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?
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?
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?
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 do you mean by geostationary satellite?
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.
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]
Which of the following statements is CORRECT in respect of a geostationary satellite?
Two satellites of masses m1 and m2 (m1 > m2) are revolving round the earth in circular orbit of radii r1 and r2 (r1 > r2) respectively. Which of the following statements is true regarding their speeds v1 and v2?
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 geostationary satellite is orbiting the earth at a height 6R above the surface of the earth, where R is the radius of the earth. This time period of another satellite at a height (2.5 R) from the surface of the earth is ______.
The period of revolution of a satellite is ______.
Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because ______.
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)
What is the typical altitude range for a polar satellite's orbit?
Which application is mainly associated with polar satellites?
