How do I calculate re-entry velocity when decaying from a circular orbit?

Question

I am trying to find the velocity of an object during re-entry so that I can calculate the peak heat flux but I'm a bit stuck.

I know how to find the velocity of the original, circular orbit (300km) but I don't know how to calculate the velocity while moving through the atmosphere.

The object is a small sphere, decaying naturally due to atmospheric drag, on a purely ballistic trajectory with no lift or retro propulsion.

I can calculate the trajectory due to drag but I don't know how to find it's speed when it reaches the point of maximum heating, at approx 70-80 km altitude.

Does anyone know the best (or easiest!) way to do this? Thank you!

Have a look at this answer for something slightly related. It shows a very simple calculation that tries to estimate what a reentry would be like for various input parameters. It is not an answer to your question because it's at the wrong (slower) velocity. Thus the peak heating is at a lower altitude as well. — uhoh, May 28 '19 at 10:55
Also have a look at these questions and their answers and comments and links, but note that none of these answer your question; At what altitude does a spacecraft slow down? as well as How does a Reentry Breakup Recorder survive reentry and then broadcast its data before impact? and also What are the three peaks in this Apollo reentry heating plot? — uhoh, May 28 '19 at 10:59
Well, orbital velocity at earth circumference gives you an upper bound, orbital velocity at original height gives you a lower bound (for the maximum velocity, end velocity will ofc need to be 0). — Polygnome, May 28 '19 at 13:13

score 1 · Answer 1 · answered May 29 '19 at 05:18

If you have trajectory, then you have position and velocity over time, so what you need next is aero heating versus velocity. If you can calculate that over the trajectory, you can easily find the peak. If all you care about is the point of maximum heating, you could get pretty close by looking at acceleration times velocity, which should be a good proxy for heat flux. All depends on how accurate you need to be.

How do I calculate re-entry velocity when decaying from a circular orbit?

1 Answers1