Gravitational potential energy dimensional formula

Equation Symbols Meaning in words U G = − G m 1 m 2 r U_G = -\dfrac U G ​ = − r G m 1 ​ m 2 ​ ​ U, start subscript, G, end subscript, equals, minus, start fraction, G, m, start subscript, 1, end subscript, m, start subscript, 2, end subscript, divided by, r, end fraction U G U_G U G ​ U, start subscript, G, end subscript is gravitational potential energy, G G G G is the gravitational constant, m 1 m_1 m 1 ​ m, start subscript, 1, end subscript and m 2 m_2 m 2 ​ m, start subscript, 2, end subscript are masses, and r r r r is the distance between centers of mass of the two objects Gravitational potential energy at large distances is directly proportional to the masses and inversely proportional to the distance between them. The gravitational potential energy increases as r r r r increases. Figure 1: An elliptical path of a planet around the Sun. When the planet is closest to the Sun, speed v v v v and kinetic energy are the highest, and gravitational potential energy is the lowest. When the planet moves farther away, the speed and kinetic energy decrease, and the gravitational potential energy increases. At all points in the orbit, angular momentum and energy are conserved. This means that the Earth’s distance from Sun r r r r varies throughout the orbit. There is no net external force or torque acting on the Sun-planet system, and the only force is gravity between the Sun and planet. Therefore, angular momentum and energy remain constant. However, the gravitational potentia...