Gravitation Physics - Gravitation

According to Kepler's law of planetary motion, if T represents time period and r is orbital radius, then for two planets these are related as:

A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as on the surface of earth. It radius in terms of radius of earth R will be:

The orbital velocity of a satellite orbiting near the surface of the earth is given by:

An artificial earth satellite of mass m is circling round the earth in an orbit of radius R. If the mass of the earth is M, then the total energy of the satellite is:

Choose the correct alternative:
Acceleration due to gravity increases/ decreases with increasing depth (assume the earth to be a sphere of uniform density).

Choose the correct alternative:
Acceleration due to gravity increases/ decreases with increasing altitude.

Choose the correct alternative:
Acceleration due to gravity is independent of mass of the earth/ mass of the body.

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (a) linear speed, (b) angular speed, (c) angular momentum, (d) kinetic energy, (e) potential energy, (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

Choose the correct alternative:
If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/ potential energy.

Answer the following:
If you compare the gravitational force on the earth due to the sun to that due to the moon, you would find that the Sun’s pull is greater than the moon’s pull. (you can check this yourself using the data available in the succeeding exercises). However, the tidal effect of the moon’s pull is greater than the tidal effect of sun. Why?

Answer the following:
An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?

Answer the following:
You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?

An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?

Two stars each of one solar mass (= 2 × 10³⁰kg) are approaching each other for a head on collision. When they are a distance 10⁹km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 10⁴km. Assume the stars to remain undistorted until they collide. (Use the known value of G).

As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly 36,000km from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the earth = 6.0 × 10²⁴kg, radius = 6400km.

Two heavy spheres each of mass 100kg and radius 0.10m are placed 1.0m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 × 10⁸km.

A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun = 2 × 10³⁰kg, mass of the earth = 6×10²⁴kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 10¹¹m).

Read the passage given below and answer the following questions from 1 to 5.
Satellites in a circular orbits around the earth in the equatorial plane with T = 24 hours are called Geostationary Satellites. Clearly, since the earth rotates with the same period, the satellite would appear fixed from any point on earth. It takes very powerful rockets to throw up a satellite to such large heights above the earth but this has been done in view of the several benefits of many practical applications. Thus radio waves broadcast from an antenna can be received at points far away where the direct wave fails to reach on account of the curvature of the earth. Waves used in television broadcast or other forms of communication have much higher frequencies and thus cannot be received beyond the line of sight. A Geostationery satellite, appearing fixed above the broadcasting station can however receive these signals and broadcast them back to a wide area on earth. The INSAT group of satellites sent up by India is one such group of geostationary satellites widely used for telecommunications in India.
Another class of satellites is called the Polar satellites. These are low altitude (500 to 800 km) satellites, but they go around the poles of the earth in a north-south direction whereas the earth rotates around its axis in an east-west direction. Since its time period is around 100 minutes it crosses any altitude many times a day. However, since its height h above the earth is about 500-800 km, a camera fixed on it can view only small strips of the earth in one orbit. Adjacent strips are viewed in the next orbit, so that in effect the whole earth can be viewed strip by strip during the entire day. These satellites can view polar and equatorial regions. at close distances with good resolution. Information gathered from such satellites is extremely useful for remote sensing, meterology as well as for environmental studies of the earth.

1. Time period of geospatial satellite is:

1. 24 hours
2. 48 hours
3. 72 hours
4. None of these

2. Polar satellites are approximately revolving at height of

1. 500 to 800km
2. 1500 to 2000km
3. 3000 to 4000km
4. None of these

3. Which satellite used to view polar and equatorial regions?

4. Write note on polar satellites

5. Write a note on geostationary satellite. Give its applications.

Read the passage given below and answer the following questions from 1 to 5.
Satellites in a circular orbits around the earth in the equatorial plane with T = 24 hours are called Geostationary Satellites. Clearly, since the earth rotates with the same period, the satellite would appear fixed from any point on earth. It takes very powerful rockets to throw up a satellite to such large heights above the earth but this has been done in view of the several benefits of much practical application. Weight of an object is the force with which the earth attracts it. We are conscious of our own weight when we stand on a surface, since the surface exerts a force opposite to our weight to keep us at rest. The same principle holds good when we measure the weight of an object by a Spring balance hung from a fixed point e.g. the ceiling. The object would fall down unless it is subject to a force opposite to gravity. This is exactly what the spring exerts on the object. This is because the spring is pulled down a little by the gravitational pull of the object and in turn the spring exerts a force on the object vertically upwards. Now, imagine that the top end of the balance is no longer held fixed to the top ceiling of the room. Both ends of the spring as well as the object move with identical acceleration g. The spring is not stretched and does not exert any upward force on the object which is moving down with acceleration g due to gravity. The reading recorded in the spring balance is zero since the spring is not stretched at all. If the object were a human being, he or she will not feel his weight since there is no upward force on him. Thus, when an object is in free fall, it is weightless and this phenomenon is usually called the phenomenon of weightlessness. In a satellite around the earth, every part and parcel of the satellite has acceleration towards the centre of the earth which is exactly the value of earth’s acceleration due to gravity at that position. Thus in the satellite everything inside it is in a state of free fall. This is just as if we were falling towards the earth from a height. Thus, in a manned satellite, people inside experience no gravity. Gravity for us defines the vertical direction and thus for them there are no horizontal or vertical directions, all directions are the same.

1. Astronaut experiences weightlessness in space because:

1. Acceleration due to gravity is zero.
2. Actual weight of astronaut is zero.
3. They are going with same acceleration due to gravity.
4. None of these.

2. Weighing machine measures:

1. Mass of the person.
2. Normal reaction exerted by machine on person.
3. Both a and b.
4. None of these.

3. What is geostationary satellite?

4. What is weight? How it is measured?

5. What is weightlessness astronaut in satellite experienced by ?

Does the escape speed of a body from the earth depend on (a) the mass of the body, (b) the location from where it is projected, (c) the direction of projection, (d) the height of the location from where the body is launched?

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250N on the surface?

A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is 1.50 × 10⁸km away from the sun?

Which of the following symptoms is likely to afflict an astronaut in space (a) swollen feet, (b) swollen face, (c) headache, (d) orientational problem.

A satellite orbits the earth at a height of 400km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200kg; mass of the earth = 6.0 × 10²⁴kg; radius of the earth = 6.4 × 10⁶m; G = 6.67 × 10^-11N m² kg^-2.