Name Date
The Mass of the Sun
The Mass of the Sun
Orbits
The planets in our Solar System all orbit the Sun in elliptical orbits. Most planetary orbits are,
however, almost circular. Since the planets are moving in circles they must be experiencing a
centripetal acceleration.
We know that the centripetal acceleration on an orbiting body (e.g. a planet) is given by:
=
where r is the distance from the central body (e.g. the Sun), and v is the velocity it is moving at.
The centripetal acceleration is caused by the gravitational attraction of the two bodies, which is given
by:
=
where M is the mass of the central body, m is the mass of the orbiting body, and G is Newton’s
Gravitational constant and is equal to 6.67 x 10-11 m3 s-2 kg-1
Since the centripetal acceleration is caused by the gravitational force, we use Newton's 2nd law:
=
Putting the first two equations into the third one we therefore know that:
=
We can then work out a relationship between the velocity, the mass of the central object, and the
orbital radius:
=
