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
Suppose there existed a planet that went around the sun twice as fast as the earth.What would be its orbital size as compared to that 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?
Two satellites going in equatorial plane have almost same radii. As seen from the earth one moves from east one to west and the other from west to east. Will they have the same time period as seen from the earth? If not which one will have less time period?
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.
At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?
A Mars satellite moving in an orbit of radius 9.4 × 103 km takes 27540 s to complete one revolution. Calculate the mass of Mars.
(a) Find the radius of the circular orbit of a satellite moving with an angular speed equal to the angular speed of earth's rotation. (b) If the satellite is directly above the North Pole at some instant, find the time it takes to come over the equatorial plane. Mass of the earth = 6 × 1024 kg.
Find the minimum colatitude which can directly receive a signal from a geostationary satellite.
Answer the following question.
Define the binding energy of a satellite.
Answer the following question.
What is periodic time of a geostationary satellite?
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
Answer the following question in detail.
Why an astronaut in an orbiting satellite has a feeling of weightlessness?
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]
The kinetic energy of a revolving satellite (mass m) at a height equal to thrice the radius of the earth (R) is ______.
What is the minimum energy required to launch a satellite of mass 'm' from the surface of the earth of mass 'M' and radius 'R' at an altitude 2R?
Two satellites of masses m and 4m orbit the earth in circular orbits of radii 8r and r respectively. The ratio of their orbital speeds 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 ____________.
Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because ______.
Is it possibe for a body to have inertia but no weight?
Show the nature of the following graph for a satellite orbiting the earth.
- KE vs orbital radius R
- PE vs orbital radius R
- TE vs orbital radius R.
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]
The ratio of binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height h above the earth's surface is ______ (R = radius of the earth).
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?
Which of the following is an example of a communication (geostationary) satellite launched by India?
