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with altitude 200 km? What are the changes in the system’s (b) kinetic energy and
(c) potential energy?
40. A comet of mass 1.20 × 1010 kg moves in an elliptical orbit around the Sun. Its
distance from the Sun ranges between 0.500 AU and 50.0 AU. (a) What is the
eccentricity of its orbit? (b) What is its period? (c) At aphelion, what is the
potential energy of the comet–Sun system? Note: 1 AU = one astronomical unit =
the average distance from the Sun to the Earth = 1.496 × 1011 m.
41. An asteroid is on a collision course with Earth. An astronaut lands on the rock to
bury explosive charges that will blow the asteroid apart. Most of the small
fragments will miss the Earth, and those that fall into the atmosphere will produce
only a beautiful meteor shower. The astronaut finds that the density of the
spherical asteroid is equal to the average density of the Earth. To ensure its
pulverization, she incorporates into the explosives the rocket fuel and oxidizer
intended for her return journey. What maximum radius can the asteroid have for
her to be able to leave it entirely simply by jumping straight up? On Earth she can
jump to a height of 0.500 m.
42. Derive an expression for the work required to move an Earth satellite of mass m
from a circular orbit of radius 2RE to one of radius 3RE.
43. (a) Determine the amount of work that must be done on a 100-kg payload to
elevate it to a height of 1 000 km above the Earth’s surface. (b) Determine the
amount of additional work that is required to put the payload into circular orbit at
this elevation.
44. (a) What is the minimum speed, relative to the Sun, necessary for a spacecraft to
escape the solar system if it starts at the Earth’s orbit? (b) Voyager 1 achieved a