Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
The time period of an earth-satellite in circular orbit is independent of
A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the earth. The escape speed from the earth is ve. Its speed with respect to the satellite
Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.
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.
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.
What is periodic time of a geostationary satellite?
State the conditions for various possible orbits of satellite depending upon the horizontal/tangential speed of projection.
Derive an expression for the critical velocity of a satellite.
Answer the following question in detail.
State any four applications of a communication satellite.
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
Answer the following question in detail.
Why an astronaut in an orbiting satellite has a feeling of weightlessness?
Answer the following question in detail.
What is a critical velocity?
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 acceleration due to gravity on the surface of Mars if the radius of Mars = 3.4 × 103 km and its mass is 6.4 × 1023 kg.
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 ____________.
A geostationary satellite is orbiting the earth at the height of 6R above the surface of earth. R being radius of earth. The time period of another satellite at a height of 2.5 R from the surface of earth is ____________.
In the case of earth, mean radius is 'R', acceleration due to gravity on the surface is 'g', angular speed about its own axis is 'ω'. What will be the radius of the orbit of a geostationary satellite?
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 ______.
A satellite is revolving in a circular orbit around the earth has total energy 'E'. Its potential energy in that orbit is ______.
The period of revolution of a satellite is ______.
Is it possibe for a body to have inertia but no weight?
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 around a planet in a circular orbit close to its surface and ρ is the mean density and R is the radius of the planet, then the period of ______.
(G = universal constant of gravitation)
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 ______.
A satellite is revolving round the earth with orbital speed ‘V0’. If it stops suddenly, the speed with which it will strike the surface of the earth would be: (V = escape velocity of a particle on earth’s surface)
