Astrophysics (Index)About

Hill radius

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

An astronomical body's Hill radius is the radius of the surrounding spherical region (Hill sphere aka Roche sphere) within which smaller body's would tend to orbit the body. If body A is orbiting B and the pair together are orbiting C, then if beyond B's Hill radius, A's orbit around B would be unstable and eventually it would directly orbit C. The size of B's Hill radius is determined by the masses and the orbit of B around C. If beyond B's Hill radius, A might still orbit B for some time before breaking away. For example, the Moon is within Earth's Hill radius, and if it weren't, it would not retain a stable orbit around Earth but would eventually orbit independently around the Sun.

A body's Hill sphere necessarily lies between the L1 and L2 Lagrangian points; of a body and its host. The formula for the Hill radius for a body ("B", such as the Earth) orbiting another ("C", such as the Sun) is:

r ≈ a(1-e)(m/3M)1/3

The term tidal radius is often used when discussing gravitationally-bound groups of objects such as an entire stellar cluster or galaxy: the dynamics of a body within the group's tidal radius is determined by that group rather than some other entity.

Further reading:

Referenced by pages:
atmospheric escape
Bondi radius
giant planet
hydrodynamic escape
isolation mass
mass loss
planet formation
Roche limit
Roche lobe