Question

A satellite moves in a circular earth orbit that has a radius of 9.96 x 10⁶ m. A model airplane is flying on a 14.6-m guideline in a horizontal circle. The guideline is nearly parallel to the ground. Find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.

Answer 1

acceleration of satellite in the orbit will be Using force balance:

Fnet = Fg

m*a = G*Me*m/R^2

a = G*Me/R^2

Now centripetal acceleration of plane will be

ac = V^2/r

Given thatboth plane and satellite have same acceleration, So

G*Me/R^2 = V^2/r

V = sqrt (G*Me*r/R^2)

Using given values:

Me = Mass of earth = 5.98*10^24 kg

r = radius of plane's circular motion = 14.6 m

R = radius of orbit of satellite = 9.96*10^6 m

So,

V = sqrt (6.67*10^-11*5.98*10^24*14.6/(9.96*10^6)^2)

V = 7.66 m/sec = Speed of plane

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