I am given an equation (attatched image) and am told that G = newtons gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance separating them. Consider m1 to be stationary with m2 undergoing uniform circular motion around m1 at a distance r. How do I show that GPE = -2KE for any gravitational circular orbit (where KE is the kinetic energy of object 2). ### Gravitational Potential Energy FormulaThe formula for Gravitational Potential Energy (GPE) is given by:\[GPE = -\frac{G m_1 m_2}{r}\]#### Explanation:- **GPE**: Gravitational Potential Energy, representing the energy due to gravitational attraction between two masses.- **G**: Universal Gravitational Constant, approximately \(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2\).- **\(m_1\) and \(m_2\)**: The masses of the two objects interacting gravitationally.- **\(r\)**: The distance between the centers of the two masses.This equation indicates that the gravitational potential energy is inversely proportional to the distance between the two objects and directly proportional to the product of their masses. The negative sign signifies that the force is attractive.

Given object 1 has mass m1 and object 2 has mass m2 which under go circular motion about first one…

am given an equation (attatched image) and am told that G = newtons gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance separating them. Consider m1 to be stationary with m2 undergoing uniform circular motion around m1 at a distance r. How do I show that GPE = -2KE for any gravitational circular orbit (where KE is the kinetic energy of object 2).

am given an equation (attatched image) and am told that G = newtons gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance separating them. Consider m1 to be stationary with m2 undergoing uniform circular motion around m1 at a distance r. How do I show that GPE = -2KE for any gravitational circular orbit (where KE is the kinetic energy of object 2).

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