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Time period and energy of a satellite is considered one the most difficult concept.
32 Questions around this concept.
A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has a radius R (R<<L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its center. If the period of the star is T and its distance from the Galaxies axis is r, then :
What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R ?
The time period of an earth satellite in circular orbit is independent of :
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A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity represents:
The time period of satellite-
It is the time taken by satellite to go once around the earth.
And the time period (T) of the satellite is given by
Where
radius of orbit
Time period
Mass of planet
i.e., h<<<R,
then
or
Density of planet
Time period
Gravitational constant
for earth
For a satellite, the time interval between the two consecutive appearances overhead
If a satellite in the equilateral planes moves from west to east Angular velocity of the satellite with respect to an observer on earth will be
Satellite angular velocity
earth angular velocity
So
if
means satellite will appear stationary relative to earth.
Height of Satellite-
Putting the value of time period in the above formula we can calculate the height of the satellite from the surface of the earth.
The energy of Satellite-
When a satellite revolves around a planet in its orbit, it possesses both kinetic energy (due to orbital motion) and potential energy (due to its position against the gravitational pull of earth).
And these energies are given by
Where
And
Where
In this Total Energy
Where
The minimum energy required to remove the satellite from its orbit to infinity is called Binding Energy.
And It is given by
where
When the satellite is transferred to a higher orbit i.e as shown in the figure.
Where
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