Question

Anyone send me the notes of gravitation chapter plz



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Answer 1

Answer:

Each body in this universe attracts other bodies towards itself with a force known as Gravitational Force, thus gravitation is a study of the interaction between two masses. Out of the two masses, the heavier one is called source mass and the lighter one is called test mass.

Gravitational force is a central force which depends only on the position of test mass from the source mass and always acts along the line joining the centres of the two masses.

F⃗ (r) = f(r) r^

The core problem of gravitation has always been in understanding the interaction between the two masses and the relativistic effects associated with it.

⇒ Check: Gravitational field intensity

History of Gravitational Theory:

Ptolemy has proposed geocentric model which failed in understanding planetary motions led to the development of heliocentric model by Nicholas Copernicus whose idea is based on rotation of a test mass around the source mass in circular orbits, although the model correctly predicts the position of planets and their motions but has failed in explaining many aspects like the occurrence of seasons which led the construction of a model based on Kepler’s laws of planetary motion.

Newton’s Law of Gravitation

According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,

Directly proportional to the product of their masses i.e. F ∝ (M1M2) . . . . (1)

Inversely proportional to the square of the distance between their centre i.e. (F ∝ 1/r2) . . . . (2)

On combining equations (1) and (2) we get,

F ∝ M1M2/r2

F = G × [M1M2]/r2 . . . . (7)

Or, f(r) = GM1M2/r2 [f(r)is a variable, Non-contact, and conservative force]

As f(r) varies inversely as a square of ‘r’ it is also known as inverse square law force. The proportionality constant (G) in the above equation is known as gravitational constant.

The dimension formula of G is [M-1L3T-2]. Also, the value of the gravitational constant,

In SI units: 6.67 × 10-11 Nm2 kg-2,

In CGS units: 6.67×10-8 dyne cm2 g-2