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FORMULA CHAPTER

Chapter 07 – Gravitation

ISCClass 11Physics11 formulas
Complete ISC Class 11 Physics Gravitation formula list covering Newton’s law of gravitation, acceleration due to gravity, gravitational potential and energy, satellites, orbital velocity and escape speed with clear notation and worked examples for exam preparation.
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1

Newton’s law of universal gravitation: Every two masses attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
Gravitational force (F) = \large\displaystyle \frac{\mathrm{G}\mathrm{m}_1\mathrm{m}_2}{\mathrm{r}^2}

2

Acceleration due to gravity at the surface (g) = \large\displaystyle \frac{\mathrm{G}\mathrm{M}}{\mathrm{R}^2}

3

Gravitational potential energy (U) = \large\displaystyle -\frac{\mathrm{G}\mathrm{M}\mathrm{m}}{\mathrm{r}}

4

Gravitational potential (V) = \large\displaystyle -\frac{\mathrm{G}\mathrm{M}}{\mathrm{r}}

5

Escape speed (vₑ) = \large\displaystyle \sqrt{\frac{2\mathrm{G}\mathrm{M}}{\mathrm{R}}}

6

Orbital speed (vₒ) = \large\displaystyle \sqrt{\frac{\mathrm{G}\mathrm{M}}{\mathrm{r}}}

7

Acceleration due to gravity at height h (gₕ) = \large\displaystyle \mathrm{g}\left(\frac{\mathrm{R}}{\mathrm{R}+\mathrm{h}}\right)^2

8

Acceleration due to gravity at depth d (g_d) = \large\displaystyle \mathrm{g}\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)

9

Orbital time period (T) = \large\displaystyle 2\pi\sqrt{\frac{\mathrm{r}^3}{\mathrm{G}\mathrm{M}}}

10

Total orbital energy (E) = \large\displaystyle -\frac{\mathrm{G}\mathrm{M}\mathrm{m}}{2\mathrm{r}}

11

Kepler’s third law: The square of a planet’s or satellite’s orbital period is proportional to the cube of its orbital radius.
\large\displaystyle \frac{\mathrm{T}^2}{\mathrm{r}^3}=\frac{4\pi^2}{\mathrm{G}\mathrm{M}}