Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
\[T=(\frac{g R^2 T^2}{4 \pi^2} )^\frac{1}{3} - R\]
\[T = \frac{4 \pi^2 (h + R )^3}{g R^2}\]
\[ = \frac{4 \times 3 . {14}^2 \times (36000 + 6400 )^3 \times {10}^9}{9 . 8 \times (6400 \times {10}^3 )^2}\]
= 24.097 Hr
Which implies that it is a geostationary satellite with a time period = 24 Hrs.
APPEARS IN
संबंधित प्रश्न
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
A body stretches a spring by a particular length at the earth's surface at the equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.
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.
Find the minimum colatitude which can directly receive a signal from a geostationary satellite.
Derive an expression for the critical velocity of a satellite.
Answer the following question in detail.
Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?
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
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.
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 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 ____________.
Reason of weightlessness in a satellite is ____________.
The ratio of energy required to raise a satellite to a height `(2R)/3` above earth's surface to that required to put it into the orbit at the same height is ______.
R = radius of the earth
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 ______.
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.
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 ______.
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 ______.
Two satellites of same mass are orbiting round the earth at heights of r1 and r2 from the centre of earth. Their potential energies are in the ratio of ______.
What is the typical altitude range for a polar satellite's orbit?
