State an expression for the acceleration due to gravity at a distance of 2R above the surface of a planet of mass M and radius R. - Leaving Cert Physics - Question d - 2021

To find the expression for the acceleration due to gravity at a distance of 2R above the surface of the planet, we can utilize the formula for gravitational acceleration:

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

where:

• G is the gravitational constant,
• M is the mass of the planet,
• d is the distance from the center of the planet.

Given that the radius of the planet is R, the distance from the center to the surface is R, and the distance above the surface to the point of interest is 2R, the total distance d becomes:

$d = R + 2R = 3R.$

Substituting this into our expression, we get:

$g = \frac{GM}{(3R)^2}$

This simplifies to:

$g = \frac{GM}{9R^2}.$

Thus, the expression for the acceleration due to gravity at a distance of 2R above the surface of the planet is:

$g = \frac{GM}{9R^2}.$