Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given: TA = 1 hour, TB = 8 hour, rB = 4 × 104 km
To find: Radius of orbit of satellite A (rA)
Formula: T = `2pi sqrt("r"^3/"GM")`
Calculation: From formula,
`"T"^2 = (4pi^2"r"^3)/"GM"`
∴ `"T"^2 prop "r"^3 ......(because (4pi^2"r"^3)/"GM" = "constant for a planet")`
∴ `(("T"_"A")/("T"_"B"))^2 = (("r"_"A")/("r"_"B"))^3`
∴ `(1/8)^2 = ("r"_"A"/(4 xx 10^4))^3`
∴ `"r"_"A"^3 = 1/(8)^2 xx (4 xx 10^4)^3`
∴ `"r"_"A"^3 = 10^12`
∴ `"r"_"A" = 1 xx 10^4` km
Radius of orbit of satellite A will be 1 × 104 km.
APPEARS IN
RELATED QUESTIONS
Suppose there existed a planet that went around the sun twice as fast as the earth.What would be its orbital size as compared to that of the earth?
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
As the earth rotates about its axis, a person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. Why does he/she not feel weightless as a satellite passenger does?
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?
Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.
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.
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.
Answer the following question.
Define the binding energy of a satellite.
Answer the following question.
What is periodic time of a geostationary satellite?
Derive an expression for the critical velocity of a satellite.
Answer the following question in detail.
State any four applications of a communication satellite.
Derive an expression for the binding energy of a body at rest on the Earth’s surface of a satellite.
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)
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.
Solve the following problem.
What is the gravitational potential due to the Earth at a point which is at a height of 2RE above the surface of the Earth?
(Mass of the Earth is 6 × 1024 kg, radius of the Earth = 6400 km and G = 6.67 × 10–11 N m2 kg–2)
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 ______
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 ______.
If the Earth-Sun distance is held constant and the mass of the Sun is doubled, then the period of revolution of the earth around the Sun will change to ____________.
Two satellites of masses m and 4m orbit the earth in circular orbits of radii 8r and r respectively. The ratio of their orbital speeds is ____________.
A satellite of mass 'm', revolving round the earth of radius 'r' has kinetic energy (E). Its angular momentum is ______.
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 ______.
An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. If the satellite is stopped in its orbit and allowed to fall freely onto the earth, the speed with which it hits the surface ______ km/s.
[g = 9.8 ms-2 and Re = 6400 km]
A satellite revolves around a planet very close to its surface. By what maximum factor can its kinetic energy be increased suddenly, such that it revolves in orbit in the same way?
What is the approximate period of revolution for the Moon, Earth's only natural satellite?
Artificial satellites are launched for all the following purposes EXCEPT ______.
