What equation represents the gravitational potential energy of two masses?

The correct equation representing the gravitational potential energy of two masses is given by the formula ( Ep = -\frac{G(m_1 \cdot m_2)}{r} ). This equation arises from the universal law of gravitation and describes the gravitational potential energy between two point masses ( m_1 ) and ( m_2 ) that are separated by a distance ( r ).

In this context, ( G ) is the gravitational constant, which quantifies the strength of the gravitational force between these two masses. The negative sign indicates that gravitational potential energy is a measure of the work done against the gravitational force to separate the two masses. As the two masses move closer together, the potential energy becomes more negative, reflecting the fact that they are in a bound state.

This equation is specifically designed for situations involving two masses in a gravitational field, making it suitable for calculations involving large distances or celestial mechanics, such as planets or stars.

The other choices represent different types of energy. The formula ( Ep = mgh ) pertains to the gravitational potential energy in a uniform gravitational field, such as near the surface of the Earth, where ( h ) is the height above a reference point. The equation ( Ep