Advertisements
Advertisements
Question
Derive an expression for the critical velocity of a satellite.
Advertisements
Solution
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
RELATED QUESTIONS
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 satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the earth. The escape speed from the earth is ve. Its speed with respect to the satellite
Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.
Answer the following question.
Why is a minimum two-stage rocket necessary for launching of a satellite?
Answer the following question in detail.
State any four applications of a communication satellite.
Answer the following question in detail.
What is a critical velocity?
Answer the following question in detail.
Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?
Describe how an artificial satellite using a two-stage rocket is launched in an orbit around the Earth.
Answer the following question in detail.
Two satellites A and B are revolving round a planet. Their periods of revolution are 1 hour and 8 hour respectively. The radius of orbit of satellite B is 4 × 104 km. Find radius of orbit of satellite A.
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 ratio of energy required to raise a satellite of mass 'm' to a height 'h' above the earth's surface of that required to put it into the orbit at same height is ______.
[R = radius of the earth]
Which of the following statements is CORRECT in respect of a geostationary satellite?
There is no atmosphere on moon because ____________.
Two satellites A and B go round a planet P in circular orbits having radii 4R and R respectively. If the speed of the satellite A is 3v, the speed of satellite B is ____________.
A geostationary satellite is orbiting the earth at the height of 6R above the surface of earth. R being radius of earth. The time period of another satellite at a height of 2.5 R from the surface of earth 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 ____________.
Out of following, the only correct statement about satellites is ____________.
A satellite of mass 'm' is revolving around the earth of mass 'M' in an orbit of radius 'r' with constant angular velocity 'ω'. The angular momentum of the satellite is ______.
(G =gravitational constant)
A satellite is to revolve round the earth in a circle of radius 9600 km. The speed with which this satellite be projected into an orbit, will be ______.
A satellite is revolving in a circular orbit around the earth has total energy 'E'. Its potential energy in that orbit is ______.
The period of revolution of a satellite is ______.
Is it possibe for a body to have inertia but no weight?
Two satellites are orbiting around the earth in circular orbits of same radius. One of them is 10 times greater in mass than the other. Their period of revolutions are in the ratio ______.
Which of the following is an example of a communication (geostationary) satellite launched by India?
Which application is mainly associated with polar satellites?
