### 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 bodies would tend to orbit the body,
despite the gravity of some third body they are orbiting together.
Beyond the Hill radius, the small body may be drawn out of its orbit.
For example, the Moon is within Earth's Hill radius and
its orbit is stable over billions of years. If it weren't within
this radius, it would not retain its 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 the body and its host (Earth and Sun
in this example).
The formula for the Hill radius for a body orbiting another is:

r ≈ a(1-e)(m/3M)^{1/3}

- r - Hill radius of the orbiting body (e.g., of Earth, in the above example).
- a - semi-major axis of the orbit around the body it is orbiting (Earth around the Sun).
- e - eccentricity of this orbit.
- m - mass of the orbiting body (Earth).
- M - mass of the central body (Sun).

(In relation to the Earth example above, this formula describes
the Hill radius from Earth's center, formed by the Earth and Sun,
affecting the orbits of objects orbiting Earth such as the Moon
as well as artificial satellites such as the Hubble Space Telescope.)

The *Hill radius* is sometimes used as an approximation of how close
to a smaller object might be to a body to be accreted, but
the Bondi radius is another such calculation based on other factors.

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.

(*astrophysics,orbits,radius*)
**Further reading:**

http://en.wikipedia.org/wiki/Hill_sphere

**Referenced by pages:**

giant planet

isolation mass

mass loss

planet formation

Roche limit

Roche lobe

Index