Table of Contents
1. Introduction to Gravitation
Gravitation, introduced in class 11 gravitation, is the force of attraction between any two objects in the universe. Important points:
- Galileo demonstrated that objects fall with the same acceleration, regardless of mass.
- Contributions from Aryabhatta and Copernicus laid the groundwork for understanding planetary motion.
2. Kepler’s Laws of Planetary Motion
These laws, crucial for class 11 gravitation, describe planetary orbits:
- Law of Orbits: Planets move in elliptical paths with the Sun at one focus.
- Law of Areas: Equal areas are swept in equal time, implying variable speeds.
- Law of Periods: The square of orbital time is proportional to the cube of the orbit’s semi-major axis.
3. Newton’s Universal Law of Gravitation
This law underpins class 11 gravitation concepts:
F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}F=Gr2m1m2
- F: Gravitational force
- G: Gravitational constant (6.67×10−11 Nm2kg−26.67 \times 10^{-11} \, \text{Nm}^2\text{kg}^{-2}6.67×10−11Nm2kg−2).
- Useful for solving force interactions between two masses.
4. Acceleration Due to Gravity (g)
The value of ggg, derived in class 11 gravitation, varies based on location:
g=GMR2g = \frac{GM}{R^2}g=R2GM
- At height hhh:
gh≈g(1−2hR)g_h \approx g \left( 1 – \frac{2h}{R} \right)gh≈g(1−R2h) - At depth ddd:
gd=g(1−dR)g_d = g \left( 1 – \frac{d}{R} \right)gd=g(1−Rd)
5. Gravitational Potential Energy
Energy in a gravitational field:
U=−GMmrU = -\frac{GMm}{r}U=−rGMm
- This equation, central to class 11 gravitation, explains why potential energy in a bound system is negative.
6. Escape Velocity
Escape velocity, covered in class 11 gravitation, is the speed required to leave Earth’s gravity:
vescape=2GMRv_{\text{escape}} = \sqrt{\frac{2GM}{R}}vescape=R2GM
- On Earth, vescape≈11.2 km/sv_{\text{escape}} \approx 11.2 \, \text{km/s}vescape≈11.2km/s.
7. Satellites and Orbital Motion
Class 11 gravitation also includes satellite motion:
- Orbital velocity:
vorbit=GMR+hv_{\text{orbit}} = \sqrt{\frac{GM}{R+h}}vorbit=R+hGM - Total energy of a satellite:
Etotal=−GMm2(R+h)E_{\text{total}} = -\frac{GMm}{2(R+h)}Etotal=−2(R+h)GMm
8. Practice Problems
To master class 11 gravitation, focus on solving:
- Gravitational force between masses.
- Variations in ggg at different locations.
- Escape velocity and satellite energy problems.