Advertisements
Advertisements
Question
State the conditions for various possible orbits of satellite depending upon the horizontal/tangential speed of projection.
Solution
The path of the satellite depends upon the value of the horizontal speed of projection vh relative to critical velocity vc and escape velocity ve.
Case (I) vh < vc:
The orbit of the satellite is an ellipse with a point of projection as the apogee and Earth at one of the foci. During this elliptical path, if the satellite passes through the Earth’s atmosphere, it experiences a nonconservative force of air resistance. As a result, it loses energy and spirals down to the Earth.
Case (II) vh = vc:
The satellite moves in a stable circular orbit around the Earth.
Case (III) vc < vh < ve:
The satellite moves in an elliptical orbit around the Earth with the point of projection as perigee.
Case (IV) vh = ve:
The satellite travels along the parabolic path and never returns to the point of projection. Its speed will be zero at infinity.
Case (V) vh > ve:
The satellite escapes from the gravitational influence of Earth traversing a hyperbolic path.
APPEARS IN
RELATED QUESTIONS
Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?
Consider earth satellites in circular orbits. A geostationary satellite must be at a height of about 36000 km from the earth's surface. Will any satellite moving at this height be a geostationary satellite? Will any satellite moving at this height have a time period of 24 hours?
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?
The time period of an earth-satellite in circular orbit is independent of
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.
A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T0. (a) Find the speed of the ship due to rotation of the earth about its axis. (b) Find the difference between T0 and the earth's attraction on the bob. (c) If the ship sails at speed v, what is the tension in the string? Angular speed of earth's rotation is ω and radius of the earth is R.
Answer the following question in detail.
State any four applications of a communication satellite.
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
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]
Two satellites of a planet have periods of 32 days and 256 days. If the radius of the orbit of the former is R, the orbital radius of the Latter 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?
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 ______.
Reason of weightlessness in a satellite is ____________.
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 ____________.
A satellite of mass 'm', revolving round the earth of radius 'r' has kinetic energy (E). Its angular momentum 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 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 ______.
The period of revolution of a satellite is ______.
Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because ______.
