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take Mercury to achieve this passage. If not, give a convincing argument that
Pluto is always farther from the Sun than is Mercury.
Section 13.5 Gravitational Potential Energy
Note: In Problems 30 through 50, assume U = 0 at r = ∞
30. A satellite in Earth orbit has a mass of 100 kg and is at an altitude of 2.00 × 106 m.
(a) What is the potential energy of the satellite–Earth system? (b) What is the
magnitude of the gravitational force exerted by the Earth on the satellite? (c)
What If? What force, if any, does the satellite exert on the Earth?
31. How much work is done by the Moon’s gravitational field on a 1 000-kg meteor
as it comes in from outer space and impacts on the Moon’s surface?
32. How much energy is required to move a 1 000-kg object from the Earth’s surface
to an altitude twice the Earth’s radius?
33. After the Sun exhausts its nuclear fuel, its ultimate fate will be to collapse to a
white dwarf state. In this state, it would have approximately the same mass as it
has now, but its radius would be equal to the radius of the Earth. Calculate (a) the
average density of the white dwarf, (b) the surface free-fall acceleration, and (c)
the gravitational potential energy associated with a 1.00-kg object at the surface of
the white dwarf.
34. An object is released from rest at an altitude h above the surface of the Earth. (a)
Show that its speed at a distance r from the Earth’s center, where RE ≤ r ≤ RE + h,
is
1
r
  2GM E  
1 

RE  h 
(b) Assume the release altitude is 500 km. Perform the integral