PRELIMS

04. Gravitation

1. Newton's Law of Gravitation

Definition: Every body attracts every other body with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Formula:
- Universal Gravitational Constant (G): .

2. Gravity and Acceleration due to Gravity (g)

3. Variation in the Value of 'g'

Height & Depth: decreases with height above or depth below the Earth's surface.
Poles vs. Equator: is maximum at the poles and minimum at the equator.
Earth's Rotation:
- decreases due to the rotation of the Earth.
- If the angular speed of the Earth increases, decreases (and vice versa).
- Weightlessness: If the Earth were to rotate 17 times faster, a body at the equator would become weightless.

4. Weight of a Body in a Lift

Stationary / Uniform Speed: Apparent weight = True weight (net acceleration = 0).
Lift Accelerating Upward: Apparent weight increases (Apparent weight = ).
Lift Accelerating Downward: Apparent weight decreases (Apparent weight = ).
Lift in Free Fall ( ): Apparent weight = zero (state of weightlessness).

5. Geostationary & Geosynchronous Satellites

Conditions for a Geostationary Satellite:
- Revolves in the equatorial plane.
- Direction: West to East (same as Earth's rotation).
- Period: 24 hours (same as Earth's rotation period), so it appears stationary relative to a point on Earth.
Height: Approximately 36,000 km above the Earth's surface.
Orbit: Also known as the Parking Orbit or Clarke Orbit.
Fact: Arthur C. Clarke was the first to predict communication satellites in geostationary orbit (1945).
Geostationary vs. Geosynchronous (Confused Pair): A geosynchronous orbit has a period equal to Earth's rotation (24 hrs) but may be inclined to the equatorial plane; a geostationary orbit is a special case of geosynchronous orbit that is additionally circular and in the equatorial plane (0° inclination), so it appears fixed over one point on Earth.
Polar Orbit (Sun-synchronous): Passes over (or near) both poles at low altitude (typically 500–800 km); period of a few hours (~100 minutes); used for remote sensing/mapping satellites (e.g., India's IRS/Cartosat series) since it scans the entire Earth as the planet rotates beneath it.

6. Kepler's Laws of Planetary Motion

First Law (Law of Orbits): Every planet revolves around the Sun in an elliptical orbit, with the Sun at one of the two foci.
Second Law (Law of Areas): The line joining the planet and the Sun sweeps out equal areas in equal intervals of time (hence a planet moves faster when nearer the Sun — Perihelion — and slower when farther — Aphelion).
Third Law (Law of Periods): The square of the time period of revolution of a planet is directly proportional to the cube of the semi-major axis of its orbit ( ).

7. Orbital Velocity

Definition: The velocity required to keep a satellite in a stable circular orbit around the Earth.
Formula: ; for a satellite close to Earth's surface, .
Relation to Escape Velocity: .

Escape Velocity (ve)

Definition: Minimum velocity required for a body to go out of Earth's gravitational field and never return.
Formula: .
- is approx. 1.41 times the orbital velocity.
- Increase by 41%, and it becomes .
Standard Values:
- Earth: 11.2 km/s.
- Moon: 2.4 km/s.
Note: Independent of mass, shape, size, or direction of projection. Also called Second Cosmic Velocity.

UPSC Relevance

Gravitation is the basis for many S&T questions on Space exploration and satellite orbits.

Concept Traps: The 17x rotation speed for weightlessness and the independent nature of relative to the object's mass.
Orbital Mechanics: Distinguishing between Geostationary and Geosynchronous, and Geostationary vs. Polar orbits (used for different satellite applications — communication vs. remote sensing).
Lift Problems: Classic conceptual questions on "apparent weight" vs "true weight", including the free-fall weightlessness case.
Kepler's Laws: Elliptical orbits and the relation are recurring conceptual questions, including perihelion/aphelion speed variation.

04. Gravitation ​