Here are some important formulas related to gravitation in physics:
Newton's Law of Universal Gravitation:
F = G * (m₁ * m₂) / r²
where F is the gravitational force between two masses m₁ and m₂ separated by a distance r, and G is the universal gravitational constant.
Gravitational Potential Energy:
U = -G * (m₁ * m₂) / r
where U is the gravitational potential energy between two masses m₁ and m₂ separated by a distance r, and G is the universal gravitational constant.
Gravitational Potential:
V = -G * m / r
where V is the gravitational potential at a distance r from a mass m, and G is the universal gravitational constant.
Escape Velocity:
v_escape = √(2 * G * M / R)
where v_escape is the escape velocity required for an object to escape the gravitational pull of a celestial body with mass M and radius R, and G is the universal gravitational constant.
Orbital Velocity:
v_orbit = √(G * M / r)
where v_orbit is the orbital velocity of a satellite or celestial object in circular orbit around a central mass M at a distance r, and G is the universal gravitational constant.
Gravitational Field Strength:
g = G * M / r²
where g is the gravitational field strength at a distance r from a mass M, and G is the universal gravitational constant.
Kepler's Third Law (Law of Periods):
T² = (4 * π² * r³) / (G * M)
where T is the orbital period of a satellite or planet, r is its average distance from the central mass M, and G is the universal gravitational constant.
These formulas play a crucial role in understanding and calculating the gravitational interactions between celestial bodies and objects in space. They have been fundamental in the study of celestial mechanics and space exploration.