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.
