Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
The time period of revolution of the satellite around a planet in terms of the radius of the planet and radius of the orbit of the satellite is given by \[T = 2\pi\sqrt{\frac{R_2^2}{g R_1^2}}\] , where g is the acceleration due to gravity at the surface of the planet.
\[\text { Now }, T^2 = 4 \pi^2 \frac{R_2^2}{g R_1^2}\]
\[ \Rightarrow g = \frac{4 \pi^2}{T^2}\frac{R_2^2}{R_1^2}\]
∴ Acceleration due to gravity of the planet = \[\frac{4 \pi^2}{T^2}\frac{R_2^2}{R_1^2}\]
APPEARS IN
संबंधित प्रश्न
A spacecraft consumes more fuel in going from the earth to the moon than it takes for a return trip. Comment on this statement.
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 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.
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.
Define the binding energy of a satellite.
Answer the following question.
Why is a minimum two-stage rocket necessary for launching of a satellite?
Derive an expression for the critical velocity of a satellite.
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.
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.
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?
Assuming that the earth is revolving around the sun in circular orbit of radius 'R', the angular momentum is directly proportional to rn. The value of 'n' is ______.
The period of revolution of a satellite is ______.
Show the nature of the following graph for a satellite orbiting the earth.
- KE vs orbital radius R
- PE vs orbital radius R
- TE vs orbital radius R.
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)
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)
