Gravity and the Universe

Constituents of the Universe

• The universe consists of galaxies, stars, planets, comets, asteroids, and meteoroids, all bound together by gravitational force.

Gravitation

• Gravitation is a natural phenomenon where material objects attract each other.
• Sir Isaac Newton published Principia Mathematica in 1687, explaining the inverse-square law of gravitation.

Newton's Law of Gravitation

• Every particle of matter attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of their separation.
• Mathematical form: F = Gm1m2/r^2, where F is the force of attraction, G is the universal constant of gravitation, m1 and m2 are the masses, and r is the distance between them.

Vector Form

• In vector form, Newton's law of gravitation is represented as: F21→ = -Gm1m2/r^2 r12^ and F12→ = Gm1m2/r^2 r12^, where r12^ is a unit vector drawn from particle m1 to particle m2.

Universal Constant of Gravitation

• The universal gravitation constant (G) is given by: G = Fr^2/m1m2.
• In SI units, G = 6.67 × 10^(-11) Nm^2/kg^2, and in CGS units, G = dynecm^2/g^2.

Dimensions of G

• The dimension of G is [M^(-1)L^3T^(-2)].

Notes

• The gravitational force is independent of the intervening medium.
• The gravitational force is a conservative force.
• The gravitational force between two particles acts along the line that connects them and is part of an action-reaction pair.

Variation in 'g'

• The acceleration due to gravity (g) at a height h above the Earth's surface is given by: gh = g * (R / (R + h))^2.
• The acceleration due to gravity at a very small height is given by: gh = g * (1 - 2h/R + h^2/R^2 ... ).