Undergrad Solving for Orbital Mechanics

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To solve for the orbital path of Sputnik 1, it's essential to understand that its trajectory can be approximated as an elliptical orbit, described by Kepler's laws. The key parameters needed for a complete 3D orbital description include the initial position and velocity vectors or the orbital elements. With the orbital period known, one can calculate the semi-major axis and relate it to perigee and apogee. Providing specific equations and numerical data may help clarify the next steps in the calculation. Utilizing available resources on orbital mechanics can further aid in resolving the problem.
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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?
 
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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.
 

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