At equator ($\lambda = 0^\circ$), $g' = g - \omega^2 R$ (maximum effect).

Condition for weightlessness at equator: $\omega = \sqrt{\frac{g}{R}}$ (new time period $T = 2\pi \sqrt{\frac{R}{g}} \approx 1.4 \text{ hr}$).

Mass of Earth: $M = \frac{gR^2}{G}$ (approx. $5.98 \times 10^{24} \text{ kg}$)
Density of Earth: $\rho = \frac{3g}{4\pi GR}$ (approx. $5478.4 \text{ kg/m}^3$)

Feature	Inertial Mass ($m_i$)	Gravitational Mass ($m_g$)
Definition	Measures inertia ($F=m_i a$)	Determines gravitational pull ($F=G \frac{M m_g}{R^2}$)
Effect of Gravity	No effect	Directly related
Measurement	Newton's 2nd Law (inertial balance)	Newton's Law of Gravitation (spring balance)
Relation	Experimentally found $m_i = m_g$

Definition: Space around a body where its gravitational attraction can be experienced.
Gravitational Field Intensity ($\vec{I}$): Force experienced by a unit test mass.
- $\vec{I} = \frac{\vec{F}}{m_{\text{test}}}$
- For point mass $M$: $I = \frac{GM}{r^2}$ (directed towards $M$).
- $I = g$ (acceleration due to gravity).
- Unit: N/kg or m/s$^2$. Dimension: $[M^0 L T^{-2}]$.
- $I=0$ at $r = \infty$.
- Superposition principle applies: $\vec{I}_{\text{net}} = \vec{I}_1 + \vec{I}_2 + \dots$

Body	Outside ($r > R$)	On Surface ($r=R$)	Inside ($r < R$)
Uniform Solid Sphere (Mass M, Radius R)	$I = \frac{GM}{r^2}$	$I = \frac{GM}{R^2}$	$I = \frac{GMr}{R^3}$
Spherical Shell (Mass M, Radius R)	$I = \frac{GM}{r^2}$	$I = \frac{GM}{R^2}$	$I = 0$

Definition: Negative of work done per unit mass in bringing a test mass from infinity to a point.
Formula: $V = -\frac{GM}{r}$ (Scalar quantity)
Unit: Joule/kg or m$^2$/s$^2$. Dimension: $[M^0 L^2 T^{-2}]$.
$V=0$ at $r=\infty$. Potential is always negative.
Relation with intensity: $I = -\frac{dV}{dr}$ (Negative gradient).
Superposition principle applies: $V_{\text{net}} = V_1 + V_2 + \dots$

Body	Outside ($r > R$)	On Surface ($r=R$)	Inside ($r < R$)
Uniform Solid Sphere (Mass M, Radius R)	$V = -\frac{GM}{r}$	$V = -\frac{GM}{R}$	$V = -\frac{GM}{2R^3}(3R^2 - r^2)$
Spherical Shell (Mass M, Radius R)	$V = -\frac{GM}{r}$	$V = -\frac{GM}{R}$	$V = -\