We are to show that the given parametric curve is a circle.
The trajectory of a circle with a radius r will satisfy the following relationship:
(with (x_c,y_c) being the center point)
We are given the x and y in a parametric form which can be further rewritten (using properties of sin/cos):
Squaring and adding both gives:
The last expression shows that the given parametric curve is a circle with the center (0,0) and radius A.
Answer:
Explanation:
We know that , for an object to remain in circular motion , a force towards centre is required which is called centripetal force. In the circular motion of
satellites around planet , this force is provided by the gravitational attraction between satellite and planet.
If M be the mass of planet and m be the mass of satellite, G be gravitational constant and R be the distance between planet and satellite or R be the radius of orbit
Gravitational force = G Mm / R²
If v be the velocity with which satellite is orbiting
centripetal force
= m v² /R
Centripetal force = gravitational attraction
m v² /R = G Mm / R²
v =
Time period = time the satellite takes to make one rotation
= distance / orbital velocity
= 2πR/ v
=
T =