Explanation 1) Concept: As we are given the distance between the farthest point and the closest point, we can find the distance between the satellite and the earth’s center. If we take the average of both distances, we can find the semi-major axis. From the formula of apogee and perigee distance, we can find the eccentricity of the orbit. 2) Formula: i) a p o g e e = R a = a 1 + e ii) p e r i g e e = R P = a 1 - e 3) Given: i) Farthest point distance (earth's surface and satellite) = 360 k m ii) Closest point distance (earth's surface and satellite) = 180 k m iii) Radius of earth = 6.37 × 10 6 m 4) Calculation: Farthest point distance (earth’s surface and satellite) = 360 k m Farthest point distance (earth's center and satellite) = 360 k m + R a d i u s o f e a r t h Farthest point distance (earth's center and satellite) = 360 × 10 3 m + 6.37 × 10 6 m Farthest point distance (earth's center and satellite) = R a = 6.73 × 10 6 m Closest point distance (earth's surface and satellite) = 180 k m Closest point distance (earth's center and satellite) = 180 k m + R a d i u s o f e a r t h Closest point distance (earth's center and satellite) = 180 × 10 3 + 6.37 × 10 6 m Closest point distance (earth's center and satellite) = R P = 6.55 × 10 6 m a) From diagram, we can say that, S e m i m a j o r a x i s = a = R a + R p 2 S e m i m a j o r a x i s = 6.73 × 10 6 + 6.55 × 10 6 2 S e m i m a j o r a x i s = a = 6

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force betwe…

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Chapter 13, Problem 51P

To determine

To Find:

a) Semi-major axis of the satellite

b) Eccentricity of the orbit of the satellite

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Chapter 13, Problem 50P

Chapter 13, Problem 52P

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The distance between the Earth and Mars when the two planets are at opposition varies greatly because of the large eccentricity of Mars's orbit. The perihelion distance of a planet is given by rmin = a (1-e) and the aphelion distance by rmax = a (1 + e) where a is the semimajor axis and e the orbital eccentricity. Find the smallest and largest opposition distances assuming that the Earth's orbit is a circle.

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A satellite, moving in an elliptical orbit, is 360 km above Earth’s surface at its farthest point and 180 km above at its closest point. Calculate (a) the semimajor axis and (b) the eccentricity of the orbit.

Chapter 13 Solutions

Fundamentals of Physics Extended

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a) Semi-major axis of the satellite b) Eccentricity of the orbit of the satellite

Solution Summary: The author explains the semi-major axis of the satellite and the eccentricity of its orbit.

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To Find: a) Semi-major axis of the satellite b) Eccentricity of the orbit of the satellite

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Chapter 13 Solutions

To Find:

a) Semi-major axis of the satellite

b) Eccentricity of the orbit of the satellite