Gravitation Lecture Review

Vocabulary practice flashcards covering the fundamental laws and equations of gravitation, orbital mechanics, and satellite motion.

Gravitation

The attraction force that exists between any two bodies in the universe.

Newton's Universal Law of Gravitation

The law stating that any two bodies in the universe attract each other with a force $F = \frac{G m_1 m_2}{r^2}$, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Universal Gravitational Constant ($G$)

The constant value in the gravitation formula, equal to $6.67 \times 10^{-11} \, Nm^2 \, kg^{-2}$.

Acceleration due to gravity ($g$)

The acceleration experienced by an object due to Earth's gravity, which is $9.8 \, m/s^2$ on the surface and calculated as $g = \frac{GM}{R^2}$.

Variation of $g$ at Earth's Centre

The value of acceleration due to gravity becomes $0$ at the Earth's center ($d = R$) because $g' = g(1 - \frac{d}{R})$.

Gravitational Potential ($V$)

The work done to bring a unit mass from infinity to a specific point, expressed as $V = -\frac{GM}{r}$ with SI units of $J/kg$.

Gravitational Potential Energy ($U$)

The energy of a mass ($m$) due to its position in a gravitational field, given by $u = -\frac{GMm}{r}$; the negative sign indicates gravity is an attractive force.

Escape Velocity ($V_e$)

The minimum velocity required for an object to escape a planet's gravitational attraction, calculated as $V_e = \sqrt{\frac{2GM}{R}}$ or $V_e = \sqrt{2gR}$. For Earth, it is $11.2 \, km/s$.

Orbital Velocity ($V_o$)

The tangential velocity required for a satellite to maintain a circular orbit around a planet, calculated as $V_o = \sqrt{\frac{GM}{r}}$. For Earth's surface, it is approximately $7.9 \, km/s$.

Relation between $V_e$ and $V_o$

The mathematical relationship where escape velocity is $\sqrt{2}$ times the orbital velocity ($V_e = \sqrt{2} V_o$).

Satellite Time Period ($T$)

The time taken for a satellite to complete one orbit, where $T = 2\pi\sqrt{\frac{r^3}{GM}}$, meaning $T \propto r^{3/2}$.

Kepler's First Law (Law of Orbits)

The law stating that every planet moves in an elliptical orbit with the Sun at one of the two foci.

Kepler's Second Law (Law of Areas)

The law stating that an imaginary line joining a planet and the Sun sweeps out equal areas in equal intervals of time, meaning areal velocity is constant.

Kepler's Third Law (Law of Periods)

The law stating that the square of the orbital period ($T$) is proportional to the cube of the semi-major axis ($a$) of its orbit ($T^2 \propto a^3$).

Geostationary Satellite

A satellite that orbits in the Earth's equatorial plane from West to East with a time period of $24 \, hours$, appearing at a fixed position from Earth.

Polar Satellite

A satellite that travels in an orbit passing near the North and South poles, used for mapping, remote sensing, and weather observation.

Total Energy of a Satellite ($E$)

The sum of kinetic and potential energy, expressed as $E = -\frac{GMm}{2r}$. The negative sign indicates the satellite is gravitationally bound to the Earth.

Weightlessness

A state where the apparent weight of an object becomes zero, often experienced in a satellite during freefall because the normal reaction force ($N$) is zero.