Respuesta :
Answer:
A satellite's motion is independent of its mass.
The launch speed of a satellite determines the shape of its orbit around Earth.
Explanation:
When a satellite is launched into the space, the centripetal force required to keep the satellite in its orbit is provided by the gravitational force of the Earth.
That means, [tex]Fc=Fg[/tex] ........ (1), where [tex]Fc[/tex] is centripetal force and [tex]Fg[/tex] is gravitational force.
Therefore, [tex]\frac{mv^{2}} {r}=G\frac{Mm}{r^{2} }[/tex] .......... (2), where [tex]m[/tex] is the mass of the satellite, [tex]M[/tex] is the mass of the Earth, [tex]r[/tex] is the distance of the satellite from the center of the Earth (radius of the orbit or orbital radius), [tex]v[/tex] is the orbital velocity of the satellite and [tex]G[/tex] is the universal gravitational constant (6.673 x 10-11 Nm²/kg²).
From equation (2), [tex]v^{2} =\frac{GM}{r}[/tex] and
[tex]v=\sqrt{\frac{GM} {r}}[/tex] ........... (3)
From equation (3), it is clear that the satellite's motion i.e., its orbital velocity is independent of its mass and depends on the mass of the Earth, the distance of the satellite from the center of the Earth (orbital radius).
A satellite that has the same orbital period as that of the Earth (moves around the earth every 23 hours 56 minutes and 4 seconds) is known as a geosynchronous satellite. The position of such satellites appears stationary with respect to a ground station since it is in a geosynchronous orbit.
The satellites are projectiles that are acted upon by the gravitational force. A satellite that launched with sufficient speed would orbit the earth. If the launch speed of the satellite is very small, it will fall into the earth. If it is launched with sufficient speed, the satellite will stay above the earth and orbit in a circular path. If the launch speed of the satellite is very high, it will orbit the earth in an elliptical path.
