Advertisements
Advertisements
प्रश्न
Derive an expression for the critical velocity of a satellite.
Advertisements
उत्तर
The expression for critical velocity:
- Consider a satellite of mass m revolving round the Earth at height h above its surface. Let M be the mass of the Earth and R be its radius.
- If the satellite is moving in a circular orbit of the radius (R + h) = r, its speed must be equal to the magnitude of critical velocity vc.
- The centripetal force necessary for the circular motion of a satellite is provided by the gravitational force exerted by the satellite on the Earth.
∴ Centripetal force = Gravitational force
∴ `"mv"_"c"^2/"r" = "GMm"/"r"^2`
∴ `"v"_"c"^2 = "GM"/"r"`
∴ `"v"_"c" = sqrt("GM"/"r")`
∴ `"v"_"c" = sqrt("GM"/("R+h")) = sqrt("g"_"h" ("R + h"))`
This is the expression for critical speed at the orbit of radius (R + h). - The critical speed of a satellite is independent of the mass of the satellite. It depends upon the mass of the Earth and the height at which the satellite is the revolving or gravitational acceleration at that altitude.
APPEARS IN
संबंधित प्रश्न
Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
As the earth rotates about its axis, a person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. Why does he/she not feel weightless as a satellite passenger does?
A spacecraft consumes more fuel in going from the earth to the moon than it takes for a return trip. Comment on this statement.
The time period of an earth-satellite in circular orbit is independent of
A body stretches a spring by a particular length at the earth's surface at the equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.
A satellite of mass 1000 kg is supposed to orbit the earth at a height of 2000 km above the earth's surface. Find (a) its speed in the orbit, (b) is kinetic energy, (c) the potential energy of the earth-satellite system and (d) its time period. Mass of the earth = 6 × 1024kg.
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?
Answer the following question.
What is periodic time of a geostationary satellite?
Answer the following question.
Why is a minimum two-stage rocket necessary for launching of a satellite?
State the conditions for various possible orbits of satellite depending upon the horizontal/tangential speed of projection.
Answer the following question in detail.
Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?
Solve the following problem.
Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth’s surface.
(ME = 5.98 × 1024 kg, R = 6.4 × 106 m)
Solve the following problem.
Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6400 km, and the acceleration due to gravity on the surface = 9.8 m/s2.
The kinetic energy of a revolving satellite (mass m) at a height equal to thrice the radius of the earth (R) is ______.
If a body weighing 40 kg is taken inside the earth to a depth to radius of the earth, then `1/8`th the weight of the body at that point is ______.
If a body weighing 40 kg-wt is taken inside the earth to a depth to `1/2` th radius of the earth, then the weight of the body at that point is ____________.
A satellite of mass 'm', revolving round the earth of radius 'r' has kinetic energy (E). Its angular momentum is ______.
A geostationary satellite is orbiting the earth at a height 6R above the surface of the earth, where R is the radius of the earth. This time period of another satellite at a height (2.5 R) from the surface of the earth is ______.
Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because ______.
An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. If the satellite is stopped in its orbit and allowed to fall freely onto the earth, the speed with which it hits the surface ______ km/s.
[g = 9.8 ms-2 and Re = 6400 km]
A satellite revolves around a planet very close to its surface. By what maximum factor can its kinetic energy be increased suddenly, such that it revolves in orbit in the same way?
A satellite is revolving around a planet in a circular orbit close to its surface and ρ is the mean density and R is the radius of the planet, then the period of ______.
(G = universal constant of gravitation)
Two satellites of same mass are orbiting round the earth at heights of r1 and r2 from the centre of earth. Their potential energies are in the ratio of ______.
Artificial satellites are launched for all the following purposes EXCEPT ______.
Which of the following is the only natural satellite of the Earth?
