Universal Gravitation Calculator

Every object with mass attracts every other object with mass. The force depends on both masses and the square of the distance between them.

where $G = 6.674 \times 10^{-11}\;\text{N}\cdot\text{m}^2/\text{kg}^2$ is the gravitational constant. The force is always attractive and acts along the line connecting the two centers of mass.

The gravitational field strength at a distance $r$ from a mass $M$ tells you the acceleration any object would experience at that point.

On Earth's surface, $g \approx 9.81\;\text{m/s}^2$. On the Moon it is about $1.62\;\text{m/s}^2$, roughly one sixth of Earth's value.

For a circular orbit, gravitational force provides the centripetal acceleration. Setting them equal gives the speed needed to maintain the orbit.

A satellite in low Earth orbit (about 400 km altitude) needs roughly 7,670 m/s. Higher orbits require less speed but take longer to complete one revolution.

Escape velocity is the minimum speed needed to leave a gravitational field without further propulsion. It comes from setting kinetic energy equal to gravitational potential energy.

Notice that escape velocity is exactly $\sqrt{2}$ times the orbital velocity at the same distance. For Earth's surface, it is about 11,200 m/s.