Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
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 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.
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?
The radius of a planet is R1 and a satellite revolves round it in a circle of radius R2. The time period of revolution is T. Find the acceleration due to the gravitation of the planet at its surface.
Choose the correct option.
The binding energy of a satellite revolving around the planet in a circular orbit is 3 × 109 J. It's kinetic energy is ______.
Answer the following question.
What do you mean by geostationary satellite?
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?
Derive an expression for the critical velocity of a satellite.
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
Calculate the kinetic energy, potential energy, total energy and binding energy of an artificial satellite of mass 2000 kg orbiting at a height of 3600 km above the surface of the Earth.
Given: G = 6.67 × 10-11 Nm2/kg2
R = 6400 km, M = 6 × 1024 kg
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.
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 ______
There is no atmosphere on moon because ____________.
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 ______.
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 ______.
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 ____________.
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 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 ______.
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 ______.
What is the approximate period of revolution for the Moon, Earth's only natural satellite?
What is the typical altitude range for a polar satellite's orbit?
Artificial satellites are launched for all the following purposes EXCEPT ______.
Which of the following is the only natural satellite of the Earth?
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)
