An artificial satellite is going round the earth, close to the surface. What is the time taken by it to complete one round?

3

(a)

The distances of two planets from the sun are 10¹³ m and 10¹² m, respectively. Calculate the ratio of time period and the speeds of the two planets

3

(a)

If the earth is 1/4 of its present distance from the sun, then what is the duration of he year?

3

(a)

The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of g and R(radius of earth) are 10\({ m }/{ { s }^{ 2 } }\)and 6400km, respectively.What is the required energy for this work done?

3

(a)

What will be the potential energy of a body of mass 67kg at a distance of \(6.6{ \times 10 }^{ 10 }m\)from the centre of the earth? Find gravitational potential at this distance.

3

(a)

Viscous force increases the velocity of a satellite.Discuss

3

(a)

Let the speed of the planet at the perihelion P in Fig. be v_P and the Sun-planet distance SP be r_P. Relate {r_P, v_P} to the corresponding quantities at the aphelion {r_A, v_A}. Will the planet take equal times to traverse BAC and CPB ?

3

(a)

What is the height at which the value of g is the same as at a depth of \(\frac{R}{2}?\)

3

(a)

Compute the mass of a planet that has a satellite whose time period is T and orbital radius is r.

3

(a)

A satellite is revolving around the earth, close to the surface of earth with a kinetic energy E. How much kinetic energy should be given to it so that it escapes from the surface of earth?

3

(a)

Taking the moon's orbit around earth to be r and mass of earth 81 times the mass of the moon. Find the position of the point from the earth, where the net gravitational field is zero.

3

(a)

The planet Saturn has a mass 95 times that of the earth, and its radius is 9.5 times the earth's radius. Calculate the escape speed of a body from Saturn's surface, if the escape speed from the earth's surface is 11.2 kms^-1.

3

(a)

Find an expression for the orbital velocity of a satellite revolving around the earth in a circular orbit at a height h above the surface of earth.

3

(a)

A satellite is revolving just near the Earth's surface. Compute its orbital velocity. Given that radius of Earth R = 6400 km and g = 9.8 ms^-2.

3

(a)

The magnitude of gravitational field at distances r₁ and r₂ from the centre of a uniform sphere of radius R and mass M are l₁ and l₂ respectively. Find the ratio of (I₁/I₂) if r₁ > R and r₂ < R.

3

(a)