Problem 4.65 Communications satellites are placed in a circular orbit where they

Question

Problem 4.65 Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is 6.37 x 10^6m, and the altitude of a geosynchronous orbit is 3.58 x 10^7m( Approximately equals to 22000 miles). Part A What is the speed of a satellite in geosynchronous orbit? V = 3070 m/s Part B What is the magnitude of the acceleration of a satellite in a geosynchronous orbit? A =

Explanation / Answer

So, the satellite travels on a circular path, and the radius of that circle is equal to the radius of the earth + the altitude

R=4.22 x 10^7 m

And so the circumference is 2(pi)(R) = 2.65 x 10^8 m

Now if its in geosynchronus orbit (and the earth makes one revolution every 24 hours) then it too makes one revoultion every 24 hours (86400 s). Since speed = distance/time

(2.65 x 10^8 m)/(86400) = 3067 m/s (or 3070 if significant figures are important)

Now for acceleration:

Acceleration of an object moving in a circular path = v^2/R

so (3067)^2/(4.22 x 10^7) = 0.22 m/s^2

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