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12 results for “orbit”

Formulae (12)

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

Speed needed for a circular orbit.

r = \frac{a(1-e^2)}{1 + e\cos\theta}

Planets orbit the Sun in ellipses with the Sun at one focus.

\frac{dA}{dt} = \text{const}

A line from a planet to the Sun sweeps equal areas in equal times.

T^2 \propto a^3

The square of the orbital period is proportional to the cube of the semi-major axis.

E_n = -\frac{13.6}{n^2}\ \text{eV}

Energy of the nth hydrogen orbit.

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

Minimum speed to escape a body's gravity.

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

Speed of a circular orbit.

T^2 = \frac{4\pi^2}{GM}a^3

Relates orbital period to semi-major axis.

U = -\frac{GMm}{r}

Energy of a mass in another body's gravitational field.

r_{ph} = \frac{3GM}{c^2}

Radius where gravity bends light into a circular orbit.

\frac{1}{S} = \left|\frac{1}{P_1} - \frac{1}{P_2}\right|

Time between repeated alignments of two orbiting bodies.

r_H \approx a\left(\frac{m}{3M}\right)^{1/3}

The zone where a body's gravity dominates over its host's.