As distance to the sun decreases, what happens to the orbital velocity?
1 Answer
As distance to the Sun decreases, orbital velocity increases.
Explanation:
he fact that orbital velocity increases as distance from the Sun decreases can easily be proved using Kepler's laws. We will assume that orbits are circular, which is a good enough approximation to prove the point.
The orbital velocity
Where
This makes the orbital velocity:
Kepler's third law relates orbital period
So the orbital velocity is:
So, the angular velocity is inversely proportional to the square root of the distance.
So, we will choose units such that velocity is in km/s and distance is in AU. Earth at 1AU has an orbital velocity of about 30km/s. This makes the constant
Mercury is at distance 0.39AU which gives a calculated orbital speed of 48km/s.
Neptune at a distance 30AU has a calculated orbital speed of 5.45km/s.
The calculated orbital speeds agree with the measured values. The closer the distance the faster the orbital velocity.