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I have searched a lot about this topic and also got similar questions but not the answers that I wanted. All answers talk about the engines that the spacecraft uses but how is that done?

I came to know that gimbaled engines are used to keep the spacecraft in a specific trajectory but, how do the spacecraft and its sensors know that when to fire the engine in a direction to maintain the trajectory. In free space in 3 dimensions, how can a spacecraft know that it is in the correct trajectory.

And also, if it goes out of trajectory, does it try to come in its own trajectory automatically or we need to give a command from Mission control.

According to me gyroscopes and accelerometers need gravity to get this all information.

I am new in this field and am curious about some of these things. Thank you.

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    $\begingroup$ your question could probably use some clarification--you're asking generally about how all spacecraft do Guidance, Navigation, and Control, and methods vary between spacecraft. You're also incorrect about gyroscopes needing gravity; gyroscopes rely on conservation of angular momentum. $\endgroup$
    – Erin Anne
    Nov 28, 2022 at 6:08
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    $\begingroup$ @ayush, can you also clarify if your question is about trajectory control from launch to orbit (due mention of gimbaling engines) or once it is in orbit and just dealing with deviations/errors (which is when an engine is fired for a short period and stops). Generally launch to orbit is mostly internal based on Gyros and accelerometers, while in orbit changes are mostly driven from ground station measurment. $\endgroup$
    – GremlinWranger
    Nov 28, 2022 at 8:44
  • $\begingroup$ @ErinAnne Sorry for that, I thought that gyroscopes needed gravity and yes, my question is about the guidance, navigation and control of the spacecraft $\endgroup$
    – Ayush
    Nov 28, 2022 at 8:54
  • $\begingroup$ @GremlinWranger, my question is about both, the insertion of spacecraft in trajectory and also the id-course corrections (like how will that correction burn accurately take place in 3-D free space) $\endgroup$
    – Ayush
    Nov 28, 2022 at 8:56
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    $\begingroup$ @Ayush if so I recommend a major edit to your question to be 'how does a spacecraft ordered to change course by X meters a second know when to stop thrusting'. The plan is basically driven from the ground, the interesting part is knowing when the engine should stop to get the result needed - see several failed missions. $\endgroup$
    – GremlinWranger
    Nov 28, 2022 at 9:01

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Note - this answer is focusing on the question in comments 'how will that burn accurately take place in 3D space'.

In general spacecraft do not know where they are or where they are going. Instead ground control uses various sensors on the ground and on the craft to determine what the craft position and speed is, and send a plan to the craft to execute, observe the results and repeat as required to get the needed orbit/trajectory.

So our craft needs to work out how to execute those plans. Orientation generally comes from star trackers, so the craft can rotate to position engines facing in the required direction.

The tricky part is the actual thrust. If we are in orbit around earth and it is decaying we know we need to thrust in the direction of orbit to boost apogee back up by a certain amount.

The simplest and earliest option was to just use time, turn engine on for X seconds and stop, and worked even before true computers would fit into spacecraft. This is vulnerable to errors with engine thrust being higher or lower than expected, because fuel pressure and temperature will change during the burn changing performance and burnt will lower mass making on the ground computation complicated.

A potentially more accurate approach is to measure acceleration. If your craft is traveling a passive orbit with no forces applied, a scale onboard will measure zero. If we start the burn, a scale with a known mass sitting on it will start to read a weight, or more precisely a force. With a known force and a known mass we can calculate the acceleration. And if we know the acceleration and our target starting and ending speed we can start to use math to know when to stop, either assuming constant acceleration or using integration to handle variable thrust.

An example of this process in use, and going wrong is with the first flight of Ariane V

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