Physics Gravitation

It is due to a concept taken from Newton's Law of Gravitation. It says that each mass element of the shell puts an attractive force on a particle inside but due to the fact that the shape of the shell is symmetrical, these forces cancel out in every direction.
To prove it mathematically, one can use Gauss's Law for Gravitation. It states that inside a uniformly distributed spherical shell, the net gravitational field is zero. It differs from electrostatics, which states that a conducting shell blocks or stops the external electric fields. The shielding concept is not part of gravitation where the external bodies exert a gravitational force on an object inside the shell. It is the fundamental property of astrophysics and helps in understanding why the gravitational field inside a star or planet depends only on the mass enclosed within a given radius.

Gravitational Potential Energy (U) is the energy an object has due to its position in a gravitational field. It is defined as:

Where M represents the mass of the larger body, m is the mass of the smaller body, r is the distance between them, and G stands for the gravitational constant.
G is written with a negative sign to show that the gravitational potential energy is always lower than zero and the values even decrease as the objects move apart from each other. It implies that to separate two masses, work should be done against the gravity. At infinity, U = 0, implying that no external force is required to keep them apart. When two objects are closer, potential energy is more negative which implies a stronger gravitational attraction. The concept is very important in fields such as orbital mechanics and astrophysics.

Kepler's laws refer to the motion of planets around the Sun and it offers various insights into the celestial mechanics. It includes the following:

• The First Law (Law of Orbits) states that all planets move in elliptical orbits, and the Sun is at one focus. It is against the previous belief that planetary orbits were perfect circles.
• The Second Law (Law of Areas) states the line joining the Sun and a planet sweeps out equal areas in equal time intervals. It means that the planets near to Sun move faster and the ones at more distance, move slower.
• The third Law (Law of Periods) says that the square of a planet's orbital period is directly proportional to the cube of the semi-major axis of its orbit. The mathematical formula is:

According to Newton's Law of Universal Gravitation, each object in the universe attracts every other object with a force that depends on the distance between them and their masses. This force is mathematically given by the following formula:

Here, F is the gravitational force, G is the gravitational constant and m? and m? refers to the masses of the objects, and r represents the distance between them.

Newton's Law of Universal Gravitation explains the behaviour of tides due to the Moon's gravity, planetary motion, and even how satellites orbit the Earth. This law is widely used in space research and astrophysics to find out the masses of the celestial bodies and how they interact with each other. It is accurate in most cases but for extreme gravitational fields, instead of Newton's law, Einstein's General Theory of Relativity is more useful.