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.
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.
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.
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) Find the radius of the circular orbit of a satellite moving with an angular speed equal to the angular speed of earth's rotation. (b) If the satellite is directly above the North Pole at some instant, find the time it takes to come over the equatorial plane. Mass of the earth = 6 × 1024 kg.
Answer the following question in detail.
State any four applications of a communication satellite.
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.
The kinetic energy of a revolving satellite (mass m) at a height equal to thrice the radius of the earth (R) is ______.
There is no atmosphere on moon because ____________.
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 ______.
