Orbital Speed

The orbital speed of a celestial body measures its speed around another object’s center of gravity. This can be its speed at a given time and place in its path or may be its average speed. Depending upon the eccentricity of heavenly body's orbit the orbital speed changes as a satellite or moon gets closer to its center of gravity or further away. The two regions where speeds can change the most are pericenter and apocenter.

A satellite in orbit moves faster (pericenter) when it is close to the planet or other body that it orbits and slower (apocenter) when it is farther away. A satellite moving in a circular orbit has a constant speed which depends only on the mass of the planet and the distance between the satellite and the center of the planet.

Calculating the Orbital Speed

The speed (v) of a satellite in circular orbit is:

`v = sqrt((GM)/r)`

Where, `G` is the universal gravitational constant and the value is `6.6726 xx 10^-11 N m^2 kg^-2`,
`M`  is the mass of the combined planet-satellite system, in case Earth's mass is `5.972 xx 10^24 kg`, and we can ignore the satellite's mass, in case for smaller man made satellites.
and `r` is the radius of the orbit measured from the planet's center.
The period `P` of a satellite in circular orbit is the orbit's circumference divided by the satellite's speed:

`P = (2*pi*r)/v`

Kepler's Law for Orbital Speed:

Kepler's second law is illustrates that the line joining the Sun and planet sweeps out equal areas in equal times, this means the planet moves faster when it is nearer the Sun (perihelion). Henceforth, a planet executes elliptical motion with constantly changing angular speed as it moves about its orbit. The point of nearest distance of the planet to the Sun is known as perihelion; the point of greatest separation is known as aphelion. Therefore, by Kepler's second law, the planet moves fastest when it is near perihelion and slowest when it is near aphelion.