Concept

Gravitational potential — where it appears

The energy per unit mass required to bring a body from infinity to a point. Its gradient is the field, and expanding it in spherical harmonics is how a planet's shape and internal density distribution are read from the motion of things orbiting it.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

$Inside a star that is holding itself up (polytrope n = 3). Temperature, density and pressure through a star, as fractions of their central values, against fractional radius. All three come from one numerical integration of the Lane–Emden equation at index 3, which is the hydrostatic balance written for a gas whose pressure is a power of its density. The inner half of the radius holds 90% of the mass, and the outer half is nearly weightless — which is why the load, and so the temperature, is concentrated where the burning is.$

A star is held up by its own weight

A star has a central temperature because it has a central pressure, and it has a central pressure because everything above is pressing down. The nuclear reactions do not set that temperature — they obey it.

stars · Hydrostatic equilibrium

Circular and escape speed. Orbital and escape speed against distance, in units of the circular speed at the surface. The escape curve is the circular one multiplied by the square root of two, at every distance without exception.

The speed that does not come back, and the √2 that separates it

Escape speed is exactly the square root of two times circular speed, at every distance from every body. Being in orbit is already 71% of the way to leaving.

spaceflight · Escape

Named alongside it

The objects these essays reach for when they reach for this one.

Black hole Eddington limit Effective temperature Escape velocity Hydrostatic equilibrium Main sequence Nuclear fusion Oberth effect Orbital energy Stellar radius

All concepts