Gravity Theories: Newton and Einstein

Study Notes

Introduced by Sir Isaac Newton in 1687
Gravity is a universal force that attracts two objects with mass
Force of gravity is proportional to the product of the two masses and inversely proportional to the square of the distance between them
Mathematical formulation:
- F = G * (m1 * m2) / r^2
- Where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them

Introduced by Albert Einstein in 1915
Gravity is not a force, but the curvature of spacetime caused by massive objects
Massive objects warp spacetime around them, and other objects follow geodesic paths, which we experience as gravity
Mathematical formulation:
- Rμν - 1/2Rgμν = (8πG/c^4)Tμν
- Where Rμν is the Ricci tensor, R is the Ricci scalar, gμν is the metric tensor, G is the gravitational constant, c is the speed of light, and Tμν is the stress-energy tensor

Regions of spacetime where gravity is so strong that not even light can escape
Formed when a massive star collapses in on itself
Characterized by their mass, charge, and angular momentum
Mathematical formulation:
- Schwarzschild metric: ds^2 = (1 - 2GM/r)dt^2 - (1 - 2GM/r)^{-1}dr^2 - r^2dθ^2 - r^2sin^2θdφ^2
- Where G is the gravitational constant, M is the mass of the black hole, and r is the radial distance from the center

Ripples in spacetime produced by the acceleration of massive objects
Predicted by Einstein's theory of general relativity
Detected directly for the first time in 2015 by LIGO
Mathematical formulation:
- h = (2G/c^4) * (1/r) * (d^2Q/dt^2)
- Where h is the strain of the gravitational wave, G is the gravitational constant, c is the speed of light, r is the distance from the source, and Q is the quadrupole moment of the source

Gravity is a universal force that attracts two objects with mass, introduced by Sir Isaac Newton in 1687
Newton's law of gravity states that the force of gravity is proportional to the product of the two masses and inversely proportional to the square of the distance between them
Mathematical formulation of Newton's law: F = G * (m1 * m2) / r^2

Albert Einstein introduced his theory of gravity in 1915, stating that gravity is not a force, but the curvature of spacetime caused by massive objects
Massive objects warp spacetime around them, and other objects follow geodesic paths, which we experience as gravity
Mathematical formulation of Einstein's theory: Rμν - 1/2Rgμν = (8πG/c^4)Tμν

Black holes are regions of spacetime where gravity is so strong that not even light can escape
Formed when a massive star collapses in on itself, characterized by their mass, charge, and angular momentum
Described by the Schwarzschild metric: ds^2 = (1 - 2GM/r)dt^2 - (1 - 2GM/r)^{-1}dr^2 - r^2dθ^2 - r^2sin^2θdφ^2

Gravitational waves are ripples in spacetime produced by the acceleration of massive objects, predicted by Einstein's theory of general relativity
Detected directly for the first time in 2015 by LIGO, with a mathematical formulation: h = (2G/c^4) * (1/r) * (d^2Q/dt^2)