The equation mgy for gravitational potential energy is valid only for objects near the surface of a planet. Consider two very large objects of mass m₁ and m₂, such as stars or planets, whose centers are separated by the large distance r. These two large objects exert gravitational forces on each other. You’ll learn in Chapter 13 that the gravitational potential energy is

where G = 6.67 × 10^-11 N m²/kg² is the gravitational constant.

a. Sketch a graph of U versus r. The mathematical difficulty at r = 0 is not a physically significant difficulty because the masses will collide before they get that close together.

b. What separation r has been chosen as the point of zero potential energy? Does this make sense? Explain.

c. Two stars are at rest 1.0 × 10¹⁴ m apart. This is about 10 times the diameter of the solar system. The first star is the size of our sun, with a mass of 2.0 × 10³⁰ kg and a radius of 7.0 × 10⁸ m. The second star has mass 8.0 × 10³⁰ kg and radius of 11.0 × 10⁸ m. Gravitational forces pull the two stars together. What is the speed of each star at the moment of impact?

Transcribed Image Text:

Gm, m2 U = r