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deff fn [24]
4 years ago
5

Two identical satellites are in orbit about the earth. One orbit has a radius r and the other 2r. The centripetal force on the s

atellite in the larger orbit is __________ as that on the satellite in the smaller orbit.
Physics
1 answer:
velikii [3]4 years ago
8 0

Answer:

the centripetal force on the satellite in the larger orbit is _one fourth_ as that on the satellite in the smaller orbit.

Explanation:

Mass of satellite, m

orbit radius of first, r1 = r

orbit radius of second, r2  = 2r

Centripetal force is given by

F= \frac{mv^{2}}{r}

Where v be the orbital velocity, which is given by

v=\sqrt{gr}

So, the centripetal force is given by

F= \frac{mgr}}{r}}=mg

where, g bet the acceleration due to gravity

g=\frac{GM}{r^{2}}

So, the centripetal force

F= \frac{GMm}}{r^{2}}}

Gravitational force on the satellite having larger orbit

F= \frac{GMm}{4r^{2}} .... (1)

Gravitational force on the satellite having smaller orbit

F'= \frac{GMm}{r^{2}} .... (2)

Comparing (1) and (2),

F' = 4 F

So, the centripetal force on the satellite in the larger orbit is _one fourth_ as that on the satellite in the smaller orbit.

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