Let us assume that our galaxy consists of $2.5 \times 10^{11}$ stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution ? Take the diameter of the Milky Way to be $10^5$ ly.

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200 kg; mass of the earth = $6.0 \times 10^{24}$ kg; radius of the earth = $6.4 \times 10^6$ m; G = $6.67 \times 10^{–11}$ N m$^2$ kg$^{–2}$.

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (b) angular speed, throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

The escape speed of a projectile on the earth’s surface is 11.2 km s$^{–1}$. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (a) linear speed, throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

Choose the correct alternative: (b) The energy required to launch an orbiting satellite out of earth’s gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence.

A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity ? (mass of the sun = $2 \times 10^{30}$ kg).

Which of the following symptoms is likely to afflict an astronaut in space (b) swollen face,

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun = $2 \times 10^{30}$ kg; mass of mars = $6.4 \times 10^{23}$ kg; radius of mars = 3395 km; radius of the orbit of mars = $2.28 \times 10^8$ km; G = $6.67 \times 10^{-11}$ N m$^2$ kg$^{–2}$.

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

Which of the following symptoms is likely to afflict an astronaut in space (c) headache,

Does the escape speed of a body from the earth depend on (c) the direction of projection,

Two stars each of one solar mass (= $2 \times 10^{30}$ kg) are approaching each other for a head on collision. When they are a distance $10^9$ km, their speeds are negligible. What is the speed with which they collide ? The radius of each star is $10^4$ km. Assume the stars to remain undistorted until they collide. (Use the known value of G).

A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is $1.50 \times 10^8$ km away from the sun ?

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (e) potential energy, throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

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

How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is $1.5 \times 10^8$ km.

Does the escape speed of a body from the earth depend on (b) the location from where it is projected,

Answer the following : (c) 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 ?

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (c) angular momentum, throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.