What is a Perigee?

Perigee refers to the closest point of the spacecraft to the center of the earth in an elliptical orbit around the earth. The astronomical perigee refers to the point at which the moon orbits the earth's orbit. The moon's perigee has a distance of 363,300 kilometers, and the perigee period is 8.85 years. The earth is in one of the two focal positions of the ellipse. Using the two focal points of the ellipse as the horizontal axis, you can draw a straight line. This straight line and the satellite orbit will produce two intersections. We will call the point closest to the earth as the apogee, and the point farthest from the earth is called the apogee; usually at the apogee , Satellites operate at the fastest angular speeds.

After the Earth satellite enters orbit, it is in a conservative field of the Earth. The total energy of the satellite is conserved without considering the loss of resistance. As a result, an energy balance of the satellite orbit can be established.

The potential energy of the satellite position is

, The kinetic energy of the satellite is

, The total energy of the satellite is:

The total energy is the same at any point in the orbit.

The total energy of the satellite's perigee and apogee are:

Among them, GM is the earth constant, GM = gR ² , r ₁ is the geocentric distance of the perigee, r ₂ is the geocentric distance of the apogee, v ₁ is the perigee velocity, and v ₂ is the apogee velocity.

Since E _perigee = E _apogee , there are:

which is:

According to Kepler's law, the ratio of the perigee and apogee speeds is equal to the inverse ratio of its geocentric distance, that

Substituting into the above formula, there are:

After finishing, you have:

make

,Have:

The above formula is called the satellite orbit perigee energy balance type, which indicates that the kinetic energy at the perigee is equal to k times its potential energy.

If

, Then:

This is a satellite orbit perigee energy balance. ^[2]