Gravitation and Motion Lecture Notes

These flashcards cover the key vocabulary and concepts of gravitation as described in the lecture notes, including Kepler's laws, Newton's universal law of gravitation, and the properties of mass, weight, and motion.

Gravitation

A universal force discovered by Sir Isaac Newton that acts not only between two objects on the earth but also between any two objects in the universe.

Centripetal force

A force that acts on any object moving along a circle and is directed towards the centre of the circle; 'centripetal' means centre seeking.

Ellipse

The curve obtained when a cone is cut by an inclined plane; it possesses two focal points where the sum of the distances from every point on the curve to these points is constant.

Kepler’s First Law

The law which states that the orbit of a planet is an ellipse with the Sun at one of the foci.

Kepler’s Second Law

The law stating that the line joining the planet and the Sun sweeps equal areas in equal intervals of time.

Kepler’s Third Law

The square of a planet's period of revolution around the Sun ($T^2$) is directly proportional to the cube of the mean distance ($r^3$) of the planet from the Sun.

Newton’s Universal Law of Gravitation

Every object in the Universe attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them: $F = G \frac{m_1m_2}{d^2}$.

Universal gravitational constant ($G$)

The constant of proportionality in Newton’s law of gravitation, with an experimentally measured value of $6.673 \times 10^{-11}\,N\,m^2\,kg^{-2}$.

Centre of mass

The point inside or outside an object at which the total mass of the object can be assumed to be concentrated.

Acceleration due to gravity ($g$)

The acceleration resulting from the earth's gravitational force on a body, directed toward the centre of the earth with a surface value of approximately $9.77\,m/s^2$.

Mass

The amount of matter present in an object; it is a scalar quantity and the measure of an object's inertia, remaining the same everywhere.

Weight

The force with which the earth attracts an object, defined as $W = m g$; it is a vector quantity directed towards the centre of the earth.

Gravitational waves

Waves on the fabric of space-time predicted by Einstein in 1916; they are emitted by astronomical objects and detected by instruments like LIGO.

Free fall

The motion of an object when it moves under the influence of the force of gravity alone, starting with an initial velocity of zero.

Gravitational potential energy

The energy stored in an object due to its position; for an object of mass $m$ at height $h$, it is given by $\Phi = -\frac{GMm}{R+h}$.

Escape velocity

The minimum initial velocity required for an object to overcome a planet's gravitational pull forever, calculated as $v_{esc} = \sqrt{\frac{2GM}{R}}$.