Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
A nut becomes loose and gets detached from a satellite revolving around the earth. Will it land on the earth? If yes, where will it land? If no, how can an astronaut make it land on the earth?
Two satellites going in equatorial plane have almost same radii. As seen from the earth one moves from east one to west and the other from west to east. Will they have the same time period as seen from the earth? If not which one will have less time period?
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.
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 Mars satellite moving in an orbit of radius 9.4 × 103 km takes 27540 s to complete one revolution. Calculate the mass of Mars.
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.
Why is a minimum two-stage rocket necessary for launching of a satellite?
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.
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.
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 ______
Two satellites of masses m1 and m2 (m1 > m2) are revolving round the earth in circular orbit of radii r1 and r2 (r1 > r2) respectively. Which of the following statements is true regarding their speeds v1 and v2?
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 ______.
A satellite of mass 'm', revolving round the earth of radius 'r' has kinetic energy (E). Its angular momentum is ______.
A satellite of mass 'm' is revolving around the earth of mass 'M' in an orbit of radius 'r' with constant angular velocity 'ω'. The angular momentum of the satellite is ______.
(G =gravitational constant)
Is it possibe for a body to have inertia but no weight?
Which application is mainly associated with polar satellites?
