Gravitational Field Equations to Know for AP Physics 1

Gravitational Field Equations

Gravitational Field Equations

Describe the attraction between masses and how gravity affects motion in space. They explain how gravitational forces govern the movement of objects like planets, satellites, and celestial bodies.

Newton's Law of Universal Gravitation

F = G(m1m2)/r^2

Gravitational Field Strength

g = GM/r^2

Gravitational Potential Energy

U = -GMm/r

Escape Velocity

v_escape = √(2GM/r)

Orbital Velocity

v_orbit = √(GM/r)

Kepler's Third Law

T^2 ∝ r^3

Gravitational Potential

V = -GM/r

Acceleration due to gravity at Earth's surface

g ≈ 9.8 m/s^2

Gravitational Field for a spherical shell

g = 0 (inside), g = GM/r^2 (outside)

Superposition principle for gravitational fields

States that the total gravitational field at a point is the vector sum of the fields due to individual masses.

Gravitational Field for a spherical shell

Inside a uniform spherical shell, the gravitational field is zero. Outside the shell, the gravitational field behaves as if all mass were concentrated at the center. Important for understanding gravitational effects of planets and stars.

Acceleration due to gravity at Earth's surface

Represents the acceleration experienced by an object in free fall near the Earth's surface. Varies slightly with altitude and geographical location. Fundamental for solving problems involving motion under gravity.

Gravitational Potential

It fully describes the potential energy per unit mass at a distance r from mass M. Like gravitational potential energy, it is negative, indicating a bound system. Useful for calculating energy changes in gravitational fields.

Kepler's Third Law

Explains the relation between the square of the orbital period (T) of a planet to the cube of the semi-major axis (r) of its orbit. Shows that more distant planets take longer to orbit the sun. Provides a foundation for understanding planetary motion and distances in the solar system.

Orbital Velocity

It is the velocity required for an object to maintain a stable orbit around a mass M. Directly related to the mass of the central body and inversely related to the radius of the orbit. Essential for understanding satellite motion and planetary orbits.

Escape Velocity

This solves for the minimum velocity needed for an object to break free from a gravitational field without further propulsion. Depends on the mass of the celestial body and the distance from its center. Higher mass or smaller radius results in a higher escape velocity.

Gravitational Potential Energy

Represents the work done to bring a mass m from infinity to a distance r from mass M. The negative sign indicates that energy is released when masses come together. Potential energy becomes less negative (increases) as the distance increases.

Gravitational Field Strength

Represents the gravitational force experienced by a unit mass at a distance (r) from a mass (M). Describes the intensity of the gravitational pull at a given location in space. Shows that the gravitational field strength diminishes with the square of the distance from the source mass.

Newton's Law of Universal Gravitation

Represents the attractive force between two masses. The force is inversely proportional to the square of the distance between the centers of the two masses.