Gravitation — Complete Formula

Newton’s Law of Gravitation

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Gravitational Force	[F = G \dfrac{m_1 m_2}{r^2}]	[F] = force, [G] = gravitational constant, [m_1, m_2] = masses, [r] = separation	N	Always attractive ⭐
Value of G	[G = 6.67 \times 10^{-11}]	—	N·m²/kg²	Universal constant

💡 Memory Hint:
Force ∝ product of masses / square of distance

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Gravitational Field	[g = \dfrac{F}{m}]	[g] = field, [F] = force, [m] = test mass	N/kg	Force per unit mass
Field due to Mass	[g = G \dfrac{M}{r^2}]	[M] = mass of body	m/s²	Same as acceleration due to gravity ⭐
On Earth Surface	[g = \dfrac{GM}{R^2}]	[R] = radius of Earth	m/s²	Standard result ⭐

💡 Memory Hint:
Field = force per unit mass

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
At Height (h)	[g_h = g\left(1 – \dfrac{2h}{R}\right)]	[h] = height	m/s²	For [h \ll R] ⚠️
At Depth (d)	[g_d = g\left(1 – \dfrac{d}{R}\right)]	[d] = depth	m/s²	Linear decrease ⭐
Due to Rotation	[g_{eff} = g – \omega^2 R]	[\omega] = angular velocity of Earth	m/s²	Minimum at equator ⚠️

💡 Memory Hint:

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Gravitational Potential	[V = -G \dfrac{M}{r}]	[V] = potential	J/kg	Negative sign important ⚠️
Potential Energy	[U = -G \dfrac{Mm}{r}]	[U] = potential energy	J	Always negative ⭐
Relation	[U = mV]	—	—	Connects PE and potential

💡 Memory Hint:
Gravitational energy = always negative (bound system)

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Escape Velocity	[v_e = \sqrt{\dfrac{2GM}{R}}]	[v_e] = escape velocity	m/s	Independent of mass ⭐
Using g	[v_e = \sqrt{2gR}]	—	m/s	Simplified form

💡 Memory Hint:
Escape → √2 times orbital velocity

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Orbital Velocity	[v = \sqrt{\dfrac{GM}{r}}]	[r] = orbital radius	m/s	For circular orbit ⭐
Time Period	[T = 2\pi \sqrt{\dfrac{r^3}{GM}}]	[T] = time period	s	Kepler’s 3rd law ⭐
Angular Velocity	[\omega = \sqrt{\dfrac{GM}{r^3}}]	—	rad/s	Related to time period

💡 Memory Hint:

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Kinetic Energy	[K = \dfrac{GMm}{2r}]	—	J	Half of magnitude of PE ⭐
Potential Energy	[U = -\dfrac{GMm}{r}]	—	J	Negative
Total Energy	[E = -\dfrac{GMm}{2r}]	—	J	Bound system ⭐

💡 Memory Hint:
[K : U : E = 1 : -2 : -1]

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Time Period	[T = 24 , \text{hours}]	—	s	Same as Earth rotation ⭐
Orbital Radius	[r^3 = \dfrac{GMT^2}{4\pi^2}]	—	m	Derived from Kepler’s law
Angular Velocity	[\omega = \dfrac{2\pi}{T}]	—	rad/s	Fixed relative to Earth

💡 Memory Hint:
Appears stationary from Earth

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