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
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?
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?
Find the minimum colatitude which can directly receive a signal from a geostationary satellite.
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.
Define the binding energy of a satellite.
Answer the following question.
Why is a minimum two-stage rocket necessary for launching of a 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.
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
Derive an expression for the binding energy of a body at rest on the Earth’s surface of a satellite.
Answer the following question in detail.
Obtain an expression for the binding energy of a satellite revolving around the Earth at a certain altitude.
Answer the following question in detail.
What is a critical velocity?
Describe how an artificial satellite using a two-stage rocket is launched in an orbit around the Earth.
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.
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)
Which of the following statements is CORRECT in respect of a geostationary satellite?
What is the minimum energy required to launch a satellite of mass 'm' from the surface of the earth of mass 'M' and radius 'R' at an altitude 2R?
If a body weighing 40 kg-wt is taken inside the earth to a depth to `1/2` th radius of the earth, then the weight of the body at that point 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?
The period of revolution of a satellite is ______.
The ratio of binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height h above the earth's surface is ______ (R = radius of the earth).
What is the typical altitude range for a polar satellite's orbit?
Which of the following is an example of a communication (geostationary) satellite launched by India?
Which of the following is the only natural satellite of the Earth?
Which application is mainly associated with polar satellites?
