CDS Physics · Formula sheet
Gravitation formulas
2 formulas, 2 reference tables and 11 common traps for CDS Physics Gravitation, grouped by subtopic.
Gravitation and Weight
Learn this subtopic in the notesNewton's law of gravitation
Universal law of gravitation
- m₁, m₂the two masses
- distance between their centres
- universal gravitational constant
Weight, mass and g
Weight and surface gravity
- weight, in newtons
- mass of the body, in kilograms
- mass and radius of the planet
Common traps
The distance is squared
Doubling the distance makes the force one quarter, not one half. Halving it makes the force four times. Always square the distance factor before dividing.
Gravitation is its own law
Newton's law of gravitation does not follow from the laws of motion. A statement claiming it does is the false one.
G is not g
G is the universal constant, the same everywhere. g is the acceleration due to gravity at a place, about 9.8 m/s² on the earth's surface, and it changes from place to place and planet to planet.
Weight is a force, mass is not
Weight is the earth's pull on a body, in newtons, and it changes with g. Mass is the amount of matter, in kilograms, and stays fixed. Options like 'mass' or 'density' for the earth's pull are wrong.
g needs both mass and radius
contains the planet's mass and its radius. Neither alone fixes g.
Weight scales with g, not with its square
With the mass fixed, : if g becomes 5 times, the weight becomes 5 times. No squaring is needed here; the square belongs to the radius inside g.
Stars and Space
Learn this subtopic in the notesNearby stars and constellations
| Star or term | Fact |
|---|---|
| Sun | The nearest star; light takes about 8 min 20 s to reach us |
| Proxima Centauri | Nearest star after the Sun, about 4.24 light yearsQ CDS 2019 (I): of Sirius, Arcturus, Spica and Proxima Centauri, the nearest is Proxima Centauri. |
| Sirius | Brightest star of the night sky, about 8.6 light years |
| Arcturus and Spica | Bright stars much farther away (tens to hundreds of light years) |
| Constellation | A pattern of stars on the sky; the stars may be at very different distancesQ CDS 2019 (I): a constellation is a pattern of stars that may not be equidistant from the earth. |
Lagrange points and the GMRT
| Place or instrument | Fact |
|---|---|
| Sun-earth L1 | On the Sun-earth line, between them; home of Aditya-L1 |
| Sun-earth L2 | On the line, beyond the earth; home of the James Webb Space Telescope |
| Sun-earth L4 (and L5) | Sun, earth and the point form an equilateral triangleQ CDS 2024 (II): the Sun, the earth and L4 form an equilateral triangle. |
| GMRT | 30 parabolic dishes, each 45 m across, near PuneQ CDS 2024 (I): the GMRT consists of multiple parabolic antennas. |
Common traps
Brightest is not nearest
Sirius is the brightest star at night, but Proxima Centauri is the nearest after the Sun. Brightness depends on how much light a star gives out as well as on its distance.
A constellation is not a group in space
Its stars are joined up only as seen from the earth. Options saying the stars are equidistant from us, or that the pattern includes planets, are wrong.
The Sun is a star too
If a question asks for the star nearest to the earth with the Sun among the options, the answer is the Sun. Proxima Centauri is the nearest other star.
L4 and L5 are off the line
Only L1, L2 and L3 lie on the straight line through the two bodies. L4 and L5 make equilateral triangles with them, not isosceles or scalene ones.
The GMRT is many dishes, not one
The GMRT is an array of 30 parabolic dishes whose signals are combined. Options of a single dish, or of circular antennas, are wrong.