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a satellite of mass ms travels in a circular orbit of radius 'a' around a planet of mass mp≫ms.

 

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A satellite of mass ms travels in a circular orbit of radius 'a' around a planet of mass mp?

Part A

Derive expressions for the orbital speed of a satellite.

Express your answer in terms of some or all of the variables mp, ms, a, and gravitational constant G.

Part B

Derive expressions for the energy of a satellite.

Express your answer in terms of some or all of the variables mp, ms, a, and gravitational constant G.

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Vikas
VikasLv10
15 Oct 2020

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Assumethe orbital of a lunched satellite around the earthiscircular.

(a)Show that there is only one speed that a satellite canhave if thesatellite is to remain in an orbit with

afixed radius and it does not depend on the mass ofthesatellite.

(b)What is the speed and heightHabove the earth’s surfaceat which all synchronoussatellite

(regardless of mass) must be placed in orbit, assumingtheearth is spherical?

(c) Ifa synchronous satellite has amassm. How muchadditional kineticenergy is needed for it to escape

fromthe earth?

(A) A satellite of mass m is in circular orbit about theearth.
The radius of the orbit is r0 and the mass of the earth isME.
Find the total mechanical energy of the satellite.



(B) Now suppose that the satellite moves in the extreme upper
atmosphere of the earth where it is retarded by a constant
weak frictional force f. The satellite will slowly spiral intoward
the earth. Since the friction force is weak, the change
in radius will be very slow. We can therefore assume that
at any instant the satellite is effectively in a circular orbitof
average radius r. Find the approximate change in radius r
per revolution of the satellite.



(C) Calculate r for these parameters: r = 1.045 RE; f =
\ensuremath{1.300\times 10ˆ{-4}} N; m = 91 kg.



(D) Find the approximate change of kinetic energy of the
satellite K per revolution, for the same parameters as (C).
Express the result as the fraction of the current kineticenergy.
Is K positive or negative? Explain briefly.

Six artificial satellites circle a space station at constant speed. The mass m of each satellite, distance L from the space station, and the speed v of each satellite are listed below. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible.

1. m = 200 kg, L = 5000 m, v = 120 m/s

2. m = 800 kg, L = 10,000 m, v = 40m/s

3. m=400 kg, L = 2500 m, v = 80m/s 

4. m = 100 kg, L = 2500 m, v = 160m/s

5. m = 300kg, L = 10,000 m, v = 80 m/s

6. m = 200 kg, L = 5000 m, v = 160 m/s

Part A Rank each satellite from largest to smallest based on its period.

Part B Rank each satellite from largest to smallest based on its acceleration.

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