The motion of planets can be explained using Keplerâ€™s laws.

**SUMMARY**

The motion of planets can be explained using Keplerâ€™s laws.

**Keplerâ€™s first law**: All the planets in the
solar system orbit the Sun in elliptical orbits** **with the Sun at one of
the foci.

**Keplerâ€™s second law:**** **The radial vector line joining the Sun to a planet sweeps equal** **areas in equal intervals of time.

**Keplerâ€™s third law:**** **The ratio of the square of the time period of planet to the cubic** **power of semi major axis is constant for all the planets in the
solar system.

**Newtonâ€™s law of
gravitation**** **states that the
gravitational force between two masses** **is directly proportional
to product of masses and inversely proportional to square of the distance between the masses. In
vector form it is given by

Gravitational
force is a central force.

Keplerâ€™s
laws can be derived from Newtonâ€™s law of gravitation.

The gravitational field due to a mass m at a point which is at a distance r from mass m is given by . It is a vector quantity.

The gravitational potential energy of two masses is given by** ** It is a scalar quantity.

The gravitational potential at a point which is at a distance r from mass m is given by . It is a scalar quantity.

Due
to rotation of the Earth, the acceleration due to gravity is maximum at poles
and minimum at Earthâ€™s equator.

The
(escape) speed of any object required to escape from the Earthâ€™s gravitational
field is v_{e} = âˆš2gRe . It is independent of mass of the object.

The
energy of the satellite is negative. It implies that the satellite is bound to
Earthâ€™s gravitational force.

Copernicus
model explained that retrograde motion is due to relative motion between
planets. This explanation is simpler than Ptolemyâ€™s epicycle explanation which
is complicated

Copernicus
and Kepler measured the distance between a planet and the Sun using simple
geometry and trigonometry.

2400
years ago, Eratosthenes measured the radius of the Earth using simple geometry
and trigonometry.

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11th Physics : UNIT 6 : Gravitation : Summary - Physics: Gravitation |

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