Chapter 4: Gravity Lecture Notes

Flashcards covering Newton's Universal Law of Gravitation, the properties of orbits, tidal forces, and their effects on celestial bodies.

Contact Forces

Forces that directly push or pull on other objects, such as a cue ball striking an eight ball.

Non-Contact Forces

Forces that cause action at a distance without physical touching, such as gravity causing an object to fall toward the ground.

Mass

A measure of the amount of material in an object that does not change regardless of location.

Weight

The gravitational force acting on an object attracted by a planet, which changes depending on the planet's gravity.

Size (Astronomical)

Usually refers to the radius ($r$) of an object rather than its mass.

Gravity

The mutually attractive force between objects that have mass.

Gravitational Acceleration ($g$)

A constant acceleration near the surface of Earth, approximately valued at $9.8\,m/s^2$, though it varies slightly between the equator ($9.78\,m/s^2$) and the poles ($9.83\,m/s^2$).

Newton’s Universal Law of Gravitation

States that gravity is an attractive force proportional to the product of the masses ($m_1 \times m_2$) and inversely proportional to the square of the distance ($r$) between their centers.

Universal Gravitational Constant ($G$)

A constant that determines the strength of gravity between objects, valued at $6.67 \times 10^{-11}\,m^3/(kg\,s^2)$.

Inverse Square Law

The principle stating that gravitational force diminishes with the square of the distance between two objects; for example, doubling the distance reduces the force to $\frac{1}{4}$ of its original strength.

Torsion Balance Technique

A method first used about a century after Newton to measure the actual value of Big $G$.

Self-gravity

The mutual gravitational attraction that occurs among all parts of the same object, pulling mass toward the center and forming massive objects into spherical shapes.

Orbit

The path of one object that freely falls around another.

Weightlessness

The state experienced by astronauts in orbit because they are in free fall, falling around Earth at the same rate as their shuttle.

Center of Mass

The common point between two objects that they orbit around, such as the point between Pluto and its moon Charon.

Universality

The principle that the laws of physics are the same everywhere and at all times in the universe.

Uniform Circular Motion

Movement on a circular path at a constant speed, occurring only when a satellite moves at the specific circular velocity ($v_{circ}$).

Circular Velocity ($v_{circ}$)

The particular speed required for a satellite to maintain a circular orbit; for Earth, this is calculated as $7.91\,km/s$.

Elliptical Orbit

A bound orbit that occurs when a satellite has a velocity larger than the circular velocity but less than the escape velocity.

Escape Velocity ($v_{esc}$)

The velocity required for an object to leave a planet’s surface and enter an unbound orbit; for Earth, this is $11.2\,km/s$, which equals $\sqrt{2} \times v_{circ}$.

Unbound Orbit

An orbital path such as a parabola or hyperbola where the object is moving fast enough to escape the gravitational pull of another body.

Newton’s form of Kepler’s Third Law

A mathematical relationship expressed as $M = \frac{4\pi^2}{G} \times \frac{A^3}{P^2}$, used to calculate the mass of a system based on orbital period ($P$) and semimajor axis ($A$).

Tidal Force

The difference between the actual gravitational force at a specific point on an object and the average force exerted on the entire object, causing the body to stretch.

Tidal Bulge

The elongation of Earth's oceans in a direction nearly pointed toward the Moon.

Spring Tides

Extreme tides that occur when the Sun and Moon are aligned, combining their gravitational pulls.

Neap Tides

Lower than normal high tides that occur when the Moon, Earth, and Sun are at right angles (quarter phases), partially canceling each other's pull.

Tidal Locking

A synchronization resulting from tidal forces where an object's rotation period equals its orbital period, causing it to always show the same face to the body it orbits.

Spin-Orbit Resonance

A ratio of rotation to orbit, such as the Moon's 1:1 resonance or Mercury's 3:2 resonance (3 spins for every 2 orbits).

Roche Limit

The distance from a gravitational object within which tidal forces can destabilize or break apart other objects.