Suppose a satellite is in a circular orbit 5.4 Earth radii above the surface of

Question

Suppose a satellite is in a circular orbit 5.4 Earth radii above the surface of the Earth (6.4 Earth radii from the center of the Earth). By how much does it have to increase its speed in order to be able to escape Earth? [Hint: You need to calculate the orbital speed and the escape speed.] Suppose a satellite is in a circular orbit 5.4 Earth radii above the surface of the Earth (6.4 Earth radii from the center of the Earth). By how much does it have to increase its speed in order to be able to escape Earth? [Hint: You need to calculate the orbital speed and the escape speed.]

Explanation / Answer

orbital speed = sqrt(G * mass of earth / distance)

orbital speed = sqrt(6.674 * 10^-11 * 5.972 * 10^24 / 6.4 * 6371 * 10^3)

orbital speed = 3126.51 m/s

escape velocity = sqrt(2 * G * mass of earth / radius)

escape velocity = sqrt(2 * 6.674 * 10^-11 * 5.972 * 10^24 / 6371 * 10^3)

escape velocity = 11185.7 m/s

satellite has to increase its speed by = 11185.7 - 3126.51

satellite has to increase its speed by = 8059.19 m/s

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