Astronomy & Gravitation formula solvers

Orbital Velocity

v = \sqrt{\frac{GM}{r}}

Astronomy & GravitationMechanicsPhysicsSpeed of a body in a circular orbit of radius r around a central mass M.

Orbital Period

T = 2\pi \sqrt{\frac{r^{3}}{GM}}

Astronomy & GravitationMechanicsPhysicsTime for one circular orbit of radius r around a central mass M — Kepler's third law in Newtonian form.

Escape Velocity

v = \sqrt{\frac{2GM}{r}}

Astronomy & GravitationMechanicsPhysicsMinimum launch speed needed to escape the gravity of a mass M starting from distance r, with no further propulsion.

Gravitational Field Strength

g = \frac{GM}{r^{2}}

Astronomy & GravitationMechanicsPhysicsGravitational acceleration produced by a mass M at distance r from its center.

Kepler's Third Law (Ratio Form)

\frac{T_1^{2}}{T_2^{2}} = \frac{a_1^{3}}{a_2^{3}}

Astronomy & GravitationMechanicsPhysicsFor two bodies orbiting the same central mass, the squares of their periods are in the same ratio as the cubes of their orbital sizes.

Gravitational Potential Energy (Orbital)

U = -\frac{GMm}{r}

Astronomy & GravitationMechanicsPhysicsGravitational potential energy of a mass m at distance r from a central mass M, taking zero at infinite separation.

Schwarzschild Radius

r_s = \frac{2GM}{c^{2}}

Astronomy & GravitationPhysicsRadius of the event horizon of a non-rotating black hole of mass M.

Apparent Brightness (Inverse-Square Law)

b = \frac{L}{4\pi d^{2}}

Astronomy & GravitationPhysicsReceived flux from a source of luminosity L spread over a sphere of radius d — brightness falls with the square of distance.

Stellar Parallax Distance

d = \frac{1\,\text{AU}}{p}

Astronomy & GravitationPhysicsDistance to a star from its annual parallax angle p, using the small-angle form of d = AU/tan p.