Question

Say that there were a planet X in our Solar System with a mass 1/4 the mass of Earth and a radius 1/2 the radius of Earth. How will the gravity on its surface compare to the surface gravity of Earth?

Answer 1

The gravity on the surface of the planet X will be equal to the gravity on the surface of the Earth.

Step-by-step explanation:

The gravity (g) on the surface of a planet can be calculated using an expression derived from Newton's law of universal gravitation.

`g=(G.M)/(r^(2) )`

where,

G: gravitational constant

M: mass of the planet

r: radius of the planet

The gravity on the surface of the Earth is:

`gE=(G.M_(E))/(r_(E)^(2) )`

For the planet X,

mX = 1/4 mE

rX = 1/2 mE

The gravity on the surface of the planet X is:

`gX=(G.M_(X))/(r_(X)^(2) )=(G.1/4M_(E))/((1/2r_(E))^(2) ) =(G.M_(E))/(r_(E)^(2) )=gE`

The gravity on the surface of the planet X will be equal to the gravity on the surface of the Earth.