# Satelite how far from center of earth?

#### ChinToka

This problem troubles me since three days and I don´t know a way to solve it:

A satelite is in a circular parking orbit 6.98x10^6m from Earth. To initiate a Hohmann transfer, a rocket gives it an accelerating thrust so that its speed is increased to 8300m/s. How far from the center of Earth will the satelite be when it reaches its apogee?

What I need is the formula(s) so I can do it by myself

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#### OlderDan

Homework Helper
ChinToka said:
This problem troubles me since three days and I don´t know a way to solve it:

A satelite is in a circular parking orbit 6.98x10^6m from Earth. To initiate a Hohmann transfer, a rocket gives it an accelerating thrust so that its speed is increased to 8300m/s. How far from the center of Earth will the satelite be when it reaches its apogee?

What I need is the formula(s) so I can do it by myself
I'm not going to quote the formulas, but if you are learning about elliptical orbits you should know something about the connection between orbit parameters and the energy and angular momentum of a satellite. You are given enough information to find the energy, speed, radius, and angular momentum for the circular orbit. I am assuming the thrust is directed tangent to this orbit, but you need to veryify that. I also assume that the velocity change will be nearly instantaneous so that the new velocity will be perpendicular to the radial position vector. The new speed will have an associated total energy and angular mometum that will determine the shape of the new orbit.

If the new velocity is, as I suspect, perpendicular to the radial postion vector to the satellite, it will be the highest velocity the satellite ever achieves, and the location of the satellite immediately after the velocity increase will be the point of closest approach in its new orbit. In other words the satellite will be at perigee. It may be that "Hohmann transfer" implies some constraint on the direction of the new velocity. It is not something I am familiar with. If the new velocity is not perpendicular to the position vector, it will may more difficult to find the new angular momentum. However, once you have found the new angular momentum and energy you have what you need to determine the orbit parameters.

#### ChinToka

Let´s check if I have the right formulas

Energy: My guess is that the satelite has potential energy P_E=1/2mv^2
Speed: I don´t have a clue I don´t think s=d/t is the right one
Angular Momentum: L=I*w

So the potential energy would be 1/2(5.97x10^24)(8300)^2 = 2.0563665x10^32J

Am I right so far?

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