Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Consider the diagram, where a satellite of mass m, moves around the earth in a circular orbit of radius R.
The orbital speed of the satellite orbiting the earth is given by `v_0 = sqrt((GM)/R)` where M and R are the mass and radius of the earth.
a. ∴ KE of a satellite of mass m,
= `1/2 mv_0^2 `
= `1/2m xx (GM)/R`
∴ `E_k ∝ 1/R`
It means the KE decrease exponentially with radius. The graph for KE versus orbital radius R is shown in figure.
b. Potential energy of a satellite `E-p = - (GMn)/R`
`E_p ∝ 1/R`
The graph for PE versus orbital radius R is shown in figure.
c. Total energy of the satellite `E = E_k + E_p`
= `(Gmm)/(2R) - (GMm)/R`
= `- (GMm)/(2R)`
The graph for total energy versus orbital radius R is shown in the figure.
APPEARS IN
संबंधित प्रश्न
A spacecraft consumes more fuel in going from the earth to the moon than it takes for a return trip. Comment on this statement.
The time period of an earth-satellite in circular orbit is independent of
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.
A satellite of mass 1000 kg is supposed to orbit the earth at a height of 2000 km above the earth's surface. Find (a) its speed in the orbit, (b) is kinetic energy, (c) the potential energy of the earth-satellite system and (d) its time period. Mass of the earth = 6 × 1024kg.
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.
Find the minimum colatitude which can directly receive a signal from a geostationary satellite.
Answer the following question.
What do you mean by geostationary satellite?
Derive an expression for the binding energy of a body at rest on the Earth’s surface of a 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.
A planet has mass 6.4 × 1024 kg and radius 3.4 × 106 m. Calculate the energy required to remove an object of mass 800 kg from the surface of the planet to infinity.
Reason of weightlessness in a satellite is ____________.
Assuming that the earth is revolving around the sun in circular orbit of radius 'R', the angular momentum is directly proportional to rn. The value of 'n' is ______.
Out of following, the only correct statement about satellites is ____________.
A satellite is revolving in a circular orbit around the earth has total energy 'E'. Its potential energy in that orbit is ______.
A satellite is revolving in a circular orbit at a height 'h' above the surface of the earth of radius 'R'. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between 'h' and 'R' is ______.
What is the approximate period of revolution for the Moon, Earth's only natural satellite?
Which of the following is an example of a communication (geostationary) satellite launched by India?
