Kepler’s third law of planetary motion is called the ‘law of periods’ According to this law, the square of the time period of a planet is directly proportional to the cube of the semi-major axis of its elliptical orbit. That is, T squared is proportional to R cubed, where T is the time taken by the planet for one rotation and R is the length of the semi-major axis of its elliptical orbit. Kepler’s laws revolutionised the field of astronomy and have helped people understand the configuration and movement of planets better.

Kepler’s second law of planetary motion is the ‘law of areas’. According to this law, the line joining the sun and a planet, sweeps equal areas in equal intervals of time. Consider a planet revolving around the sun.
 
Let ‘P₁’ and ‘P₂’ represent its positions at the start and end of 30-day duration. Let A₁ represent the area swept during this period. Similarly, let ‘P₃’ and ‘P₄’ represent two positions of the planet during its revolution for a 30-day duration represented by A₂. According to Kepler’s second law of planetary motion, area A₁ equals area A₂. The concept of Kepler’s second law can be understood by the fact that the angular momentum of the planet revolving in its orbit remains constant. This is because it is under the influence of a central force.
 
The force of attraction pulls the planet towards the sun and the magnitude depends on the distance between them. For a body under the action of a central force, the angular momentum, ‘L’, which is the product of ‘mvr,’ remains constant. Where, ‘r’ is the radius vector; ‘v’ is the velocity vector and ‘m’ the mass of the body.
 

Kepler’s first law, the ‘law of orbits’, states that all the planets revolve in elliptical orbits with the sun at one of the focii of the ellipse (path of the planets).
 
Observe the figure of ellipse. Points F₁ and F₂ are called the focii, and ‘O,’ is the centre of the ellipse. For any point ‘P’ on the ellipse, the sum of the lengths PF₁ and PF₂ is constant. So, as per the first law, the sun is at one of the focii of the ellipse and the planets rotate around it in elliptical orbits. Also the sum of the lengths PF₁ and PF₂ is always constant.

Work done by a variable force

• The variable force is more commonly encountered than the constant force.
• If the displacement Dx is small, we can take the force F (x) as approximately constant and the work done is then
  DW =F (x) Dx

For total work, we add all work done along small displacements.

Bernoulli’s principle states that

The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure and the kinetic energy of the fluid motion, remains constant.

Ratio of the density of a substance to the density of water at 4° C is called specific gravity of the substance.

The space in the surrounding of any body in which its gravitational pull can be experienced by other bodies is called gravitational field. The gravitational force acting per unit mass at Earth any point in gravitational field is called intensity of gravitational field at that point.

The axis about which a body rotates is called the axis of rotation.

Magnus effect is the generation of a sidewise force on a spinning cylindrical or spherical solid immersed in a fluid (liquid or gas) when there is relative motion between the spinning body and the fluid. This effect explains commonly observed deviations from the typical trajectories of spinning balls in sport like table tennis, tennis, volleyball, golf, baseball and cricket. 

Polar satellites revolve around the earth in a north-south direction around the earth as opposed to east-west like the geostationary satellites. They are very useful in applications where the field vision of the entire earth is required in a single day. Since the entire earth moves below them, this can be done easily. They are used in weather applications where predicting weather and climate-based disasters can be done in a short time. They are also used as relay stations.

Examples are: SPOT, IERS, etc..

Magnus Effect

• Dynamic lift by virtue of spinning is known as Magnus effect.
• Magnus effect is a special name given to dynamic lift by virtue of spinning.
• Example:-Spinning of a ball.
  • Case1:-When the ball is not spinning.
    • The ball moves in the air it does not spin, the velocity of the ball above and below the ball is same.
    • As a result there is no pressure difference.(ΔP= 0).
    • Therefore there is no dynamic lift.