## Question

Halley’s comet has a period of 76 years and in 1986, had a distance of closest approach to the sun equal to What is the comet’s farthest distance from the sun if the mass of sun is units?

### Solution

From the problem it is self-evident that the orbit of the comet is elliptic with sun being at one focus [see fig]. Now as for elliptic orbits, according to Kepler’s third law,

But in case of ellipse,

#### SIMILAR QUESTIONS

Three particles each of mass *m* are placed at the corners of an equilateral triangle of side *d*. Calculate (*a*) the potential energy of the system, (*b*) work done on this system if the side of the triangle is changed from *d* to 2*d*.

What will be the acceleration due to gravity on the surface of the moon if its radius were (1/4)th the radius of earth and its mass (1/80)th the mass of earth? What will be the escape velocity on the surface of moon if it is 11.2 km/s on the surface of the earth? (Given that *g* = 9.8 m/s^{2})

The masses and radii of the earth and moon are *M*_{1}, *R*_{1} and *M*_{2}, *R*_{2}respectively. Their centres are at distance *d* apart. What is the minimum speed with which a particle of mass *m* should be projected from a point midway between the two centres so as to escape to infinity?

Distance between the centres of two stars is 10*a*. The masses of these stars are *M* and 16*M* and their radii *a* and 2*a*, respectively. A body of mass *m* is fired straight from the surface of the larger star towards the smaller star. What should be its minimum initial speed to reach the surface of the smaller star? Obtain the expression in terms of *G*, *M* and *a*.

A mass (= mass of earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 10^{8} m/s (equal to that of light). What should be the radius of the sphere?

A projectile is fired vertically upward from the surface of earth with a velocity *Kv _{e}* where

*v*is the escape velocity and

_{e}*K*< 1. Neglecting air resistance, show that the maximum height to which it will rise measured from the centre of earth is

*R/*(1 –

*K*

^{2}) where

*R*is the radius of the earth.

A particle is fired vertically upwards from the surface of earth and reaches a height 6400 *km*. find the initial velocity of the particle if *R* = 6400 *km* and*g* at the surface of earth is 10 *m/s*^{2}.

Calculate the mass of the sun if the mean radius of the earth’s orbit is

Imagine a light planet revolving around a very massive star in a circular orbit of radius *r* with a period of revolution *T*. On what power of *r*, will the square of time period depend if the gravitational force of attraction between the planet and the star is proportional to

Consider on earth satellite so positioned that it appears stationary to an observer on earth and serves the purpose of a fixed relay station for intercontinental transmission of *TV* and other communications. What would be the height at which the satellite should be positioned and what would be the direction of its motion? Given that the radius of the earth is 6400 km and acceleration due to gravity on the surface of the earth is 9.8*m/s*^{2}.