Home
Class 11
PHYSICS
Show the nature of the following graph f...

Show the nature of the following graph for a satellite orbiting the earth.
(a) KE versus orbital radius R
(b) PE versus orbital radius R
(b) TE versus orbital radius R 

Text Solution

Verified by Experts

`implies` consider the diagram, where a satellite of mass m, moving around the earth in a circular orbit of radius R.

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,
`K=1/2 mv_0^2 =1/2 mxx(GM)/R`
`:. K prop 1/R`

It means the KE decreases exponentially with radius. The graph for KE versus orbital radius R is shown in figure
(b) Potential energy of a satellite.
P.E. `=-(GMm)/R`
`P.E. prop -1/R`

The graph for PE versus orbital radius R is shown in figure
(c) Total energy of the satellite
`E = K +U = (GMm)/(2R) - (GMm)/R`
`=- (GMm)/(2R)`

The graph for total energy versus orbital radius R is shown in figure
Note : We should keep in mind that Potential energy (PE) and Kinetic Energy (KE) of the satellite-earth system is always negative.
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    KUMAR PRAKASHAN|Exercise Section - D NCERT Exemplar Solutions (Long Answer Type Question )|5 Videos

  • GRAVITATION

    KUMAR PRAKASHAN|Exercise Section - E Multiple Choice Questions (MCQs)|73 Videos

  • GRAVITATION

    KUMAR PRAKASHAN|Exercise Section - D NCERT Exemplar Solutions (Very Short Answer Type Question )|11 Videos

  • LAW OF MOTION

    KUMAR PRAKASHAN|Exercise (QUESTION PAPER) SECTION-D|1 Videos

Similar Questions

Explore conceptually related problems

A satellite of earth of mass 'm' is taken from orbital radius 2R to 3R, then minimum work done is :-

The period of revolution of a satellite in an orbit becomes 8 times then what will be its radius of orbit?

A satellite is moving around the earth's with speed v in a circular orbit of radius r . If the orbit radius is decreases by 1% , its speed will

An astronaut of mass m is working on a satellite orbitting the earth at a distance h from the earth's surface the radius fo the earth is R while its mass is M the gravitational pull F_(G) on the astronaut is

It is known that the time of revolution T of a satellite around the earth depends on the universal gravitational constant G, the mass of the earth M, and the radius of the circular orbit R. Obtain an expression for T using dimensional analysis.

These both situation is truely shown in graph (D) A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g_0 , the value of acceleration due to gravity at the earth's surface, is

in which of the following system will the radius of the second orbit be minimum ?

Length of a year on a planet is the duration in which it completes one revolution around the sun. Assume path of the planet known as orbit to be circular with sun at the centre. The length T of a year of a planet orbiting around the sun in circular orbit depends on universal gravitational constant G, mass m_(s) of the sun and radius r of the orbit. if TpropG^(a)m_(s)^(b)r^(c) find value of a+b+2c.

In Bohr’s model, the atomic radius of the first orbit is r. Then, the radius of the third orbit is

In which of the following system will the radius of the first orbit (n = 1) be minimum ?