Gravity, Universal Gravitation Constant - Gravitational Force Between Earth, Moon & Sun, Physics

The video begins by illustrating how to calculate the force of gravity between a 60 kg person and an 80 kg person who are 50 cm apart. The formula F = G * (m1 * m2) / r^2 is introduced. The distance is converted from centimeters to meters, and the universal gravitational constant (G) value is provided. The calculation results in a very small gravitational force of 1.28 * 10^-6 Newtons.

The second problem calculates the force of gravity on a 25 kg block resting on Earth. The mass of Earth and its radius are provided. The distance 'r' in the formula is approximated as the Earth's radius. The resulting gravitational force is approximately 245 Newtons, which can also be easily found by multiplying mass by Earth's gravitational acceleration (9.8 m/s^2).

The video then tackles the gravitational force exerted on the Earth by the Sun. The masses of both the Sun and Earth, and the distance between them, are given. The calculation using the universal gravitation formula yields a significant force of 3.54 * 10^22 Newtons, emphasizing that the forces exerted by each body on the other are equal in magnitude.

Problem four involves finding the distance between two planets, Planet X and Planet Y, given their masses and the gravitational force between them. The universal gravitation formula is rearranged to solve for 'r' (distance). After plugging in the given values, the calculated distance between the centers of the two planets is approximately 5.0 * 10^9 meters (5 billion meters).

The fifth problem calculates the net force on the Moon when it is positioned between the Earth and the Sun. The forces exerted by the Sun and Earth on the Moon are calculated separately. Since these forces are anti-parallel (opposing directions), the net force is their difference. The sun's gravitational pull on the moon is found to be greater than Earth's, resulting in a net force directed towards the Sun (negative direction) with a value of -2.398 * 10^20 Newtons.

Finally, the video addresses the net force on the Moon when the gravitational forces from the Earth and the Sun act at right angles to each other. Using the previously calculated individual forces from problem five, the net force is found using the Pythagorean theorem (as the hypotenuse of a right triangle). The result is a net force of 4.812 * 10^20 Newtons acting on the Moon.