Universal Gravitation and Orbital Mechanics

Universal Gravitational Constant (G)

A constant used in the law of universal gravitation, equal to 6.67 x 10^-11 N·m²/kg².

Newton’s Law of Universal Gravitation

Every particle of matter attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Action-Reaction Pairs

According to Newton's Third Law, forces exerted by two objects on each other are equal in magnitude and opposite in direction.

Inverse-Square Law

The gravitational force decreases with the square of the distance between two objects.

Superposition Principle

The net gravitational force on a mass due to multiple other masses is the vector sum of the individual forces.

Gravitational Field (g)

A region of space where a mass experiences a force due to gravity, defined as the force per unit mass.

Shell Theorem

Newton's theorem that describes the gravitational effects of spherical shells, stating that outside a shell, it behaves as if mass were concentrated at its center.

Gravitational Potential Energy (U_g)

The work done by an external agent in bringing a system of masses from infinite separation to a distance r.

Negative Gravitational Potential Energy

Indicates that positive work is required to separate masses due to the attractive force of gravity.

Kepler’s First Law

Every planet moves in an elliptical orbit with the Sun at one of the foci.

Eccentricity (e)

A parameter that determines the amount by which an orbit deviates from being circular; e=0 is a circle.

Law of Areas

A line drawn from the Sun to a planet sweeps out equal areas during equal intervals of time.

Conservation of Angular Momentum

In the absence of external torques, the total angular momentum of a system remains constant.

Kepler’s Third Law

The square of the orbital period is directly proportional to the cube of the semi-major axis of the orbit.

Escape Velocity (v_esc)

The minimum speed required for an object to break free from a planet's gravitational field.

Total Mechanical Energy (E)

The sum of kinetic and potential energy in an orbit, given as E = K + U_g.

Orbital Velocity (v_orb)

The speed required to maintain a stable circular orbit, calculated as v_{orb} = sqrt(GM/r).

Gravitational Force (F_g)

The attractive force acting between two masses, represented by the equation Fg = G(m1m_2/r^2).

Center of Mass (Barycenter)

The common center of mass around which two or more bodies orbit; for the Earth-Sun system, it is inside the Sun.

Distance (r)

The separation between the centers of mass of two objects, used in gravitational force calculations.

Potential Energy (U)

An energy stored due to position in a force field, which can perform work when released.

Newton's Third Law

For every action, there is an equal and opposite reaction.

Centripetal Force

The force that keeps an object moving in a circular path, directed towards the center of the circle.

Positive Work

Work done against the gravitational force to separate two masses.

Scalar Quantity

A quantity that has magnitude but no direction, such as gravitational potential energy.

Magnitude of Gravitational Force

The strength of the gravitational force between two objects, dependent on their masses and distance apart.

Gravitational Acceleration (g)

The acceleration experienced by an object due to the gravitational force acting on it.

Linear Increase of g

Inside a uniform sphere, gravitational field strength increases linearly with distance from the center.

Negative Energy State

Refers to the condition in which a bound system has a total energy less than zero due to attractive forces.

Vector Sum

The combination of two or more vectors to yield a resultant vector.

Work-Energy Principle

The work done on an object is equal to the change in its kinetic energy.

Potential Energy Zero Reference Point

Gravitational potential energy is defined as zero when two masses are infinitely far apart.

Mass of the Sun (M)

The mass used as the central body in gravitational calculations for solar system bodies.

Spherical Shell

A hollow sphere with uniform mass distribution that has specific gravitational characteristics.

Work Done Against Gravity

The energy required to move a mass from a lower gravitational potential to a higher one.

Gravitational Field Strength Formula

g = GM/r², where G is the gravitational constant, M is the mass creating the field, and r is the distance from the mass.

Diameter of Orbit

Twice the radius (r) of the orbit, representing the full distance across the circular path.

Universal Law of Gravitation Equation

Fg = G(m1m_2/r²), illustrating the relationship between mass, distance, and gravitational force.

Zero Net Force Inside Shell

A particle experiences no gravitational force when located inside a uniform spherical shell of mass.

Perihelion

The point in the orbit of a planet at which it is closest to the Sun.

Aphelion

The point in the orbit of a planet at which it is farthest from the Sun.

Gravitational Energy Well

A visual representation of gravitational potential energy, depicting how energy changes with distance from a mass.

Satellite Motion

The movement of a satellite around a central body, influenced by gravitational forces.

Gravitational Binding Energy

The energy required to disassemble a system of bodies into separate parts against gravitational attraction.

Orbital Period (T)

The time it takes for a satellite or planet to complete one full orbit around its central body.

Distance Above Surface (h)

The altitude above the surface of a planet used in calculating gravitational effects.

Gravity at High Altitude

Gravitational force that decreases with increasing distance from the center of the Earth.

Conservation of Energy in Orbits

The principle that total energy remains constant, with potential and kinetic energy transforming into each other.

Work Done to Escape

The amount of energy required for an object to reach escape velocity from a gravitational field.