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Problems 295

11. Does the radial line from the Sun to Mars sweep out area 16. A Russian and an American astronaut are in two separate space-
at the same rate as the radial line from the Sun to the craft in the same circular orbit around the Earth.The Russian is
Earth? slightly behind the American, and he wants to overtake him.The
12. Why were the Apollo astronauts able to jump much higher on Russian fires his thrusters in the forward direction, braking for a
the Moon than on the Earth (Fig. 9.28)? If they had landed brief instant.This changes his orbit into an ellipse. One orbital
on a small asteroid, could they have launched themselves into period later, the astronauts return to the vicinity of their initial
a parabolic or hyperbolic orbit by a jump? positions, but the Russian is now ahead of the American. He
then fires his thrusters in the backward direction.This restores
his orbit to the original circle. Carefully explain the steps of this
maneuver, drawing diagrams of the orbits.
17. The gravitational force that a hollow spherical shell of uni-
formly distributed mass exerts on a particle in its interior is
zero. Does this mean that such a shell acts as a gravity shield?
18. Consider an astronaut launched in a rocket from the surface of
the Earth and then placed in a circular orbit around the Earth.
Describe the astronaut’s weight (measured in an inertial refer-
ence frame) at different times during this trip. Describe the
astronaut’s apparent weight (measured in his own reference
frame) at different times.
19. Several of our astronauts suffered severe motion sickness while
under conditions of apparent weightlessness. Since the astro-
nauts were not being tossed about (as in an airplane or a ship
in a storm), what caused this motion sickness? What other
difficulties does an astronaut face in daily life under conditions
of weightlessness?
FIGURE 9.28 The jump of the astronaut. 20. An astronaut on the International Space Station lights a
candle. Will the candle burn like a candle on Earth?
21. Astrology is an ancient superstition according to which the
13. The Earth reaches perihelion on January 3 and aphelion on
planets influence phenomena on the Earth.The only force that
July 6. Why is it not warmer in January than in July?
can reach over the large distances between the planets and act
14. When the Apollo astronauts were orbiting around the Moon on pieces of matter on the Earth is gravitation (planets do not
at low altitude, they detected several mass concentrations have electric charge, and they therefore do not exert electric
(“mascons”) below the lunar surface. What is the effect of a forces; some planets do have magnetism, but their magnetic
mascon on the orbital motion? forces are too weak to reach the Earth). Given that the Earth is
15. An astronaut in a circular orbit above the Earth wants to take in free fall under the action of the net gravitational force of the
his spacecraft into a new circular orbit of larger radius. Give planets and the Sun, is there any way that the gravitational
him instructions on how to do this. forces of the planets can affect what happens on the Earth?

PROBLEMS

9.1 Newton’s Law of Universal Gravitation balances that of the Moon. At what distance from the Earth is
9.2 The Measurement of G † this point?
4. Calculate the value of the acceleration of gravity at the surface
1. Two supertankers, each with a mass of 700 000 metric tons, are of Venus, Mercury, and Mars. Use the data on planetary masses
separated by a distance of 2.0 km. What is the gravitational and radii given in the table printed inside the book cover.
force that each exerts on the other? Treat them as particles.
5. What is the magnitude of the gravitational force that the Sun
2. What is the gravitational force between two protons separated exerts on you? What is the magnitude of the gravitational
by a distance equal to their diameter, 2.0 10 15 m? force that the Moon exerts on you? The masses of the Sun and
3. Somewhere between the Earth and the Moon there is a point the Moon and their distances are given inside the book cover;
where the gravitational pull of the Earth on a particle exactly assume that your mass is 70 kg. Compare these forces with

† For help see Online Concept Tutorial 11 at www wwnorton com/physics