Radius of the earth is 6400 km. The radius of the orbit of a stationary satellite is abouta)36000 kmb)29600 kmc)42400 kmd)infinityCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

For geostationary satellite,
Time period = 24 hrs, Height=35800km, Escape velocity= 3.1 km/s.These are called stationary satellite because such satellites appear stationary due to zero relative velocity w. r. t. earth.

Answer

For a circular orbit with radius r, a centripetal force is required to maintain the orbit, described by:
F = m r w2
(m is the mass of the object, w is the angular velocity, typically measured in radians per second (radians are a unit of angle, a full circle corresponds to 2 pi radians)).
In the Earth-satellite system, this force is provided by gravity, which is given by:
F = G M m / r2
(G is the Newtonian constant of gravity, M the mass of the Earth) Equating the two yields:
m r w2 = G M m / r2
the m terms cancel, shuffle some of the others:
r3 = G M / w2
Fill in the values for G, M and w and you can compute the value of r, which should give you an outcome just over 42000 km. If you subtract the radius of the Earth (i.e.,6400) you'll find the value 35600. Option A i.e., 3600 is nearest to this value. Hence it is the correct answer.

Answer

The radius of the earth is 6400 km. The radius of the orbit of a stationary satellite is about 36000 km.

Explanation:
To understand why the radius of the orbit of a stationary satellite is about 36000 km, we need to consider the concept of geostationary satellites.

Geostationary Satellites:
A geostationary satellite is a satellite that orbits the Earth at the same rate as the Earth rotates on its axis. This means that the satellite appears to be stationary from the perspective of an observer on the ground. Geostationary satellites are commonly used for communication purposes, such as television broadcasting and telephone services.

Orbit of a Geostationary Satellite:
The orbit of a geostationary satellite is a circular orbit that is directly above the equator. From the perspective of an observer on the ground, the satellite appears to be stationary because it completes one orbit in the same amount of time it takes for the Earth to rotate once on its axis (approximately 24 hours).

Calculating the Radius of the Orbit:
To calculate the radius of the orbit of a geostationary satellite, we need to consider the gravitational force between the Earth and the satellite. The gravitational force provides the necessary centripetal force to keep the satellite in orbit.

The centripetal force can be calculated using the following equation:
Fc = (mv^2) / r

Where Fc is the centripetal force, m is the mass of the satellite, v is the orbital velocity, and r is the radius of the orbit.

The orbital velocity of a geostationary satellite can be calculated using the following equation:
v = √(GM / r)

Where G is the gravitational constant and M is the mass of the Earth.

Substituting the value of v in the centripetal force equation, we get:
Fc = (m * GM) / r^2

For the satellite to remain stationary, the centripetal force must be equal to the gravitational force between the Earth and the satellite:
Fc = G * (m * M) / r^2 = (m * GM) / r^2

Simplifying this equation, we get:
G * M / r^2 = G * M / R^2

Where R is the radius of the Earth.

Solving for r, we get:
r = R

Therefore, the radius of the orbit of a geostationary satellite is equal to the radius of the Earth, which is 6400 km.

Answer

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