Gravitation: Comprehensive NEET Physics Notes

1. Introduction to Gravitation

1.1 Historical Background

Early in our lives, we become aware of the tendency of all material objects to be attracted towards the earth. Historically, it was the Italian physicist Galileo who recognized that all bodies, irrespective of their masses, are accelerated towards the earth with a constant acceleration. Galileo’s experiments with rolling bodies on inclined planes led to the accurate value of the acceleration due to gravity.

Did You Know? Galileo's observations paved the way for future scientists like Newton to explore gravitational laws.

2. Kepler’s Laws

2.1 Law of Orbits

All planets move in elliptical orbits with the Sun situated at one of the foci.

Diagram of an elliptical orbit with the Sun at one focus

NEET Tip: Remember that orbits are not perfect circles but ellipses, which can appear as stretched circles.

2.2 Law of Areas

The line that joins any planet to the Sun sweeps out equal areas in equal intervals of time. This implies that planets move faster when they are nearer to the Sun and slower when they are farther from the Sun.

2.3 Law of Periods

The square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of its orbit.

$T^2\propto a^3$

Mnemonic: "Orbits Areas Periods" - Kepler's laws of planetary motion: Orbits (elliptical), Areas (swept equal in equal time), Periods ($T^2\propto a^3$).

3. Universal Law of Gravitation

3.1 Newton’s Universal Law

Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

$F=G\frac{m_1{m}_2}{r^2}$

Where:

• $F$ is the gravitational force between two masses,
• $G$ is the universal gravitational constant ($6.67\times 10^{-11}{\text{Nm}}^2{\text{kg}}^{-2}$),
• $m_1$​ and $m_2$​ are the masses of the objects,
• $r$ is the distance between the centers of the two masses.

Common Misconception: The gravitational force between two bodies is not influenced by the presence of other masses nearby.

4. The Gravitational Constant

4.1 Measurement of G

The gravitational constant GGG was first measured by Henry Cavendish using a torsion balance. The value is approximately $6.67\times 10^{-11}{\text{Nm}}^2{\text{kg}}^{-2}$.

Diagram of Cavendish's torsion balance experiment

Did You Know? Henry Cavendish’s experiment was so accurate that it is still used as a standard method for measuring $G$.

5. Acceleration due to Gravity of the Earth

5.1 Value of $g$

The acceleration due to gravity $g$ on the surface of the Earth is given by:

$g=\frac{G{M}_E}{R_E^2}$

Where:

• $M_E$​ is the mass of the Earth,
• $R_E$​ is the radius of the Earth.

5.2 Variation of g

The value of $g$ decreases with altitude and depth. At a height $h$ above the Earth's surface, the acceleration due to gravity is:

$g_h=g\left(1-\frac{2h}{R_E}\right)$

At a depth $d$below the Earth's surface, the acceleration due to gravity is:

$g_d=g\left(1-\frac{d}{R_E}\right)$

Real-life Application: This variation is crucial for satellite launches and underground engineering projects.

Quick Recap

• Kepler's Laws: Describe planetary motion.
• Universal Law of Gravitation: Explains the force between any two masses.
• Gravitational Constant (G): Essential for calculating gravitational force.
• Acceleration due to Gravity (g): Varies with altitude and depth.

Concept Connection

Understanding gravitation is crucial for topics in both Biology (e.g., the effect of gravity on the human body) and Chemistry (e.g., the behavior of gases under different gravitational forces).

Practice Questions

1. Question: Calculate the gravitational force between two masses of 5 kg and 10 kg separated by a distance of 2 meters. Solution: $F=G\frac{m_1{m}_2}{r^2}=6.67\times 10^{-11}\times \frac{5\times 10}{2^2}=8.34\times 10^{-10}\text{N}$
2. Question: A satellite is at a height of 300 km above the Earth's surface. Calculate the acceleration due to gravity at that height. Solution: $g_h=g\left(1-\frac{2h}{R_E}\right)=9.8\left(1-\frac{2\times 300,000}{6,400,000}\right)\approx 9.2{\text{m/s}}^2$
3. Question: Using Kepler's third law, calculate the orbital period of a planet if the semi-major axis of its orbit is 4 AU (astronomical units). Solution: $T^2\propto a^3$, $T^2=4^3$ , $T=\sqrt{64}=8\text{years}$
4. Question: What is the escape velocity from the Earth’s surface? Solution: $v_e=\sqrt{2g{R}_E}$, $v_e=\sqrt{2\times 9.8\times 6.4\times 10^6}\approx 11.2\text{km/s}$
5. Question: A body weighs 63 N on the surface of the Earth. What is its weight at a height equal to the Earth's radius? Solution: $g_h=g(\genfrac{}{}{0ex}{}{}{(R_E+h{)}^2}$