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1800-102-2727In this chapter, various concepts related to gravitation, such as gravitational field, Kepler's law, black holes etc., have been discussed. Initially, historical introductions about space, Newton's assumptions and the universal law of gravitation have been explained. The concepts like gravitational potential energy, gravitational potential, calculation of Potential due to a Point Mass, and so on have been explained in a detailed yet simple manner.
All planets move in elliptical orbits surrounding the sun. At a focus point, the radius vector connecting the sun to a planet is said to sweep equal areas in equal time. In addition, the square of the time period of a planet is proportional to the cube of the semi-major axis of the ellipse. Newton further generalised the law. He said that the Earth and all the other material bodies in the universe attract each other as per the equation. Thus, the constant G is called the universal constant of gravitation, and its value is found to be 6.67 × 10 – 11 N–m^{2}/kg^{2}.
Further, in the next section, the concepts of the gravitational field, the relation between the gravitational field and potential, calculation of gravitational field due to a Point Mass, calculation of gravitational field due to a Uniform Circular Ring at a Point on its axis, calculation of gravitational field due to a Uniform Disc at a Point on its axis, calculation of gravitational field due to a Uniform Thin Spherical Shell in different cases, calculation of gravitational field due to a Uniform Solid Sphere in different cases have been discussed.
For a two-particle system, the gravitational potential energy U(r) = -Gm_{1} m_{2}/r Here, m_{1} and m_{2} are said to be the masses of the particles, r is the separation between the particles and the potential energy is chosen to be zero when the separation is infinite.
In the next section, Kepler's law, weightlessness in a satellite, escape velocity, and gravitational binding energy has been explained. Then, a brief explanation about black holes has been provided. Next, inertial and gravitational masses are explained, and the equivalence of inertial and gravitational masses has been stated. Finally, possible changes in the law of gravitational force have been discussed.