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
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?
Is it necessary for the plane of the orbit of a satellite to pass through the centre of 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 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.
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.
What is a critical velocity?
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 body weighs 5.6 kg wt on the surface of the Earth. How much will be its weight on a planet whose mass is 7 times the mass of the Earth and radius twice that of the Earth’s radius?
The ratio of energy required to raise a satellite of mass 'm' to a height 'h' above the earth's surface of that required to put it into the orbit at same height is ______.
[R = radius of the earth]
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' 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?
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?
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 ______.
What is the typical altitude range for a polar satellite's orbit?
Artificial satellites are launched for all the following purposes EXCEPT ______.
Which application is mainly associated with polar satellites?
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)
