Chapter 3: Gravitation (Newtonian Mechanics)

Vocabulary practice flashcards covering Newton's Universal Law of Gravitation, Kepler's Laws, centripetal force, and satellite mechanics.

Newton's Universal Law of Gravitation

A law stating that gravitational force is directly proportional to the product of the masses of two bodies and inversely proportional to the square of the distance between the centers of the two bodies: $F = \frac{G m_1 m_2}{r^2}$.

Gravitational Constant ($G$)

The universal constant of proportionality in Newton's law of gravitation, with an experimental value of $6.67 \times 10^{-11}\,\text{N}\,\text{m}^2\,\text{kg}^{-2}$.

Gravitational Acceleration ($g$)

The acceleration acquired by an object due to gravitational attraction, formulated on the surface of a planet as $g = \frac{GM}{r^2}$ ($9.81\,\text{m}\,\text{s}^{-2}$ on Earth).

Variation of Gravitational Acceleration ($g$ vs. $r$)

Below the Earth's surface ($r < R$), $g$ is directly proportional to $r$ ($g \propto r$); on the surface ($r = R$), $g = \frac{GM}{R^2}$; and at or above the surface ($r \ge R$), $g$ is inversely proportional to $r^2$ ($g \propto \frac{1}{r^2}$).

Centripetal Force

The net force acting on an object continuously changing direction in an orbit, directed towards the center of the circular path: $F = \frac{m v^2}{r}$.

Centripetal Acceleration

The inward acceleration of an object undergoing circular motion, derived by equating $F = ma$ and $F = \frac{m v^2}{r}$, yielding $a = \frac{v^2}{r}$.

Centripetal Force Kit

An experimental apparatus comprising a rubber stopper, plastic/glass tube, string, paperclip, and slotted weights, where the weight of the slotted weights provides the string tension acting as centripetal force.

Kepler's First Law (Law of Orbits)

All planets move in elliptical orbits with the Sun positioned at one of the two foci.

Major Axis

The longest axis passing through the center and both foci of an elliptical orbit.

Radius of Orbit (Elliptical)

The average value of the distance between an orbiting planet and the Sun.

Kepler's Second Law (Law of Areas)

A line that connects a planet to the Sun sweeps out equal areas in equal intervals of time, causing a planet to travel faster when it is closer to the Sun.

Kepler's Third Law (Law of Periods)

The square of the orbital period of any planet is directly proportional to the cube of the radius of its orbit ($T^2 \propto r^3$), represented as $\frac{T_1^2}{T_2^2} = \frac{r_1^3}{r_2^3}$.

Kepler's Constant ($k$)

The proportionality constant between orbital period squared and orbital radius cubed, given by the expression $k = \frac{4 \pi^2}{GM}$.

Satellite Orbital Speed

The necessary linear velocity required to maintain a satellite at a specific orbital radius $r$, given by $v = \sqrt{\frac{GM}{r}}$.

Geostationary Satellite

A satellite that orbits Earth in the same direction as Earth's rotation with a period of $T = 24\,\text{hours}$, staying above the same geographical location (used for communications, e.g., MEASAT).

Non-geostationary Satellite

A satellite whose orbital period can be greater or less than $24\,\text{hours}$ and whose direction does not need to align with Earth's rotation, positioning it over varying geographical locations (used for Earth imaging, GPS, and weather forecasting; e.g., TiungSAT, RazakSAT, Pipit, ISS).

Escape Velocity

The minimum velocity needed by an object on the surface of a body to overcome gravitational force and escape to outer space ($v = \sqrt{\frac{2GM}{r}}$).

Earth's Escape Velocity

The threshold velocity needed to escape Earth's gravitational pull, valued at $11200\,\text{m}\,\text{s}^{-1}$ (or $40300\,\text{km}\,\text{h}^{-1}$).

Gravitational Potential Energy ($U$)

The energy stored in an object due to its position in a gravitational field, defined mathematically as $U = -\frac{GMm}{r}$.