Gravitation

Introduction

• Gravitation is the force of attraction between any two objects in the universe.

• It is a fundamental force of nature that keeps celestial bodies in orbit and governs the motion of objects on Earth.

Newton's Law of Universal Gravitation

• Every object in the universe attracts every other object with a force that is:

  • Directly proportional to the product of their masses.  

  • Inversely proportional to the square of the distance between them.

• The force acts along the line joining the centers of the two objects.  

• Mathematically, F = G (m₁ m₂) / r² where:

  • F is the gravitational force.

  • G is the universal gravitational constant (6.674* 10^-11 N m² kg^-2).

  • m₁ and m₂ are the masses of the two objects.

  • r is the distance between the centers of the two objects.

Kepler’s law of Planetary Motion:

1. Kepler's First Law (Law of Orbits):

• Statement: The orbit of every planet is an ellipse with the Sun at one of the two foci.  

  • Explanation: This law states that planetary orbits are not perfect circles, as previously believed, but rather elliptical. An ellipse is an oval-shaped curve with two focal points (foci). The Sun is located at one of these foci. This means that the distance between a planet and the Sun varies as the planet moves along its orbit.  

2. Kepler's Second Law (Law of Areas):

• Statement: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.  

  • Explanation: This law describes the speed of a planet's orbit. It implies that a planet moves faster when it is closer to the Sun and slower when it is farther away. This is because, in order to sweep out equal areas in equal times, the planet must cover a greater distance when it is closer to the Sun.  

3. Kepler's Third Law (Law of Periods):

• Statement: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.  

  • Explanation: This law relates the time it takes a planet to complete one orbit (its period) to the size of its orbit. The semi-major axis is half of the longest diameter of the ellipse. This law implies that planets farther from the Sun take longer to orbit it, and there is a precise mathematical relationship between their periods and distances.  

In simpler terms:

• Law 1: Planets move in elliptical paths around the Sun.  

• Law 2: Planets move faster when they are closer to the Sun.  

• Law 3: Larger orbits take longer to complete.

 Acceleration Due to Gravity

• When an object falls freely towards the Earth, it accelerates due to the Earth's gravitational pull.

• This acceleration is called the acceleration due to gravity ((g)).

• The value of (g) on Earth is approximately (9.8 m/s^2).

• (g) varies slightly with altitude and latitude.

Free Fall

• When an object falls freely under the influence of gravity alone, it is said to be in free fall.

• In free fall, the only force acting on the object is gravity.

Mass and Weight

• Mass is the amount of matter in an object.

• Weight is the force of gravity acting on an object.

• Weight (W) is related to mass (m) by the equation (W = mg).

• Mass is constant, while weight varies with the acceleration due to gravity.

Thrust and Pressure

• Thrust is the force acting perpendicularly on a surface.

• Pressure is the force acting per unit area on a surface.

• Pressure ((P)) is related to thrust ((F)) and area ((A)) by the equation (P = {F}/{A}).

Buoyancy

• Buoyancy is the upward force exerted by a fluid (liquid or gas) on an object immersed in it.

• The buoyant force is equal to the weight of the fluid displaced by the object (Archimedes' principle).

Archimedes' Principle

• When an object is fully or partially immersed in a fluid, it experiences an upward force equal to the weight of the fluid displaced by it.  

• This principle is used in the design of ships and submarines.

Relative Density

• Relative density is the ratio of the density of a substance to the density of a reference substance (usually water).

• It is a dimensionless quantity.  

• Relative density = ({Density of the substance}/ {Density of water})

Applications of Gravitation

• Gravitation explains the motion of planets around the Sun, the motion of the Moon around the Earth, and the tides in the oceans.

• It also explains why objects fall to the ground when dropped.

Remember:

• Gravitation is a universal force that affects all objects in the universe.

• The strength of the gravitational force depends on the masses of the objects and the distance between them.

• The acceleration due to gravity on Earth is approximately (9.8 m/s^2).

• Buoyancy is the upward force exerted by a fluid on an object immersed in it.

• Archimedes' principle states that the buoyant force is equal to the weight of the fluid displaced by the object.