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So as item of personal curiosity, if I were to have a rod from god say a 10 ton rod of tungsten orbiting in a orbit identical to the ISS for arguments sake, would it make more sense to 'fire it backwards' in effect applying a retrograde deceleration on it or would it make more sense to fire down in a radial 'inwards' velocity pointed straight at the center of gravity the satellite is orbiting (Earth). If necessary lets assume that any trust required can be applied but the rod is always 10 tons in weight.

The hypothesis I have is that it would take less energy to utilize aerobreaking via the radial acceleration than it would to do a full deorbiting retrograde burn. But won't lie the math I'm looking at confuses me and I'm almost certain I'd flat do it wrong.

For simplicity sake lets assume that accuracy is not a factor. If it's a hard calc the burn up temp of tungston does not have to be a factor in itself (though knowing a theoretical maximum velocity might be handy, don't know).

As I understand it, the ISS is around 420 km altitude, and the point of maximum heat generated on a heat sheild (I assume this means point of maximum drag) is around 70 km altitude, so we'd assume the rod is in final unassisted approach at that altitude

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The Hohmann transfer is usually the most efficient way of moving between two orbits around a single body. You can do better in some cases when moving between orbits of very different sizes, but here we're only lowering the periapsis by 400km to go from ISS altitude to the ground. You'll want to fire the rocket directly retrograde, which will lower the periapsis by the maximum amount. Either the radial or the retrograde burn can take advantage of aerobraking, it's just a matter of which maneuver can get you to the edge of the atmosphere more efficiently, which in most cases will be the retrograde burn. You might do better with the radial burn if we're starting in a large elliptical orbit.

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  • $\begingroup$ Is there a step by step text out there for calculation these sorts of things? I know it's vector math but don't know the equations and it seems a little elusive. Mostly I just want to program it into an excel spreadsheet that will calc out delta V requirements for this that and the other manouver and calc time to ground and things like that. $\endgroup$
    – Chris T
    Commented Sep 13, 2023 at 19:20
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    $\begingroup$ @ChrisT Optimization of orbital trajectories is a very tricky thing, and can be optimized for different things like minimum time, minimum propellant, minimum distance, and so on. There are some rules of thumb for how you can propose reasonable candidate trajectories to evaluate explicitly, but in general it comes down to lots of simulation. See space.stackexchange.com/questions/27058/… $\endgroup$
    – Nuclear Hoagie
    Commented Sep 13, 2023 at 19:24

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