.The answers are: a. 3.94 x 10^7 m b. –2.12 x 10^10 J PLEASE SHOW ME THE PROCEDU

Question

.The answers are:

a. 3.94 x 10^7 m

b. –2.12 x 10^10 J

PLEASE SHOW ME THE PROCEDURE

P. “Geostationary" satellites have an orbital period equal to exactly 1 day, so they can stay above the same point on the Earth. This makes them useful for relaying TV programs, satellite phone transimissions, etc. We wish to place a 2500 kg satellite in such an orbit around an imaginary planet of mass 5 x 10 kg and a day of 8.5 x 10s. Please answer each of the folowing questions a) What is the radius of the orbit for this satellite? b) What is is the potential energy of the satellite in this orbit? Use the usual convention that the potential energy goes to zero as the radius goes to infinity.

Explanation / Answer

r^3=T^2 G M/ 4pi^2

r^3 = ( 8.5x 10^4 ) ^2 ( 6.67 x 10^-11 x 5 x10^24 ) / ( 4 x 3,14^2)

r=3.94 x 10^ 7 m

b) pe =- 6.67 x 10^-11 (2500) (5 x 10^24)/3.94 x 10^7 =21161x 10^6 = -2.12 x1 0^ 10 J

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