Explanation Given info: The speed of the satellite at apogee is 3.64 km / s , speed of the satellite at perigee is 4.46 km / s and distance from the center of earth at perigee is 2.00 × 10 4 km . The universal gravitational constant is 6.67 × 10 − 11 N ⋅ m 2 / kg 2 and mass of the earth is 5.97 × 10 24 kg . The formula for gravitational potential energy is, U = − G m M e r e (1) Here, U is the gravitational potential energy m is mass of satellite M e is mass of earth. r e is the distance between earth and the satellite. G is the universal gravitational constant The formula for kinetic energy is, K = 1 2 m v 2 (2) Here, K is the kinetic energy of satellite. v is the velocity of the satellite. From equation (1) and equation (2), the expression for the total energy is, E = U + K Here, E is the expression for total energy Substitute expressions for U and K from equation (1) and equation (2) in the above expression. E = − G m M e r e + 1 2 m v 2 For satellite at perigee, substitute r p for r e , v p for v and E P for E in the above expression. E p = − G m M P r p + 1 2 m v P 2 (3) For satellite at apogee, substitute r a for r e , v a for v and E a for E in the above expression. E a = − G m M P r a + 1 2 m v a 2 (4) Equate equation (3) to equation (4) for conservation of total energy. − G m M P r p + 1 2 m v P 2 = − G m M P r a + 1 2 m v a 2 Rearrange the above equation for r a

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Chapter 12, Problem 46PCE

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The distance of the satellite from center of the earth at apogee.

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Chapter 12, Problem 45PCE

Chapter 12, Problem 47PCE

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The distance of the satellite from center of the earth at apogee.

Solution Summary: The author calculates the distance of the satellite from apogee and perigee. The formula for gravitational potential energy is U=-G

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The distance of the satellite from center of the earth at apogee.

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