Question

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.

Answer 1

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

Step-by-step explanation:

Mass of satellite, m

orbit radius of first, r1 = r

orbit radius of second, r2 = 2r

Centripetal force is given by

`F= (mv^(2))/(r)`

Where v be the orbital velocity, which is given by

`v=√(gr)`

So, the centripetal force is given by

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

where, g bet the acceleration due to gravity

`g=(GM)/(r^(2))`

So, the centripetal force

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

Gravitational force on the satellite having larger orbit

`F= (GMm)/(4r^(2))` .... (1)

Gravitational force on the satellite having smaller orbit

`F'= (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.