An earth satellite is moved from one stable circular orbit to another ...
Let’s see the formulae for each quantity given there,
Gravitational potential energy =−GMm/r
angular velocity =(GM/r3)0.5
linear orbital velocity =(GM/r)0.5
centripetal acceleration =GM/ r2
We can observe that, the quantities in the options B,C,D are all indirectly proportional to r
i.e. ω, v, a α(1/rn) where n is a distinct positive integer in each quantity.
So, with increase in r all these quantities decrease.
Now, (-potential energy) α(1/r) i.e. negative of potential energy decreases with increase in r. Therefore, potential increases with increase in orbital radius.
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An earth satellite is moved from one stable circular orbit to another ...
Gravitational Potential Energy:
When the earth satellite is moved from one stable circular orbit to another larger and stable circular orbit, its gravitational potential energy increases.
Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. It is given by the equation:
PE = -GMm/r
where PE is the gravitational potential energy, G is the gravitational constant, M is the mass of the earth, m is the mass of the satellite, and r is the distance between the center of the earth and the satellite.
As the satellite is moved to a larger orbit, the distance between the center of the earth and the satellite increases. Since the gravitational potential energy is inversely proportional to the distance, an increase in distance leads to an increase in gravitational potential energy.
Angular Velocity:
The angular velocity of the satellite remains constant when it is moved from one stable circular orbit to another larger and stable circular orbit.
Angular velocity is the rate at which an object rotates around a fixed axis. In a stable circular orbit, the satellite moves in a circular path at a constant speed. The angular velocity is given by the equation:
ω = v/r
where ω is the angular velocity, v is the linear orbital velocity, and r is the radius of the orbit.
As the satellite is moved to a larger orbit, the radius of the orbit increases. However, the linear orbital velocity also increases in order to maintain a stable circular orbit. The ratio of the linear orbital velocity to the radius remains constant, resulting in a constant angular velocity.
Linear Orbital Velocity:
The linear orbital velocity of the satellite increases when it is moved from one stable circular orbit to another larger and stable circular orbit.
Linear orbital velocity is the speed at which an object moves around an orbit. It is given by the equation:
v = √(GM/r)
where v is the linear orbital velocity, G is the gravitational constant, M is the mass of the earth, and r is the radius of the orbit.
As the satellite is moved to a larger orbit, the radius of the orbit increases. Since the linear orbital velocity is directly proportional to the square root of the radius, an increase in radius leads to an increase in linear orbital velocity.
Centripetal Acceleration:
The centripetal acceleration of the satellite remains constant when it is moved from one stable circular orbit to another larger and stable circular orbit.
Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is given by the equation:
a = v^2/r
where a is the centripetal acceleration, v is the linear orbital velocity, and r is the radius of the orbit.
As the satellite is moved to a larger orbit, the radius of the orbit increases. However, the linear orbital velocity also increases in order to maintain a stable circular orbit. The ratio of the square of the linear orbital velocity to the radius remains constant, resulting in a constant centripetal acceleration.
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