Answer:
The following are true:
A satellite's motion is independent of its mass.
The launch speed of a satellite determines the shape of its orbit around Earth.
Explanation:
A satellite's motion is independent of its mass.
The speed of a satellite can be determined by means of the Universal law of gravity:
[tex]F = G\frac{M\cdot m}{r^{2}}[/tex] (1)
Where G is the gravitational constant, M and m are masses of the two objects and r is the distance between them.
In equation 1, Newton's second law can be replaced:
[tex]F = m\cdot a[/tex]
[tex]m. a = G\frac{M\cdot m}{r^{2}}[/tex] (2)
Since it is a circular motion, the centripetal acceleration can be used:
[tex]a = \frac{v^{2}}{r}[/tex] (3)
Then, equation 3 can be replaced in equation 2:
[tex]m\frac{v^{2}}{r} = G\frac{M\cdot m}{r^{2}}[/tex] (4)
In this case, m is the satellite's mass and M is the Earth mass. Therefore, v can be isolated from equation 4:
[tex]v^{2} = G\frac{M\cdot m r}{mr^{2}}[/tex]
[tex]v^{2} =\frac{G M}{r}[/tex]
[tex]v = \sqrt{\frac{G M}{r}}[/tex]
Where G is the gravitational constant, M is the mass of the Earth and r is the orbital radius of the satellite.
Notice, how the speed of the satellite does not depend in its mass, only in the Earth mass and its orbital radius.
The launch speed of a satellite determines the shape of its orbit around Earth.
Depending on the launch speed the satellite can reach a lower or higher height above the surface of the Earth and, therefore, its orbital radius will be bigger or smaller according with that height.
Remember that the orbital radius for the satellite will be the sum of the Earth radius and the height above the surface.
Key term:
Geosynchronous satellite: It is a satellite with the same orbital period as Earth rotation period (24 hours).
