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`M = {v^2 * R}/G`

375.332

The **Mass from Speed and Separation** calculator computes the mass of the object (e.g., star or planet) based on the orbital speed of its satellite, and the separation (**R**) and the universal gravity constant (G).

**INSTRUCTIONS:** Choose units and enter the following:

- (
**V**) Orbital Velocity. - (
**R**) Separation Distance

**Mass (M):** The calculator returns the mass of the object in Earth Masses (multiples of the mass of the Earth). However, this can be automatically converted to other mass units (e.g. kilograms) via the pull-down menu.

The formula for computing the mass of an astronomical object based on the orbital velocity and distance from the greater mass (e.g. stellar object) is:

M = (v^{2} ⋅ R) / G

where:

- M = mass of object
- v = orbital velocity
- R = distance between objects or orbital radius
- G = universal gravity constant (6.67384E-11 N·m²/kg²)

The orbital velocity of the Earth as it goes about the Sun is approximately: 29784.7357 m/s. Use this velocity and one astronomical unit for R, and you will get a mass equal to 332968.774 Earth Masses. If you click on the pull-down menu and select solar_mass, you will see that the mass is equal to 1 solar mass.

- Kepler's 3
^{rd}Law formula T² = (4π • R³)/(G • M) - Small Angle Formula
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