Solving for Orbital Mechanics

[JoeyNoMad]

TL;DR Summary

I'm working on solving for Orbital Mechanics of a satellite. I have the velocity and the momentum and now I'm stuck and don't know what to do next.

I'm working on solving the orbital path of Sputnik 1(even though it's not in orbit any more) and I'm stuck. I have the circumference of the original orbit, and I have the time it took to orbit which gave me the velocity, which I then used to get the momentum. Can anyone tell me what to do next?

 

[Filip Larsen]

Welcome to PF.

In general, the path of a satellite that continues to free-fall around a planet can as a good approximation be described as an elliptical orbit, which is a specialization of a Kepler orbit. For a more complete (3D) description of the orbit of a particular object in relation to the Earth one needs 7 parameters, usually given by the initial position and velocity vectors at epoch or by the set of orbital elements for the object, which historically has been given as 2-line elements.

So if you have the orbital period of a satellite around Earth you should be able to locate the equation that that will yield you, say, the semi-major axis of the orbit. From this you can further relate perigee and apogee if that is what you seek. If this doesn't help, perhaps you can show us what equations and numbers you have so far and what measure it is you seek.

 

[Janus]

Here's a good resource for equations useful when dealing with orbital mechanics:
https://www.bogan.ca/orbits/kepler/orbteqtn.html
The main page that this is from is:
https://www.bogan.ca/index.php?id=astronomy
Which has other links you may find useful.