Physics Fundamentals 1: Universal Gravitation and Orbits

Vocabulary flashcards covering historical foundations, Newton's law of gravitation, circular and non-circular orbits, gravitational potential energy, escape speed, and gravitational fields.

al-Bīrūnī

A Muslim astronomer, mathematician, ethnographist, anthropologist, historian, and geographer (born Sept. 4, 973 ce, Khwārezm, Khorāsān—died c. 1052) whose works included an early theory of gravity.

Nicolaus Copernicus

The astronomer who published a heliocentric theory of the solar system in 1543.

Johannes Kepler

The astronomer who brilliantly summarized Tycho Brahe's planetary motion measurements into three laws of planetary motion after Brahe's death in 1601.

Newton's Law of Universal Gravitation

The law stating that any two point particles attract each other with a force proportional to the product of their masses and inversely proportional to the square of their separation: $F = \frac{G m_1 m_2}{r^2}$.

Constant of Universal Gravitation ($G$)

The proportionality constant in universal gravitation, approximately equal to $6.67 \times 10^{-11}\,N\,m^2/kg^2$.

Cavendish Experiment

The 1798 experiment in which Henry Cavendish made the first experimental measurement of $G$ using masses suspended by a thin fiber, allowing the determination of Earth's mass.

Orbital Speed (Circular Orbit)

The speed needed to maintain a circular orbit of radius $r$ about a central mass $M$, given by $v = \sqrt{\frac{GM}{r}}$.

Orbital Period (Circular Orbit)

The time required to complete one circular orbit around mass $M$, expressed as $T = \left(\frac{2\pi r}{v}\right) = \sqrt{\frac{4\pi^2 r^3}{GM}}$, which confirms Kepler's third law ($T^2 \propto r^3$).

Low-Earth Orbit Period

The orbital period for satellites orbiting near Earth's surface, which is approximately $90\,minutes$.

Bound Orbit

A closed, elliptical (or circular) trajectory followed by an orbiting body when its total mechanical energy is negative ($E < 0$).

Unbound Orbit

An open trajectory followed by an object that can escape to infinity, being hyperbolic when total energy $E > 0$ and parabolic in the borderline case where $E = 0$.

Gravitational Potential Energy ($U(r)$)

The potential energy of a system of two masses separated by distance $r$ (taking the reference point of zero potential energy at infinity), given by $U(r) = -\frac{GMm}{r}$.

Escape Speed ($v_{\text{esc}}$)

The minimum launch speed required for an object to escape to infinitely far from a gravitating body of mass $M$ from distance $r$, given by $v_{\text{esc}} = \sqrt{\frac{2GM}{r}}$.

Earth Escape Speed

The speed required to escape Earth's gravitational pull from its surface, approximately equal to $11\,km/s$ (or about $40\,000\,km/h$).

Total Energy in a Circular Orbit

The total mechanical energy of an object in a circular orbit, satisfying $U = -2K$ such that $E = K + U = -K = \frac{1}{2}U = -\frac{GMm}{2r}$.

Gravitational Field ($\mathbf{g}$)

A field created in space by a massive object $M$, described by the vector equation $\mathbf{g} = -\frac{GM}{r^2}\hat{r}$, which other masses respond to at their immediate locations.

Geostationary Equatorial Constraint

The orbital mechanics principle requiring a satellite that remains permanently over a single spot to orbit above the equator, because an orbit must be centered on the center of Earth rather than an off-equator latitude like $45^\circ\text{ N}$.

Potential Well

The negative gravitational potential energy region trapping an object near a massive body; larger masses create deeper wells requiring greater kinetic energy to escape.