Question

If the same satellite orbited at the same velocity around a planet with three times the force of gravity, the orbit radius would be (multiplied, divided) by ___________.

Answer 1

Answer:

the orbit radius would be divided by 3

Explanation:

In order to orbit the planet, the centripetal force of satellite must balance the gravitational force between planet and satellite.

centripetal Force = Gravitational Force

(Ms)(V)²/r = (G)(Ms)(Mₓ)/r²

V² = GMₓ/r

where,

V = velocity of satellite

G = Gravitational Constant

Mₓ = Mass of Planet

r = orbit radius

but, G = gr²/Mₓ

Therefore,

V² = (Mₓ/r)(gr²/Mₓ)

V = √gr   --------------------- equation (1)

where,

g = force of gravity

Now, for change in force of gravity:

V' = √g'r'  

where,

g' = 3g

V' = V

Therefore,

V = √3gr'   ---------------- equation (2)

Comparing equation (1) and equation (2), we get:

√gr = √3gr'

gr = 3gr'

r = 3r'

r' = r/3

Hence, the orbit radius would be divided by 3.