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Let us say there is an antenna on earth and I have a satellite in an orbit how do I make the trajectory (not control, so body velocities of the satellite) to make it point toward the earth when it is in view and when the antenna is not in view I have no requirement for that. Currently, I have no constraints but constraints such as input constraints and attitude constraints can be added later. I know I have solve an optimization problem but can formulate it myself.

Can someone refer me to some papers/theories of what I will need for this? I am not looking for an answer but for research direction because I could not find what I needed.

I have found this paper that solves an optimization problem given constraints but this goes from an initial state to a goal configuration. I however want the goal configurations given the orbit.

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  • $\begingroup$ The simplest solution - put it into Geostationary orbit, point at the interesting point on Earth, and leave it be. The point is always in view. Anything else will be between awfully complicated and impossible. Normally, you select the trajectory to have the point of interest in view for most of the time, and just control the attitude using reaction wheels or antenna/camera gimbals to point at the point of interest. $\endgroup$
    – SF.
    Nov 18, 2022 at 9:26
  • $\begingroup$ I am not sure what level you are referring to when you say it is complicated. I am doing a first-year master's project. Do you mean generally complicated and impossible? If not do you know papers/literature that solves the non-Geostationary orbit? We are doing an attitude determination project so we cannot have the attitude to be simply "standing still". We could interpolate between random attitudes but what I described is a more "real-life" case. Is it still hard even not considering constraints? $\endgroup$
    – Hamzalihi
    Nov 18, 2022 at 9:35
  • $\begingroup$ @ Hamzalihi I'm assuming what you mean is that the satellite is free-spinning, stabilized once and attitude controls switched off - and you want such orbit that the orbital position coincides with the spin, keeping the satellite always pointed at one place on Earth. That's not a realistic scenario, and the only orbit I can imagine that could match the requirements is GEO - due to Earth spinning independently from the Satellite's orbital travel in other orbits, the track of the antenna would be extremely random. If you meant something else, please specify. $\endgroup$
    – SF.
    Nov 18, 2022 at 13:58
  • $\begingroup$ Additionally, attitude control of a satellite is easy enough no-one's going to invent insane orbits just to get a narrow cone view of a given point with zero attitude control. Think "How to drive a racecar around the race track operating only accelerator, brake and handbrake, without use of the steering wheel". Maybe, maybe possible, but nobody does it because why not use the steering wheel? $\endgroup$
    – SF.
    Nov 18, 2022 at 14:01
  • $\begingroup$ I get your point. I think am gonna follow the advice from the answer and keep it simple and just give a trajectory that makes it free-spinning and not think of a case for now (since the goal for the project is only attitude determination and nothing else). Then I can extend the project to other areas since my idea doesn't look so "good" after all. $\endgroup$
    – Hamzalihi
    Nov 18, 2022 at 14:07

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The easy solution is not to bother with that. Instead use an antenna with a wide enough beam width that the broadcast goes from horizon to horizon, or at least close to horizon to horizon. If the signal has a low bandwidth, even the ground station can simply use a non-tracking omni antenna. If the signal has a high bandwidth, a tracking antenna will be needed on the ground, but that tracking is not the spacecraft designer's problem. Being able to keep the vehicle nadir-pointing (or whatever) so it can perform its primary mission is the simple solution.

The hard solution is to keep a very narrow beam antenna pointing toward a specific ground station. This will most likely entail temporarily suspending the primary mission and switching to comm mode that keeps the antenna pointing in just the right direction. I suspect there are some very expensive military satellites that do just that. However, this is not the realm of a first-year master's project. Instead, Keep It Short and Simple (KISS) for your master's project.

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    $\begingroup$ Alternative deacronymizations of KISS include "Keep It Simple and Stupid" and "Keep It Simple, Stupid", the latter being a derogation at the person who wants to make a system overly complex. $\endgroup$
    – David Hammen
    Nov 18, 2022 at 10:51

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