A satellite is in circular orbit around Earth at an altitude of three Earth radii above the surface. If the satellite uses onboard retro rockets to cut its speed to one half, at what distance from Earth can it establish a new stable circular orbit? Hint: vorbit = More than four Earth radii above the surface. Between three Earth radii and four Earth radii above the surface. Between two Earth radii and three Earth radii above the surface. Less than two Earth radii above the surface.

Orbital velocity (vorbit) = GMR where, G is the gravitation constant = 6.6743 x 10-11 m3 kg-1 s-2 M is the mass of the Earth = 5.972 x 1024 kg R is the radius of the Earth = 6.378 x 106 m If a satellite is orbiting the earth at an altitude of 3 times the earth's radius, it orbital velocity is: vorbit = GM3R = 6.6743 x 10-11 m3kg.s2 5.972 x 1024 kg36.378 x 106 mvorbit = 4564.15 msIf the orbital velocity of the satellite is reduced by half, then the satellite will be located distance (d) of: d =GMvorbit2 The new vorbit = 4564.15/2 = 2282.075 m/s Using the formula above, the distance from the center of the earth for the satellite to sustain its new orbital velocity is: d =6.6743 x 10-11 m3kg.s2 5.972 x 1024 kg2282.075 ms2 = 7.6536 x 107 m This new distance is 12 times the radius of the Earth. Therefore, the correct answer is More than four Earth radii above the surface.

Answered: A satellite is in circular orbit around…

Applications and Investigations in Earth Science (9th Edition)

9th Edition

ISBN:9780134746241

Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

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A satellite is in circular orbit around Earth at an altitude of three Earth radii above the surface. If the satellite uses onboard retro rockets to cut its speed to one half, at what distance from Earth can it establish a new stable circular orbit? Hint: v_orbit =

		More than four Earth radii above the surface.
		Between three Earth radii and four Earth radii above the surface.
		Between two Earth radii and three Earth radii above the surface.
		Less than two Earth radii above the surface.