The semi-major axis of the orbit of Saturn is approximately nine times that of Earth. The time period of revolution of Saturn is approximately equal to
81 years
27 years
729 years
B.
27 years
Given,
Semi-major axis of the orbit of Saturn = 9 rE
where, rE = semi major axis of earth
According to Kepler's law,
T2 ∝ r3
Let the time period of revolution of saturn around the sun is TS
A comet orbits around the Sun in an elliptical orbit. Which of the following quantities remains constant during the course of its motion ?
Linear velocity
Angular velocity
Angular momentum
Kinetic energy
C.
Angular momentum
When comet orbits around Sun in an elliptical orbit, it is under action of a central force and its angular momentum remains constant.
Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius R around the sun will be proportional to
Rn
Rn
A.
The necessary centripetal force required for a planet to move round the sun = gravitational force exerted on it
Consider a satellite moving in a circular orbit around Earth. If K and V denote its kinetic energy and potential energy respectively, then (Choose the convention, where V = 0 as r → ∞)
K = V
K = 2V
V = − 2K
K = − 2V
C.
V = − 2K
When a satellite moves in a circular orbit around the earth its
(i) Potential Energy,
(ii) Kinetic Energy,
Assuming the mass of Earth to be ten times the mass of Mars, its radius to be twice the radius of Mars and the acceleration due to gravity on the surface of Earth is 10 m/s2. Then the acceleration due to gravity on the surface of Mars is given by
0.2 m/s2
0.4 m/s2
2 m/s2
4 m/s2
D.
4 m/s2
Given, mass of earth = 10 x Mm
where, Mm = Mass of mars
Radius of earth = 2 Rm
where, Rm = radius of mass
and
Let gravity on the surface of mass is gm