Orbital Period Calculator | Binary System

where:

• TTT — Orbital period;
• GGG — Universal gravitational constant; and
• ρ\rhoρ — Mean density of the central body.

We can use this simple equation to calculate the orbital period of any satellite around any celestial body. For example, in the case of the Earth, the density is 5.51 g/cm35.51\ \mathrm{g/cm^3}5.51g/cm3, which would give a period of 1.4063 hours1.4063\ \mathrm{hours}1.4063hours.

It is important to remember that as we move away from the surface of the Earth (or the central body) this approximation falls off. This is clearly visible when we consider that different satellites have different orbital periods. For example, the geostationary orbit and geosynchronous orbits. These orbits have an orbital period of exactly 1 day=23.934446 hours1\ \mathrm{day} = 23.934446\ \mathrm{hours}1day=23.934446hours. The difference between the geostationary orbit and the geosynchronous orbit is the position with respect to the equator.

The geostationary orbit is exactly above the equator, so the satellites in this orbit stay all over the same point on Earth's surface.

The geosynchronous orbit, however, can be located anywhere and doesn't have a one-to-one mapping of any particular point on the Earth.

You are probably wondering how many satellites orbit the Earth currently. We have the answer! Space debris is a big problem due to how many satellites orbit the Earth at the moment, and the number is only increasing. Nowadays, it is becoming such a problem that space agencies are starting to consider possible solutions to be implemented in the near future.

But enough rambling, let's give you the figure; just how many satellites orbit the Earth? The latest statistics point at over 3700 satellites orbiting the Earth right now, of which only about 1100 are operative.