What is meant by Apogee and perigee,Eccentricity? How do we Calculate them?

Planets, moon and satellites follow elliptic orbits. There are a number of parameters which can be used to describe an orbit. At least two parameters are required.

The semi-major axis #a# is half of the greatest width of the ellipse.

The eccentricity #0<=e<1# describes the shape of the ellipse. An eccentricity of zero is a perfect circle.

Apogee means the furthest distance the Moon or a satellite gets from Earth in its orbit. The related term aphelion is the furthest distance a planet or other body gets from the Sun. The generic term is apapsis which describes the furthest distance an orbit gets from anything. Apogee #A# is related to the semi-major axis and eccentricity.

#A = a(1+e)#

Perigee means the closest distance the Moon or a satellite gets to Earth in its orbit. The related term perihelion is the closest distance a planet or other body gets to the Sun. The generic term is periapsis which describes the closest distance an orbit gets to anything. Perigee #P# is related to the semi-major axis and eccentricity.

#P = a(1-e)#

Given any two of apogee, perigee, eccentricity and semi-major axis, it is easy to calculate the other two and completely define the ellipse.