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33. Putting a satellite in orbit The strength of Earth's gravitational field varies with the distancer from Earth's center, and the magni- tude of the gravitational force experienced by a satellite of mass m during and after launch is тMG F(r) = p2 Here, M = 5.975 × 10²4 kg is Earth's mass, G = 6.6720 × 10-11 N • m² kg-² is the universal gravitational constant, and r is measured in meters. The work it takes to lift a 1000-kg satellite from Earth's surface to a circular orbit 35,780 km above Earth's center is therefore given by the integral r 35,780,000 1000MG dr joules. Work = 6,370,000 Evaluate the integral. The lower limit of integration is Earth's radi- us in meters at the launch site. (This calculation does not take into account energy spent lifting the launch vehicle or energy spent bringing the satellite to orbit velocity.)

33. Putting a satellite in orbit The strength of Earth's gravitational field varies with the distancer from Earth's center, and the magni- tude of the gravitational force experienced by a satellite of mass m during and after launch is тMG F(r) = p2 Here, M = 5.975 × 10²4 kg is Earth's mass, G = 6.6720 × 10-11 N • m² kg-² is the universal gravitational constant, and r is measured in meters. The work it takes to lift a 1000-kg satellite from Earth's surface to a circular orbit 35,780 km above Earth's center is therefore given by the integral r 35,780,000 1000MG dr joules. Work = 6,370,000 Evaluate the integral. The lower limit of integration is Earth's radi- us in meters at the launch site. (This calculation does not take into account energy spent lifting the launch vehicle or energy spent bringing the satellite to orbit velocity.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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33. Putting a satellite in orbit The strength of Earth's gravitational field varies with the distancer from Earth's center, and the magni- tude of the gravitational force experienced by a satellite of mass m during and after launch is тMG F(r) = p2 Here, M = 5.975 × 10²4 kg is Earth's mass, G = 6.6720 × 10-11 N • m² kg-² is the universal gravitational constant, and r is measured in meters. The work it takes to lift a 1000-kg satellite from Earth's surface to a circular orbit 35,780 km above Earth's center is therefore given by the integral r 35,780,000 1000MG dr joules. Work = 6,370,000 Evaluate the integral. The lower limit of integration is Earth's radi- us in meters at the launch site. (This calculation does not take into account energy spent lifting the launch vehicle or energy spent bringing the satellite to orbit velocity.)
Transcribed Image Text:33. Putting a satellite in orbit The strength of Earth's gravitational field varies with the distancer from Earth's center, and the magni- tude of the gravitational force experienced by a satellite of mass m during and after launch is тMG F(r) = p2 Here, M = 5.975 × 10²4 kg is Earth's mass, G = 6.6720 × 10-11 N • m² kg-² is the universal gravitational constant, and r is measured in meters. The work it takes to lift a 1000-kg satellite from Earth's surface to a circular orbit 35,780 km above Earth's center is therefore given by the integral r 35,780,000 1000MG dr joules. Work = 6,370,000 Evaluate the integral. The lower limit of integration is Earth's radi- us in meters at the launch site. (This calculation does not take into account energy spent lifting the launch vehicle or energy spent bringing the satellite to orbit velocity.)
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