A geosynchronous satellite orbits the earth once every day. For the earth, all s

Question

A geosynchronous satellite orbits the earth once every day. For the earth, all satellites in geosynchronous orbit must rotate at a distance of 4.23 times 10^7 m from the earth's center. (a) What is the distance a geosynchronous satellite travels in one day? (b) What is a geosynchronous satellite's average speed? (c) What (if any) is the magnitude of a geosynchronous satellite's centripetal acceleration? (d) The figure below shows the top view of the geosynchronous satellite's path. Indicate the direction of the satellite s acceleration at the points labeled a, b, and c with an arrow. If there is no acceleration at any point, write "none."

Explanation / Answer

(A) r = 4.23 x 10^7 m

d = 2 pi r = 2.66 x 10^8 m

(B) average speed, v = d / t

= (2.66 x 10^8 m) / (24 x 3600 s)

= 3076 m/s

(C) a_c = v^2 / r

= 0.224 m/s^2

(d) acceleration will be towards the center of earth (radially) for all the point on orbit.

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