Gravitation


Planets move round the sun in elliptic or nearly circular orbits and the satellites move around their respective planets. What is the force that keeps all these in motion?

The gravity provides the necessary centripetal force to keep all the celestial objects moving in their orbits that qualified this as universal law of gravitation. So now we can come to the conclusion that the whole universe is held together by this universal law of gravitation.


Universal Law of Gravity

The gravitational force of attraction between any two particles is directly proportional to the product of their masses and inversely proportional to the square of the distance between them and the direction of force is along the line joining the two particles.

Universal Law of Gravity

$$F = \frac{G m1 m2}{r^2}$$



    


Acceleration Due to Gravity

When an object is dropped from some height, its velocity increases at constant rate due to gravitational force of earth, this acceleration is called acceleration due to gravity.

Relation between acceleration due to gravity and gravitational constant

From Newton's second law we have F1= mg

F2 = $\frac{G m M}{r^2}$

F2 = F1

$\frac{G m M}{r^2}$ = mg

$\frac{GM}{R^2}$ = g

Accelaration Due to Gravity


Keplars law

First law: All planets revolve round the sun in elliptical orbits with sun as the one of the foci.

Second law: A line joining any planet to sun draws out equal areas in equal intervals of time.

Keplars Law

Third law: Square of the period of any planet around the sun is proportional to the cube of the planets mean distance from the sun. T2a r2.


Orbital Velocity of Satellites

Orbital velocity: Orbital velocity is the velocity with which the satellite is revolving round the earth.

Geostationary satellite: The earth completes a rotation about its own axis once in 24 hrs. If the satellite also rotates around the earth for 24 hours then we say such a satellite as geostationary satellite and is placed at the height of 36000 km.


Weightlessness in a satellite

A satellite moves around the earth in a circular orbit under the action of gravity and the weightlessness is due to the fact that it is under the rotating frame of reference.


Gravity Worked Examples

What is the mass of the object whose weight is 980 newton?

Answer: W = mg

980 = m x 9.8

m = $\frac{980}{9.8}$ = 100 kg.


Gravity Practice Questions

A. According to the equation of gravity, what happens to the force between two bodies?

1) If the mass of one body is doubled
2) If the mass of both the bodies are doubled.
3) Is newton's law of gravitation universal?
4) Light from the sun, like gravity obeys the inverse square law. If you were on a planet thrice as far from the sun, how bright would the sun look?

B. A body has a weight of 40kg on the earth. What will be the weight when taken from the centre of the earth?

If your mass increases, does your weight also increases.






Next Chapters

Velocity Kinematics Gravitation


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