Gravitation Lecture Vocabulary

Vocabulary flashcards covering core definitions, equations, principles, and key concepts from the lecture on Universal Gravitation, Gravitational Fields, Potential Energy, and Satellite Motion.

Law of Universal Gravitation

A law stating that every particle of matter attracts every other particle with a gravitational force directly proportional to the product of their masses and inversely proportional to the square of the distance between them, calculated using $F_g = \frac{G m_1 m_2}{r^2}$.

Gravitational Constant ($G$)

A universal constant determined by Henry Cavendish using a torsion balance, with an exact value of $6.67428 \times 10^{-11}\,\text{N}\cdot\text{m}^2/\text{kg}^2$ and a commonly rounded value of $6.673 \times 10^{-11}\,\text{N}\cdot\text{m}^2/\text{kg}^2$.

Free Fall

The state of motion in which gravity is the only force acting upon an object, causing it to fall continuously toward Earth regardless of whether its acceleration is exactly $9.80\,\text{m/s}^2$.

Gravity

A force that acts at a distance without requiring physical contact between objects.

Weight

The gravitational force acting on a body due to other bodies, particularly Earth near its surface, calculated using $w = mg$.

Acceleration Due to Gravity ($g$)

The acceleration experienced by an object at Earth's surface, calculated as $g = \frac{G M_E}{R_E^2}$, which depends specifically on Earth's mass ($M_E$) and Earth's radius ($R_E$).

Gravitational Field

The gravitational force experienced per unit mass at a point in space, represented by the formula $g = \frac{F}{m}$.

Gravitational Field Strength

The magnitude of gravitational force per unit mass exerted by Earth near its surface, equal to $9.8\,\text{N/kg}$, which is equivalent to $9.8\,\text{m/s}^2$.

Gravitational Potential Energy

The stored energy of an object due to its position in a gravitational field, expressed near Earth's surface as $\text{GPE} = mgh$ or $U = mgy$.

Conservative Force

A force for which the work done depends only on the initial and final positions of an object and not on the path taken, satisfying the relation $W_{\text{grav}} = U_1 - U_2$.

Closed Orbits

Orbital trajectories, all considered ellipses (with circles being a special case), that eventually return to their starting point.

Open Orbits

Orbital trajectories in which a projectile never returns to its starting point and continues traveling farther away from Earth.

Uniform Circular Motion

The motion of a satellite in a circular orbit moving at a constant speed while continuously accelerating toward Earth's center.

Orbital Speed

The speed required for a satellite to stay in a circular orbit at a radius $r$ from Earth's center, given by $v = \sqrt{\frac{G M_E}{r}}$.

Apparent Weightlessness

The condition in which an astronaut feels weightless because both the astronaut and the spacecraft are accelerating toward Earth at the same rate, resulting in no net reaction force.

True Weightlessness

The condition in which gravitational force becomes zero, occurring only if an object is infinitely far from other masses.

Orbital Period ($T$)

The time required for a satellite to complete one full revolution around its circular orbit, defined by $T = \frac{2\pi r}{v}$.

Geosynchronous Orbit

An orbit in which a satellite matches the rotational velocity of Earth to remain over the same spot on Earth, having an orbital radius of $4.23 \times 10^7\,\text{m}$ measured from Earth's center.