Mechanics

# Satellites in Circular Orbits

Satellite is nothing more than a secondary planet or a body (launched by man) that revolves around a main planet. Orbiting around the planet Earth we have the Moon (natural satellite) and several other satellites launched by man (artificial satellites); we cannot forget that other planets such as Mars (natural satellites: Phobos and Deimos), Neptune (natural satellite: Charon), Uranus (natural satellites: Miranda, Ariel, Umbriel, Titania and Oberon) also have natural satellites.

Artificial Satellite

The force of gravitational attraction that holds us to Earth is the same force that makes the Moon and other satellites rotate around it.
Is there a possibility that we can do what satellites do? If there is this possibility, which variables are determinant?
The answers can be given based on the equations that we will see below:
The force of gravitational attraction between the Earth and the Moon is given by the following expression: F TL = GM T .M L /d²

G = gravitational constant = 6,67.10 -11 N.m²/kg²
T = mass of the Earth (kg)
L = mass of the Moon (kg)
d = distance between the center of the Earth and the center of the Moon (m)

The gravitational force of attraction between Earth and Moon is the centripetal resultant needed to keep the Moon in orbit.

Fc = mv 2 /r

Then we have: F TL = F c such that d = re Ml = m

G.MT.ML/d² = m.v2/r
G.MT./d = v2
v = [√(G .MT./r)] – translation speed

The translational velocity equation is a function of r. When launching any body (even us), in order to keep it in a circular orbit around the Earth, we must make the following observation: the smaller the distance between Earth-body, the greater the speed of the body, so that it manages to enter a circular orbit.