Chapter 10.1, Problem 74E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

# Satellite Orbit The apogee(the point in orbit farthest from Earth) and the perigee (the point in orbit closest to Earth) of an elliptical orbit of an Earth satellite are given by A and P, respectively. Show that the eccentricity of the orbit is e = A − P A + P .

To determine

To prove: The eccentricity of the orbit of the Earth is, e=APA+P.where A is the farthest point and P is the closest point from the Earth in the orbit.

Explanation

Given:

The Apogee and Perigee of in elliptical orbit of an Earth is given by A and P, which is farthest and closest point to earth respectively. The eccentricity of an elliptical orbit is e.

Formula used:

Eccentricity of ellipse, e=ca.

proof:

The apogee and perigee are the points in orbit that are nearest and farthest from planet Earth. Consider an elliptical orbit for Earth such that, 2a is the length of major axis and 2b is the length of minor axis.

Let the point E denotes the Earth, then A be the farthest point and P be the closest point from the E in the elliptical orbit and c is the distance between the centre of ellipse and Earth.

So, the nearest point from Earth is,

A=ac …...…... (1)

The farthest point from the earth,

P=a+c …..... (2)

Add equation (1) and equation (2),

A+P=2aa=A+P2

Put the

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