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}](https://tex.z-dn.net/?f=F%3D%20%5Cfrac%7Bmv%5E%7B2%7D%7D%7Br%7D)
Where v be the orbital velocity, which is given by
![v=\sqrt{gr}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7Bgr%7D)
So, the centripetal force is given by
![F= \frac{mgr}}{r}}=mg](https://tex.z-dn.net/?f=F%3D%20%5Cfrac%7Bmgr%7D%7D%7Br%7D%7D%3Dmg)
where, g bet the acceleration due to gravity
![g=\frac{GM}{r^{2}}](https://tex.z-dn.net/?f=g%3D%5Cfrac%7BGM%7D%7Br%5E%7B2%7D%7D)
So, the centripetal force
![F= \frac{GMm}}{r^{2}}}](https://tex.z-dn.net/?f=F%3D%20%5Cfrac%7BGMm%7D%7D%7Br%5E%7B2%7D%7D%7D)
Gravitational force on the satellite having larger orbit
.... (1)
Gravitational force on the satellite having smaller orbit
.... (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.