Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Time period of revolution of the satellite around the Mars is give by \[T = 2\pi\sqrt{\frac{r^3}{GM}}\] where M is the mass of the Mars and r is the distance of the satellite from the centre of the planet.
\[\text { Now }, 27540 = 2 \times 3 . 14\sqrt{\frac{\left( 9 . 4 \times {10}^3 \times {10}^3 \right)^3}{6 . 67 \times {10}^{- 11} \times M}}\]
\[ \Rightarrow \left( 27540 \right)^2 = \left( 6 . 28 \right)^2 \times \frac{\left( 9 . 4 \times {10}^5 \right)^3}{6 . 67 \times {10}^{- 11} \times M}\]
\[ \Rightarrow M = \frac{\left( 6 . 28 \right)^2 \times \left( 9 . 4 \right)^3 \times {10}^{18}}{6 . 67 \times {10}^{- 11} \times \left( 27540 \right)^2}\]
\[ \Rightarrow M = 6 . 5 \times {10}^{23} kg\]
APPEARS IN
संबंधित प्रश्न
Is it necessary for the plane of the orbit of a satellite to pass through the centre of 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?
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 satellite of mass 1000 kg is supposed to orbit the earth at a height of 2000 km above the earth's surface. Find (a) its speed in the orbit, (b) is kinetic energy, (c) the potential energy of the earth-satellite system and (d) its time period. Mass of the earth = 6 × 1024kg.
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?
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?
Answer the following question.
Why is a minimum two-stage rocket necessary for launching of a satellite?
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.
Why an astronaut in an orbiting satellite has a feeling of weightlessness?
Answer the following question in detail.
Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?
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 the universal gravitational constant from the given data. Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6400 km, and the acceleration due to gravity on the surface = 9.8 m/s2.
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 ____________.
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 ____________.
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)
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?
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]
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).
