Question

Exoplanets (planets outside our solar system) are an active area of modern research. Suppose astronomers find such a planet that has the same mass as Earth, but has a radius that is about 10% less. Roughly, what acceleration due to gravity would you expect if you were standing on the surface of this new planet?

Answer 1

Answer:

$g' = 12.11 m/s^2$

Explanation:

As we know that the acceleration due to gravity is given as

$g = \frac{GM}{R^2}$

now for earth we know that

$\frac{GM}{R^2} = 9.81 m/s^2$

now if on the surface of another planet we know that the mass is same as that the mass of Earth but radius is 10% less than the radius of Earth

so we have

$r = 0.9 R$

so we will have

$g' = \frac{GM}{(0.9R)^2}$

$g' = \frac{GM}{0.81 R^2}$

$g' = 1.23 \times 9.81$

$g' = 12.11 m/s^2$