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A satellite in an elliptical orbit around Earth has a speed of 8122 m/s when it is at perigee,...

Question:

A satellite in an elliptical orbit around Earth has a speed of 8122 m/s when it is at perigee, the position in the orbit closest to Earth. At this position, the satellite is 123 km above Earth's surface. How far above the ground is the satellite when it is at apogee, the position in its orbit farthest from Earth?

Gravity and Orbits:

An object in the gravitational field moves according to the Newton's Universal Gravitation Law and the Newton's Second Law. The orbit of the object can be finite, if its total energy is negative, or infinite, if it is positive. The finite trajectory is an ellipse, the non-finite motion is along either parabolic or hyperbolic trajectory.

Answer and Explanation:

Let {eq}r_p {/eq} be the distance from the Earth's center to the satellite in perigee;

{eq}r_p = R_E + h {/eq}

Here

  • {eq}R_E = 6370 \ km {/eq} is...

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How Orbits Are Influenced by Gravity & Energy

from Basics of Astronomy

Chapter 25 / Lesson 6
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