How is the acceleration of gravity calculated for planets?

Question

Olivia Aldridge · Accepted Answer

You can use the expression of gravitational force.

We use a bit of the expression of Gravitational Force (in red): #F_g=color(red)(G)*(mcolor(red)(M))/color(red)(r^2)# Where: #G# is the Universal Gravitational Constant; #M# is the mass of the planet; #r# is the radius of the planet. (You can find these values in the literature). Try with Earth you should find #9.8m/s^2#. For other planets simply choose the specific #M# and #r#.

Asher Cohen · Answer

undefined The acceleration of gravity on a planet is calculated using Newton's law of universal gravitation, which states that the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula for acceleration due to gravity (g) on a planet is:

$$ g = \frac{G \times M}{r^2} $$

Where:
- $ g $ is the acceleration due to gravity.
- $ G $ is the gravitational constant ($6.67430 × 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}$).
- $ M $ is the mass of the planet.
- $ r $ is the distance from the center of the planet to the object.