HP-25 came out; it could hold 49 program steps. I programmed it to act as a lunar lander, where the user entered burn duration and thrust. All the physical constants, lander mass, fuel mass, initial velocity, and altitude were correct. I ignored attitude / vector control, but the point is that it was 49 steps and correct. And it was damn hard to land. Neil Armstrong was one hell of a pilot!
      $endgroup$
      – andy256
      Oct 16 at 9:44












    Your Answer








    StackExchange.ready(function()
    var channelOptions =
    tags: "".split(" "),
    id: "508"
    ;
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function()
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled)
    StackExchange.using("snippets", function()
    createEditor();
    );

    else
    createEditor();

    );

    function createEditor()
    StackExchange.prepareEditor(
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader:
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/4.0/"u003ecc by-sa 4.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    ,
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    );



    );














    draft saved

    draft discarded
















    StackExchange.ready(
    function ()
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fspace.stackexchange.com%2fquestions%2f39336%2fgiven-small-computational-resources-how-navigation-was-implemented-not-samples%23new-answer', 'question_page');

    );

    Post as a guest















    Required, but never shown


























    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    19
















    $begingroup$

    In many of the early probes, up until close to Apollo there were not true computers on space probes. All computing was done on earth and the onboard electronics was known as a sequencer, for Pioneer 10 it had 222 possible commands 5 of which could be readied. Early Venus probes sent data by mechanically switching different sensors to modulate a CW transmitter in turn and sorting it all apart on earth.



    This also applied to much of the Apollo launch process, where the hardware in the launch platform did not run true software but a sequence (from here) of 'wait, activate this, wait, measure that and if out of bounds hold else continue'.



    Along with the AGC code link by Ludo you can look at the abort controller as a smaller scale example of how things were done (fixed loop of known steps and timing).



    Even today it is very rare to send code to a space craft that does not boil down to a sequence of very specific instructions to be run in order. Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code.



    In general terms code was made to fit the same way people program for microcontrollers today:



    Not having any form of user interface in code (Apollo DSKY was largely hardware)



    Using approximation or integer math over floating point (lots of things are possible where pi = 3) or precompute constants on earth and upload when required (say gravity or engine performance)



    Custom designing supporting hardware like star trackers to be preloaded with constants from earth and to output pre formatted and bound checked for the next processing step.
    In fact, bounds check only once, where data is sourced and ensure no following step can overflow it.



    Design algorithms to work in register(s) rather than memory locations (which makes horrible source since you do not have variables) but means you can avoid lots of moving values in and out of memory.



    Avoid general problems for the specific, for space craft this was all about navigation, reporting sensor/instrument states and pointing. All of these could have carefully crafted code that worked well over a specific range of inputs (Though see).



    Trust your data (in security sense) (though nature can still get you)






    share|improve this answer










    $endgroup$










    • 2




      $begingroup$
      "Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code." Well, Mars Pathfinder (from the 90s) had a real-time operating system (VxWorks) with sufficent complexity of task schedule that it could run into a priority inversion problem. Complex, Complex.
      $endgroup$
      – David Tonhofer
      Oct 16 at 6:06
















    19
















    $begingroup$

    In many of the early probes, up until close to Apollo there were not true computers on space probes. All computing was done on earth and the onboard electronics was known as a sequencer, for Pioneer 10 it had 222 possible commands 5 of which could be readied. Early Venus probes sent data by mechanically switching different sensors to modulate a CW transmitter in turn and sorting it all apart on earth.



    This also applied to much of the Apollo launch process, where the hardware in the launch platform did not run true software but a sequence (from here) of 'wait, activate this, wait, measure that and if out of bounds hold else continue'.



    Along with the AGC code link by Ludo you can look at the abort controller as a smaller scale example of how things were done (fixed loop of known steps and timing).



    Even today it is very rare to send code to a space craft that does not boil down to a sequence of very specific instructions to be run in order. Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code.



    In general terms code was made to fit the same way people program for microcontrollers today:



    Not having any form of user interface in code (Apollo DSKY was largely hardware)



    Using approximation or integer math over floating point (lots of things are possible where pi = 3) or precompute constants on earth and upload when required (say gravity or engine performance)



    Custom designing supporting hardware like star trackers to be preloaded with constants from earth and to output pre formatted and bound checked for the next processing step.
    In fact, bounds check only once, where data is sourced and ensure no following step can overflow it.



    Design algorithms to work in register(s) rather than memory locations (which makes horrible source since you do not have variables) but means you can avoid lots of moving values in and out of memory.



    Avoid general problems for the specific, for space craft this was all about navigation, reporting sensor/instrument states and pointing. All of these could have carefully crafted code that worked well over a specific range of inputs (Though see).



    Trust your data (in security sense) (though nature can still get you)






    share|improve this answer










    $endgroup$










    • 2




      $begingroup$
      "Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code." Well, Mars Pathfinder (from the 90s) had a real-time operating system (VxWorks) with sufficent complexity of task schedule that it could run into a priority inversion problem. Complex, Complex.
      $endgroup$
      – David Tonhofer
      Oct 16 at 6:06














    19














    19










    19







    $begingroup$

    In many of the early probes, up until close to Apollo there were not true computers on space probes. All computing was done on earth and the onboard electronics was known as a sequencer, for Pioneer 10 it had 222 possible commands 5 of which could be readied. Early Venus probes sent data by mechanically switching different sensors to modulate a CW transmitter in turn and sorting it all apart on earth.



    This also applied to much of the Apollo launch process, where the hardware in the launch platform did not run true software but a sequence (from here) of 'wait, activate this, wait, measure that and if out of bounds hold else continue'.



    Along with the AGC code link by Ludo you can look at the abort controller as a smaller scale example of how things were done (fixed loop of known steps and timing).



    Even today it is very rare to send code to a space craft that does not boil down to a sequence of very specific instructions to be run in order. Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code.



    In general terms code was made to fit the same way people program for microcontrollers today:



    Not having any form of user interface in code (Apollo DSKY was largely hardware)



    Using approximation or integer math over floating point (lots of things are possible where pi = 3) or precompute constants on earth and upload when required (say gravity or engine performance)



    Custom designing supporting hardware like star trackers to be preloaded with constants from earth and to output pre formatted and bound checked for the next processing step.
    In fact, bounds check only once, where data is sourced and ensure no following step can overflow it.



    Design algorithms to work in register(s) rather than memory locations (which makes horrible source since you do not have variables) but means you can avoid lots of moving values in and out of memory.



    Avoid general problems for the specific, for space craft this was all about navigation, reporting sensor/instrument states and pointing. All of these could have carefully crafted code that worked well over a specific range of inputs (Though see).



    Trust your data (in security sense) (though nature can still get you)






    share|improve this answer










    $endgroup$



    In many of the early probes, up until close to Apollo there were not true computers on space probes. All computing was done on earth and the onboard electronics was known as a sequencer, for Pioneer 10 it had 222 possible commands 5 of which could be readied. Early Venus probes sent data by mechanically switching different sensors to modulate a CW transmitter in turn and sorting it all apart on earth.



    This also applied to much of the Apollo launch process, where the hardware in the launch platform did not run true software but a sequence (from here) of 'wait, activate this, wait, measure that and if out of bounds hold else continue'.



    Along with the AGC code link by Ludo you can look at the abort controller as a smaller scale example of how things were done (fixed loop of known steps and timing).



    Even today it is very rare to send code to a space craft that does not boil down to a sequence of very specific instructions to be run in order. Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code.



    In general terms code was made to fit the same way people program for microcontrollers today:



    Not having any form of user interface in code (Apollo DSKY was largely hardware)



    Using approximation or integer math over floating point (lots of things are possible where pi = 3) or precompute constants on earth and upload when required (say gravity or engine performance)



    Custom designing supporting hardware like star trackers to be preloaded with constants from earth and to output pre formatted and bound checked for the next processing step.
    In fact, bounds check only once, where data is sourced and ensure no following step can overflow it.



    Design algorithms to work in register(s) rather than memory locations (which makes horrible source since you do not have variables) but means you can avoid lots of moving values in and out of memory.



    Avoid general problems for the specific, for space craft this was all about navigation, reporting sensor/instrument states and pointing. All of these could have carefully crafted code that worked well over a specific range of inputs (Though see).



    Trust your data (in security sense) (though nature can still get you)







    share|improve this answer













    share|improve this answer




    share|improve this answer










    answered Oct 14 at 11:54









    GremlinWrangerGremlinWranger

    5,3278 silver badges27 bronze badges




    5,3278 silver badges27 bronze badges










    • 2




      $begingroup$
      "Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code." Well, Mars Pathfinder (from the 90s) had a real-time operating system (VxWorks) with sufficent complexity of task schedule that it could run into a priority inversion problem. Complex, Complex.
      $endgroup$
      – David Tonhofer
      Oct 16 at 6:06













    • 2




      $begingroup$
      "Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code." Well, Mars Pathfinder (from the 90s) had a real-time operating system (VxWorks) with sufficent complexity of task schedule that it could run into a priority inversion problem. Complex, Complex.
      $endgroup$
      – David Tonhofer
      Oct 16 at 6:06








    2




    2




    $begingroup$
    "Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code." Well, Mars Pathfinder (from the 90s) had a real-time operating system (VxWorks) with sufficent complexity of task schedule that it could run into a priority inversion problem. Complex, Complex.
    $endgroup$
    – David Tonhofer
    Oct 16 at 6:06





    $begingroup$
    "Curiosity has some autonomous navigation and photo taking capability but generally branching code is there to trigger fallback/fail safe 'oops stop, solve antenna pointing problem and call home for instructions' rather than AI or learning code." Well, Mars Pathfinder (from the 90s) had a real-time operating system (VxWorks) with sufficent complexity of task schedule that it could run into a priority inversion problem. Complex, Complex.
    $endgroup$
    – David Tonhofer
    Oct 16 at 6:06














    21
















    $begingroup$

    (originally answered to "Samples of old guidance software")



    The first that comes to mind is the Github repository of the Apollo 11 Guidance Computer (AGC). The repository has both Command Module and Lunar Module software, but note that it is transcribed from hardcopies, so it might not be fully complete (yet). You can find a simulator of the AGC on the Virtual AGC website (there's a ton of other references there also).






    share|improve this answer












    $endgroup$



















      21
















      $begingroup$

      (originally answered to "Samples of old guidance software")



      The first that comes to mind is the Github repository of the Apollo 11 Guidance Computer (AGC). The repository has both Command Module and Lunar Module software, but note that it is transcribed from hardcopies, so it might not be fully complete (yet). You can find a simulator of the AGC on the Virtual AGC website (there's a ton of other references there also).






      share|improve this answer












      $endgroup$

















        21














        21










        21







        $begingroup$

        (originally answered to "Samples of old guidance software")



        The first that comes to mind is the Github repository of the Apollo 11 Guidance Computer (AGC). The repository has both Command Module and Lunar Module software, but note that it is transcribed from hardcopies, so it might not be fully complete (yet). You can find a simulator of the AGC on the Virtual AGC website (there's a ton of other references there also).






        share|improve this answer












        $endgroup$



        (originally answered to "Samples of old guidance software")



        The first that comes to mind is the Github repository of the Apollo 11 Guidance Computer (AGC). The repository has both Command Module and Lunar Module software, but note that it is transcribed from hardcopies, so it might not be fully complete (yet). You can find a simulator of the AGC on the Virtual AGC website (there's a ton of other references there also).







        share|improve this answer















        share|improve this answer




        share|improve this answer








        edited Oct 18 at 9:48

























        answered Oct 14 at 10:53









        LudoLudo

        1,9696 silver badges30 bronze badges




        1,9696 silver badges30 bronze badges
























            10
















            $begingroup$


            I am a software developer and with all the resources available today I cannot fathom where one could even start such an endeavour.




            There are plenty of computer-based systems to this day that have to live with such limitations. There are plenty of embedded systems where 2^16 (65536) bytes of memory remains a luxury. After all, on machines that use 16 bit memory addresses (plenty of which still exist and are plenty of which are still manufactured to this day), there's no point in having over 65636 bytes of memory. And just as there's no problem with a computer with 64 bit addresses having less than 18+ exabytes of memory, there's no problem with a computer that uses 16 bit addresses having less than 2^16 bytes of memory.



            There are many ways to start with such an endeavor. The number one rule is to eschew the use of an operating system. Many (most?) embedded systems are bare machines. There's no OS, and there's only one program running, ever. Your microwave oven has a computer operating as an embedded system, and it has no operating system. If your car was manufactured in the last 25+ years, it has lots of embedded systems running in it. If your car is anywhere close to modern, it has several dozens of microcontrollers that collectively run several million lines of code.



            Many of the microcontrollers in a modern car are not subject to the 64K (2^16, or 65536) address limit. Back in the day, that was a very common limit, and it inherently limited the size of memory. But it did not limit storage. The problem of having disk size exceed address limitations was solved in the 1950s and 1960s. A common solution was to use memory overlays. This technique, one I'm glad to have (mostly) forgotten about, remains common to this day in embedded systems programming.



            Another widely used technique was and is to have the embedded machine follow a Harvard architecture as opposed to a von Neumann architecture. There is no distinction between code and data in a Von Neumann machine. Code and data are very different things in a Harvard architecture machine, possibly with different word sizes. Your laptop or desktop machine most likely is a von Neumann architecture machine, at least on the surface. Deep under the hood it looks more like a Harvard machine, with separate caches for code and data.






            share|improve this answer










            $endgroup$














            • $begingroup$
              Yes, I should have said application developer on PCs with (almost) unlimited amounts of everything, forgot about the embedded systems and all their challenges for a extremely limited memory and storage. Shouldn't be throwing around "I am a software developer" so lightly.
              $endgroup$
              – Arjang
              Oct 15 at 21:08






            • 1




              $begingroup$
              When I was a physics student the HP-25 came out; it could hold 49 program steps. I programmed it to act as a lunar lander, where the user entered burn duration and thrust. All the physical constants, lander mass, fuel mass, initial velocity, and altitude were correct. I ignored attitude / vector control, but the point is that it was 49 steps and correct. And it was damn hard to land. Neil Armstrong was one hell of a pilot!
              $endgroup$
              – andy256
              Oct 16 at 9:44















            10
















            $begingroup$


            I am a software developer and with all the resources available today I cannot fathom where one could even start such an endeavour.




            There are plenty of computer-based systems to this day that have to live with such limitations. There are plenty of embedded systems where 2^16 (65536) bytes of memory remains a luxury. After all, on machines that use 16 bit memory addresses (plenty of which still exist and are plenty of which are still manufactured to this day), there's no point in having over 65636 bytes of memory. And just as there's no problem with a computer with 64 bit addresses having less than 18+ exabytes of memory, there's no problem with a computer that uses 16 bit addresses having less than 2^16 bytes of memory.



            There are many ways to start with such an endeavor. The number one rule is to eschew the use of an operating system. Many (most?) embedded systems are bare machines. There's no OS, and there's only one program running, ever. Your microwave oven has a computer operating as an embedded system, and it has no operating system. If your car was manufactured in the last 25+ years, it has lots of embedded systems running in it. If your car is anywhere close to modern, it has several dozens of microcontrollers that collectively run several million lines of code.



            Many of the microcontrollers in a modern car are not subject to the 64K (2^16, or 65536) address limit. Back in the day, that was a very common limit, and it inherently limited the size of memory. But it did not limit storage. The problem of having disk size exceed address limitations was solved in the 1950s and 1960s. A common solution was to use memory overlays. This technique, one I'm glad to have (mostly) forgotten about, remains common to this day in embedded systems programming.



            Another widely used technique was and is to have the embedded machine follow a Harvard architecture as opposed to a von Neumann architecture. There is no distinction between code and data in a Von Neumann machine. Code and data are very different things in a Harvard architecture machine, possibly with different word sizes. Your laptop or desktop machine most likely is a von Neumann architecture machine, at least on the surface. Deep under the hood it looks more like a Harvard machine, with separate caches for code and data.






            share|improve this answer










            $endgroup$














            • $begingroup$
              Yes, I should have said application developer on PCs with (almost) unlimited amounts of everything, forgot about the embedded systems and all their challenges for a extremely limited memory and storage. Shouldn't be throwing around "I am a software developer" so lightly.
              $endgroup$
              – Arjang
              Oct 15 at 21:08






            • 1




              $begingroup$
              When I was a physics student the HP-25 came out; it could hold 49 program steps. I programmed it to act as a lunar lander, where the user entered burn duration and thrust. All the physical constants, lander mass, fuel mass, initial velocity, and altitude were correct. I ignored attitude / vector control, but the point is that it was 49 steps and correct. And it was damn hard to land. Neil Armstrong was one hell of a pilot!
              $endgroup$
              – andy256
              Oct 16 at 9:44













            10














            10










            10







            $begingroup$


            I am a software developer and with all the resources available today I cannot fathom where one could even start such an endeavour.




            There are plenty of computer-based systems to this day that have to live with such limitations. There are plenty of embedded systems where 2^16 (65536) bytes of memory remains a luxury. After all, on machines that use 16 bit memory addresses (plenty of which still exist and are plenty of which are still manufactured to this day), there's no point in having over 65636 bytes of memory. And just as there's no problem with a computer with 64 bit addresses having less than 18+ exabytes of memory, there's no problem with a computer that uses 16 bit addresses having less than 2^16 bytes of memory.



            There are many ways to start with such an endeavor. The number one rule is to eschew the use of an operating system. Many (most?) embedded systems are bare machines. There's no OS, and there's only one program running, ever. Your microwave oven has a computer operating as an embedded system, and it has no operating system. If your car was manufactured in the last 25+ years, it has lots of embedded systems running in it. If your car is anywhere close to modern, it has several dozens of microcontrollers that collectively run several million lines of code.



            Many of the microcontrollers in a modern car are not subject to the 64K (2^16, or 65536) address limit. Back in the day, that was a very common limit, and it inherently limited the size of memory. But it did not limit storage. The problem of having disk size exceed address limitations was solved in the 1950s and 1960s. A common solution was to use memory overlays. This technique, one I'm glad to have (mostly) forgotten about, remains common to this day in embedded systems programming.



            Another widely used technique was and is to have the embedded machine follow a Harvard architecture as opposed to a von Neumann architecture. There is no distinction between code and data in a Von Neumann machine. Code and data are very different things in a Harvard architecture machine, possibly with different word sizes. Your laptop or desktop machine most likely is a von Neumann architecture machine, at least on the surface. Deep under the hood it looks more like a Harvard machine, with separate caches for code and data.






            share|improve this answer










            $endgroup$




            I am a software developer and with all the resources available today I cannot fathom where one could even start such an endeavour.




            There are plenty of computer-based systems to this day that have to live with such limitations. There are plenty of embedded systems where 2^16 (65536) bytes of memory remains a luxury. After all, on machines that use 16 bit memory addresses (plenty of which still exist and are plenty of which are still manufactured to this day), there's no point in having over 65636 bytes of memory. And just as there's no problem with a computer with 64 bit addresses having less than 18+ exabytes of memory, there's no problem with a computer that uses 16 bit addresses having less than 2^16 bytes of memory.



            There are many ways to start with such an endeavor. The number one rule is to eschew the use of an operating system. Many (most?) embedded systems are bare machines. There's no OS, and there's only one program running, ever. Your microwave oven has a computer operating as an embedded system, and it has no operating system. If your car was manufactured in the last 25+ years, it has lots of embedded systems running in it. If your car is anywhere close to modern, it has several dozens of microcontrollers that collectively run several million lines of code.



            Many of the microcontrollers in a modern car are not subject to the 64K (2^16, or 65536) address limit. Back in the day, that was a very common limit, and it inherently limited the size of memory. But it did not limit storage. The problem of having disk size exceed address limitations was solved in the 1950s and 1960s. A common solution was to use memory overlays. This technique, one I'm glad to have (mostly) forgotten about, remains common to this day in embedded systems programming.



            Another widely used technique was and is to have the embedded machine follow a Harvard architecture as opposed to a von Neumann architecture. There is no distinction between code and data in a Von Neumann machine. Code and data are very different things in a Harvard architecture machine, possibly with different word sizes. Your laptop or desktop machine most likely is a von Neumann architecture machine, at least on the surface. Deep under the hood it looks more like a Harvard machine, with separate caches for code and data.







            share|improve this answer













            share|improve this answer




            share|improve this answer










            answered Oct 15 at 5:55









            David HammenDavid Hammen

            35.6k3 gold badges84 silver badges155 bronze badges




            35.6k3 gold badges84 silver badges155 bronze badges














            • $begingroup$
              Yes, I should have said application developer on PCs with (almost) unlimited amounts of everything, forgot about the embedded systems and all their challenges for a extremely limited memory and storage. Shouldn't be throwing around "I am a software developer" so lightly.
              $endgroup$
              – Arjang
              Oct 15 at 21:08






            • 1




              $begingroup$
              When I was a physics student the HP-25 came out; it could hold 49 program steps. I programmed it to act as a lunar lander, where the user entered burn duration and thrust. All the physical constants, lander mass, fuel mass, initial velocity, and altitude were correct. I ignored attitude / vector control, but the point is that it was 49 steps and correct. And it was damn hard to land. Neil Armstrong was one hell of a pilot!
              $endgroup$
              – andy256
              Oct 16 at 9:44
















            • $begingroup$
              Yes, I should have said application developer on PCs with (almost) unlimited amounts of everything, forgot about the embedded systems and all their challenges for a extremely limited memory and storage. Shouldn't be throwing around "I am a software developer" so lightly.
              $endgroup$
              – Arjang
              Oct 15 at 21:08






            • 1




              $begingroup$
              When I was a physics student the HP-25 came out; it could hold 49 program steps. I programmed it to act as a lunar lander, where the user entered burn duration and thrust. All the physical constants, lander mass, fuel mass, initial velocity, and altitude were correct. I ignored attitude / vector control, but the point is that it was 49 steps and correct. And it was damn hard to land. Neil Armstrong was one hell of a pilot!
              $endgroup$
              – andy256
              Oct 16 at 9:44















            $begingroup$
            Yes, I should have said application developer on PCs with (almost) unlimited amounts of everything, forgot about the embedded systems and all their challenges for a extremely limited memory and storage. Shouldn't be throwing around "I am a software developer" so lightly.
            $endgroup$
            – Arjang
            Oct 15 at 21:08




            $begingroup$
            Yes, I should have said application developer on PCs with (almost) unlimited amounts of everything, forgot about the embedded systems and all their challenges for a extremely limited memory and storage. Shouldn't be throwing around "I am a software developer" so lightly.
            $endgroup$
            – Arjang
            Oct 15 at 21:08




            1




            1




            $begingroup$
            When I was a physics student the HP-25 came out; it could hold 49 program steps. I programmed it to act as a lunar lander, where the user entered burn duration and thrust. All the physical constants, lander mass, fuel mass, initial velocity, and altitude were correct. I ignored attitude / vector control, but the point is that it was 49 steps and correct. And it was damn hard to land. Neil Armstrong was one hell of a pilot!
            $endgroup$
            – andy256
            Oct 16 at 9:44




            $begingroup$
            When I was a physics student the HP-25 came out; it could hold 49 program steps. I programmed it to act as a lunar lander, where the user entered burn duration and thrust. All the physical constants, lander mass, fuel mass, initial velocity, and altitude were correct. I ignored attitude / vector control, but the point is that it was 49 steps and correct. And it was damn hard to land. Neil Armstrong was one hell of a pilot!
            $endgroup$
            – andy256
            Oct 16 at 9:44


















            draft saved

            draft discarded















































            Thanks for contributing an answer to Space Exploration Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid


            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.

            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fspace.stackexchange.com%2fquestions%2f39336%2fgiven-small-computational-resources-how-navigation-was-implemented-not-samples%23new-answer', 'question_page');

            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown









            Popular posts from this blog

            Invision Community Contents History See also References External links Navigation menuProprietaryinvisioncommunity.comIPS Community ForumsIPS Community Forumsthis blog entry"License Changes, IP.Board 3.4, and the Future""Interview -- Matt Mecham of Ibforums""CEO Invision Power Board, Matt Mecham Is a Liar, Thief!"IPB License Explanation 1.3, 1.3.1, 2.0, and 2.1ArchivedSecurity Fixes, Updates And Enhancements For IPB 1.3.1Archived"New Demo Accounts - Invision Power Services"the original"New Default Skin"the original"Invision Power Board 3.0.0 and Applications Released"the original"Archived copy"the original"Perpetual licenses being done away with""Release Notes - Invision Power Services""Introducing: IPS Community Suite 4!"Invision Community Release Notes

            Canceling a color specificationRandomly assigning color to Graphics3D objects?Default color for Filling in Mathematica 9Coloring specific elements of sets with a prime modified order in an array plotHow to pick a color differing significantly from the colors already in a given color list?Detection of the text colorColor numbers based on their valueCan color schemes for use with ColorData include opacity specification?My dynamic color schemes

            Tom Holland Mục lục Đầu đời và giáo dục | Sự nghiệp | Cuộc sống cá nhân | Phim tham gia | Giải thưởng và đề cử | Chú thích | Liên kết ngoài | Trình đơn chuyển hướngProfile“Person Details for Thomas Stanley Holland, "England and Wales Birth Registration Index, 1837-2008" — FamilySearch.org”"Meet Tom Holland... the 16-year-old star of The Impossible""Schoolboy actor Tom Holland finds himself in Oscar contention for role in tsunami drama"“Naomi Watts on the Prince William and Harry's reaction to her film about the late Princess Diana”lưu trữ"Holland and Pflueger Are West End's Two New 'Billy Elliots'""I'm so envious of my son, the movie star! British writer Dominic Holland's spent 20 years trying to crack Hollywood - but he's been beaten to it by a very unlikely rival"“Richard and Margaret Povey of Jersey, Channel Islands, UK: Information about Thomas Stanley Holland”"Tom Holland to play Billy Elliot""New Billy Elliot leaving the garage"Billy Elliot the Musical - Tom Holland - Billy"A Tale of four Billys: Tom Holland""The Feel Good Factor""Thames Christian College schoolboys join Myleene Klass for The Feelgood Factor""Government launches £600,000 arts bursaries pilot""BILLY's Chapman, Holland, Gardner & Jackson-Keen Visit Prime Minister""Elton John 'blown away' by Billy Elliot fifth birthday" (video with John's interview and fragments of Holland's performance)"First News interviews Arrietty's Tom Holland"“33rd Critics' Circle Film Awards winners”“National Board of Review Current Awards”Bản gốc"Ron Howard Whaling Tale 'In The Heart Of The Sea' Casts Tom Holland"“'Spider-Man' Finds Tom Holland to Star as New Web-Slinger”lưu trữ“Captain America: Civil War (2016)”“Film Review: ‘Captain America: Civil War’”lưu trữ“‘Captain America: Civil War’ review: Choose your own avenger”lưu trữ“The Lost City of Z reviews”“Sony Pictures and Marvel Studios Find Their 'Spider-Man' Star and Director”“‘Mary Magdalene’, ‘Current War’ & ‘Wind River’ Get 2017 Release Dates From Weinstein”“Lionsgate Unleashing Daisy Ridley & Tom Holland Starrer ‘Chaos Walking’ In Cannes”“PTA's 'Master' Leads Chicago Film Critics Nominations, UPDATED: Houston and Indiana Critics Nominations”“Nominaciones Goya 2013 Telecinco Cinema – ENG”“Jameson Empire Film Awards: Martin Freeman wins best actor for performance in The Hobbit”“34th Annual Young Artist Awards”Bản gốc“Teen Choice Awards 2016—Captain America: Civil War Leads Second Wave of Nominations”“BAFTA Film Award Nominations: ‘La La Land’ Leads Race”“Saturn Awards Nominations 2017: 'Rogue One,' 'Walking Dead' Lead”Tom HollandTom HollandTom HollandTom Hollandmedia.gettyimages.comWorldCat Identities300279794no20130442900000 0004 0355 42791085670554170004732cb16706349t(data)XX5557367