Surface Gravity Calculator

Formula

The formula to calculate the surface gravity is:

\[ g = \frac{G \cdot M}{r^2} \]

Where:

\(g\) is the surface gravity
\(G\) is the gravitational constant
\(M\) is the mass of the planet or celestial body
\(r\) is the radius of the planet or celestial body

What is Surface Gravity?

Surface gravity refers to the gravitational force experienced at the surface of a celestial body like a planet, moon, or star. It determines the weight of an object on that body and influences the body’s escape velocity, atmosphere retention, and the formation of natural satellites. Surface gravity is typically measured in relation to Earth’s gravity (g), with Earth’s surface gravity being 1g. It varies based on the mass of the celestial body and its radius.

Example Calculation

Let's assume the following values:

Mass of the Celestial Body (M) = 5.972 × 10^24 kg (Earth's mass)
Radius of the Celestial Body (r) = 6.371 × 10^6 m (Earth's radius)

Using the formula:

\[ g = \frac{6.67430 \times 10^{-11} \times 5.972 \times 10^{24}}{(6.371 \times 10^6)^2} = 9.81 \text{ m/s²} \]

The Surface Gravity (g) is 9.81 m/s².