### Hill radius

**(tidal radius)**
(radius of gravitational influence of a body)

An astronomical body's **Hill radius** is the radius
of the sphere (**Hill sphere**) within which smaller
bodies would tend to orbit the body.
Outside the radius, the body would be drawn to orbit around the
next larger body which the initial body is orbiting. For example,
the Moon is within Earth's Hill radius because otherwise it
would not retain a stable orbit around Earth but would end up in
orbit around the Sun. It might take multiple orbits before
the smaller body breaks away.

The Hill sphere lies between the L1 and L2
Lagrangian points; of the two bodies.
The formula for the Hill radius for a body
(e.g., Earth) orbiting another (e.g., the Sun) is:

r ≈ a(1-e)^{3}√(m/3M)

- r - Hill radius.
- a - semi-major access of the orbiting body.
- e - eccentricity of the orbit.
- m - mass of the orbiting body.
- M - mass of the central body.

The term **tidal radius** is often used when discussing entire star
clusters or galaxies, distinguishing whether the dynamics of a
body at that distance is determined by the cluster/galaxy or some
separate entity.

(*astrophysics,orbits,radius*)
http://en.wikipedia.org/wiki/Hill_sphere

**Referenced by:**

Bondi radius

giant planet

mass loss

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