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?
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
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.
(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.
Answer the following question.
Why is a minimum two-stage rocket necessary for launching of a satellite?
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
Describe how an artificial satellite using a two-stage rocket is launched in an orbit around the Earth.
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.
There is no atmosphere on moon because ____________.
An aircraft is moving with uniform velocity 150 m/s in the space. If all the forces acting on it are balanced, then it will ______.
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 ____________.
Out of following, the only correct statement about satellites 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 ______.
Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because ______.
Is it possibe for a body to have inertia but no weight?
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 ______.
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?
