Orbits & Gravity

The speed of a body on a circular orbit at a given distance from a central mass. The Earth circles the Sun at about 29.8 km/s.

The minimum speed an object needs to break free of a body's gravity, ignoring drag. Set by the body's mass and radius alone.

The radius within which a body's gravity dominates over the larger body it orbits — the region where its moons can hold. Earth's Hill sphere reaches about 1.5 million kilometres.

The average density of a body from its mass and radius — a clue to its composition. Earth's ~5510 kg/m³ points to a rock-and-iron world; the giant planets are far less dense.

Kepler's third law: the time to complete one orbit, from the semi-major axis and the central mass. A planet at 1 AU around the Sun takes one year.

The distance within which a fluid satellite held together only by gravity is pulled apart by tides. Inside the Earth–Moon fluid Roche limit — about 18,000 km — a Moon-like body could not survive.

The radius of the event horizon of a non-rotating black hole of a given mass — the size to which that mass must be compressed to become one. The Sun's is just under three kilometres.

The gravitational acceleration at a body's surface, from its mass and radius. Earth's is about 9.8 m/s².

How often two orbiting bodies return to the same relative alignment — the interval between successive oppositions, say. Earth and Mars line up about every 2.14 years.