One consequence of general relativity is that a clock in a gravitational field runs slower. This time dilation is distinct from the time dilation from relative motion (special relativity) and is given by ∆t = ∆t₀/√ 1 - 2 2GM/(Rc²), where ∆t is the dilated time, ∆t₀ is the time when no gravitational field is present, G is the universal gravitational constant, M is the mass of the object producing the gravitational field, R is the distance from the center of the mass, and c is the speed of light. In 1976, the Smithsonian Astrophysical Observatory sent aloft a Scout rocket to a height of 10,000 km to confirm this effect. Show that at this height a clock should run faster than an identical clock on the Earth by a factor of 4.5 × 10¹⁰.