Two identical satellites are in orbit about the earth. One orbit has a radius r and the other 2r. The centripetal force on the satellite in the larger orbit is __________ as that on the satellite in the smaller orbit.

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Vespertilio Vespertilio · Answer 1 · 2019-11-23T08:43:13+01:00

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

[tex]F= \frac{mv^{2}}{r}[/tex]

Where v be the orbital velocity, which is given by

[tex]v=\sqrt{gr}[/tex]

So, the centripetal force is given by

[tex]F= \frac{mgr}}{r}}=mg[/tex]

where, g bet the acceleration due to gravity

[tex]g=\frac{GM}{r^{2}}[/tex]

So, the centripetal force

[tex]F= \frac{GMm}}{r^{2}}}[/tex]

Gravitational force on the satellite having larger orbit

[tex]F= \frac{GMm}{4r^{2}}[/tex] .... (1)

Gravitational force on the satellite having smaller orbit

[tex]F'= \frac{GMm}{r^{2}}[/tex] .... (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.