Advertisements
Advertisements
Question
Answer the following question in detail.
Obtain an expression for the binding energy of a satellite revolving around the Earth at a certain altitude.
Advertisements
Solution
An expression for the binding energy of satellite revolving in a circular orbit around the Earth:
- Consider a satellite of mass m revolving at height h above the surface of the Earth in a circular orbit. It possesses potential energy as well as kinetic energy.
- Let M be the mass of the Earth, R be the Radius of the Earth, vc be the critical velocity of satellite, r = (R + h) be the radius of the orbit.
- Kinetic energy of satellite = `1/2 "mv"_"c"^2 = 1/2 "GMm"/"r"`
- The gravitational potential at a distance r from the centre of the Earth is `- "GM"/"r"`
∴ The potential energy of a satellite
= Gravitational potential × mass of a satellite
= `- "GMm"/"r"` - The total energy of satellite is given as
T.E. = K.E. + P.E.
`= 1/2 "GMm"/"r" - "GMm"/"r" = - 1/2 "GMm"/"r"` - The total energy of a circularly orbiting satellite is negative. The negative sign indicates that the satellite is bound to the Earth, due to the gravitational force of attraction. For the satellite to be free from the Earth’s gravitational influence its total energy should become zero or positive.
- Hence the minimum energy to be supplied to unbind the satellite is `+ 1/2 "GMm"/"r"`. This is the binding energy of a satellite.
APPEARS IN
RELATED QUESTIONS
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?
A nut becomes loose and gets detached from a satellite revolving around the earth. Will it land on the earth? If yes, where will it land? If no, how can an astronaut make it land on the earth?
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?
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.
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.
Answer the following question.
Define the binding energy of a satellite.
Answer the following question.
What is periodic time of a geostationary satellite?
State the conditions for various possible orbits of satellite depending upon the horizontal/tangential speed of projection.
Answer the following question in detail.
State any four applications of a communication satellite.
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 value of acceleration due to gravity on the surface of Mars if the radius of Mars = 3.4 × 103 km and its mass is 6.4 × 1023 kg.
A body weighs 5.6 kg wt on the surface of the Earth. How much will be its weight on a planet whose mass is 7 times the mass of the Earth and radius twice that of the Earth’s radius?
An aircraft is moving with uniform velocity 150 m/s in the space. If all the forces acting on it are balanced, then it will ______.
Two satellites of masses m1 and m2 (m1 > m2) are revolving round the earth in circular orbit of radii r1 and r2 (r1 > r2) respectively. Which of the following statements is true regarding their speeds v1 and v2?
Reason of weightlessness in a satellite 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 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)
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 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)
What is the typical altitude range for a polar satellite's orbit?
Artificial satellites are launched for all the following purposes EXCEPT ______.
A satellite is revolving round the earth with orbital speed ‘V0’. If it stops suddenly, the speed with which it will strike the surface of the earth would be: (V = escape velocity of a particle on earth’s surface)
