Newtonian Gravity and Kepler's Laws

Practice flashcards based on key concepts related to Newtonian gravity and Kepler's laws.

Newton's Second Law

States that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

Newton's Third Law

For every action, there is an equal and opposite reaction; the force exerted by one object on another is equal in magnitude and opposite in direction to the force exerted by the second object on the first.

Law of Universal Gravitation

Describes the gravitational attraction between two masses, given by the formula F = G(Mm/r²), where G is the gravitational constant, M and m are the masses, and r is the distance between their centers.

Gravitational Potential Energy

The potential energy associated with the gravitational force between two objects; calculated as U = - GMm (1/r_f - 1/r_i), where G is the gravitational constant.

Escape Speed

The minimum speed required for an object to escape the gravitational influence of a massive body, given by v_e = √(2GM/R).

Centripetal Acceleration

The acceleration directed towards the center of a circular path, calculated as a_c = v²/r, where v is the tangential speed and r is the radius.

Period of Orbit

The time taken for one complete orbit; related to radius and mass by Kepler's third law: T² = (4π²/GM)a³.

Semi-Major Axis

Half of the longest diameter of an ellipse, used in describing the shape of an orbit.

Eccentricity

A measure of how much an orbit deviates from being circular; ranges from 0 (circular) to 1 (parabola).

Kepler's First Law

The orbit of a planet around the sun is an ellipse with the sun at one of the two foci.

Kepler's Second Law

The line connecting a planet to the sun sweeps out equal areas in equal times.

Kepler's Third Law

The square of the period of a planet's orbit is directly proportional to the cube of the semi-major axis of its orbit.