Kepler's Laws of Planetary Motion

Planetary motion follows three laws described by Johannes Kepler, known as Kepler's laws
Kepler's laws were derived from studying data on planetary positions and motion
Kepler's First Law: The orbit of a planet is an ellipse with the Sun at one of the foci
Kepler's Second Law: The line joining the planet and the Sun sweeps equal areas in equal intervals of time
Kepler's Third Law: The square of the period of revolution of a planet is directly proportional to the cube of the mean distance of the planet from the Sun

Newton formulated his theory of Universal Gravity, which states that every object in the Universe attracts every other object with a definite force
The force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them
The gravitational force can be expressed mathematically as F = G * (m1 * m2) / d^2, where G is the Universal Gravitational constant

Johannes Kepler (1571-1630) was a German astronomer and mathematician who discovered Kepler's laws
Sir Isaac Newton (1642-1727) was an English scientist who formulated Newton's laws of motion and the law of Universal Gravitation

A force is necessary to change the speed or direction of motion of an object
Newton's laws of motion and the law of Universal Gravitation help explain the behavior of objects on Earth and in the Universe

An object moving in a circle experiences a force directed towards the centre of the circle, known as the centripetal force
The centripetal force is necessary to keep the object moving in a circle and not flying off in a straight line
Examples of circular motion include the moon orbiting the Earth and the Earth orbiting the Sun

Gravitation is a universal force that acts between all objects with mass
The force of gravitation is responsible for the motion of planets, stars, and galaxies
The force of gravitation is also responsible for the falling of objects on Earth

The centripetal force is related to the speed and radius of the circle by the equation F = m * v^2 / r
The force of gravitation provides the centripetal force necessary for uniform circular motion
The speed of an object in uniform circular motion can be expressed in terms of the period of revolution and the radius of the circle

Example 1: Calculating the gravitational force between two objects
Example 2: Calculating the velocity of an object in uniform circular motion### Mahendra's Acceleration
Mahendra's mass is 75 kg, and the force applied to him is 733 N.
Mahendra's acceleration is calculated as 9.77 m/s² using the formula a = F/m.
After 1 second, Mahendra's velocity is 9.77 m/s.

Every object attracts every other object with the same force.
The gravitational force due to the earth acts on the moon and artificial satellites, causing them to orbit the earth.

The earth exerts a gravitational force on objects near it, resulting in acceleration.
This acceleration is called acceleration due to gravity, denoted by 'g', and is directed towards the center of the earth.
The value of g on the surface of the earth is 9.77 m/s².

The value of g can be calculated using Newton's universal law of gravitation.
The formula for g is g = GM/r², where G is the gravitational constant, M is the mass of the earth, and r is the distance from the center of the earth.
The value of g on the surface of the earth is 9.77 m/s².

The value of g changes along the surface of the earth due to the earth's slightly ellipsoidal shape.
The value of g is highest at the poles (9.832 m/s²) and lowest at the equator (9.78 m/s²).
The value of g also changes with height, decreasing as the distance from the center of the earth increases.
The value of g changes if we go inside the earth, decreasing as the distance from the center of the earth decreases.

The value of g decreases with increasing height, but the decrease is small for heights compared to the earth's radius.
The value of g also changes with depth, decreasing as we go deeper inside the earth.

Mass is the amount of matter present in an object, measured in kilograms (kg).
Mass is a scalar quantity and does not change, even when going to another planet.
Weight is the force with which the earth attracts an object, measured in Newtons (N).
Weight is a vector quantity and changes from place to place, depending on the value of g.
Colloquially, weight is often used to refer to mass, but scientifically, weight refers to the gravitational force on an object.

Gravity is a universal force, acting between every point mass, attracting them to each other along the line intersecting both points.
This force is a two-way interaction, where both objects attract each other with the same force, but in opposite directions.
Compared to other fundamental forces, gravity is much weaker, but it can act over vast distances, even across millions of kilometers.

The gravitational force (F) between two objects is calculated by the equation: F = G * (m1 * m2) / r^2, where G is the gravitational constant (6.67408e-11 N*m^2/kg^2).
The masses of the two objects are represented by m1 and m2, and r is the distance between their centers.
A gravitational field is a region around an object where the gravitational force can be detected, and it is a vector field surrounding every object with mass.
Gravitational potential energy (U) is the energy an object has due to its position within a gravitational field, calculated by the equation: U = m * g * h.
The variables in this equation are the mass of the object (m), the acceleration due to gravity (g, approximately 9.8 m/s^2 on Earth), and the height of the object above the ground (h).