Gravitation Lecture Notes Flashcards

Vocabulary flashcards covering key concepts, formulas, and constants from the Gravitation lecture transcript.

Sir Isaac Newton

The scientist who discovered gravitation.

Gravitational Force

An attractive universal force acting on any two bodies on the surface of the Earth as well as any two celestial objects, calculated as $F = \frac{GMm}{d^2}$.

Kepler's Third Law of Time Period

The law stating $T^2 \propto r^3$, which helped in formulating Newton's Universal Law of Gravitation and explaining the inverse square law.

Value of Universal Gravitational Constant ($G$)

$6.67 \times 10^{-11}\,N\,m^2/kg^2$.

Centripetal Force

A centre-seeking force or force that acts towards the centre of a circle.

Acceleration Due to Gravity ($g$)

The acceleration caused by gravitational force, given by the formula $g = \frac{GM}{R^2}$.

Weight ($W$)

The force given by the product of mass and acceleration due to gravity, expressed as $W = mg$.

Value of $g$ at the Pole

$9.832\,m/s^2$.

Value of $g$ at the Equator

$9.78\,m/s^2$.

Effect of Altitude on $g$

As altitude increases, the value of $g$ decreases.

Effect of Depth on $g$

As depth increases, the value of $g$ decreases.

Escape Velocity ($v_{esc}$)

The velocity required to escape the influence of gravitational force, given by $v_{esc} = \sqrt{2gR}$.

Escape Velocity Value on Earth

$11.2\,km/s$.

Centripetal Force

The force between the Sun and the planet Earth is responsible for the revolution of the planet and is inversely proportional to the square of the distance between them.

Earth's Gravitational Force

The force that the Earth exerts on any object at or around its surface, producing acceleration due to gravity.

Acceleration Due to Gravity

Denoted by $g$, it is calculated using the formula $g = \frac{GM}{R^2}$.

Acceleration due to Gravity Value

The average value of $g$ is considered as $9.77\,m/s^2$ for practical purposes.

Mass of Earth

The mass of Earth is approximately $6 \times 10^{24}$ kg.

Equatorial vs Polar Value of $g$

The value of $g$ is maximum at the poles ($9.83\,m/s^2$) and minimum at the equator ($9.78\,m/s^2$).

Effect of Altitude on $g$

As altitude increases, the value of $g$ decreases.

Effect of Depth on $g$

As depth increases, the value of $g$ decreases.

Weight of a Body

Defined as the force with which the Earth attracts it towards its center, expressed as $W = mg$.

Weight as a Vector Quantity

Weight changes from place to place on the surface of the Earth and varies with location.

Spring Balance

Used for measuring weight; two scale balances are used to compare masses.

Kepler's First Law

The orbit of a planet is an ellipse with the sun at one of the foci.

Kepler's Second Law

The line joining the planet and the sun sweeps equal areas in equal intervals of time.

Kepler's Third Law

The square of the time period of revolution around the sun is directly proportional to the mean distance of a planet from the sun.

Gravitational Potential Energy

Energy due to the shape or position, expressed as $U = -\frac{GMm}{R+h}$.

Escape Velocity

The initial velocity required to overcome the Earth's gravitational attraction, calculated as $v_{esc} = \sqrt{2gR}$.