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Problems 297

TABLE 9.2 SOME MOONS OF SATURN

MOON DISTANCE FROM SATURN PERIOD ORBITAL SPEED

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Tethys (Fig. 9.30) 2.95 10 km 1.89 days —
Dione 3.77 — —
Rhea 5.27 — —
Titan 12.22 — —
Iapetus 35.60 — —
FIGURE 9.30 Tethys, one of the
moons of Saturn.

25. Before clocks with long-term accuracy were constructed, it *31. The Discoverer II satellite had an approximately circular orbit
was proposed that navigators at sea should use the motion of passing over both poles of the Earth. The radius of the orbit
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the moons of Jupiter as a clock. The moons Io, Europa, and was about 6.67 10 km. Taking the rotation of the Earth
3
3
Ganymede have orbital radii of 422 10 , 671 10 , and into account, if the satellite passed over New York City at one
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1070 10 km, respectively. What are the periods of the instant, over what point of the United States would it pass
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orbits of these moons? The mass of Jupiter is 1.90 10 kg. after completing one more orbit?
26. A satellite is to be put into an equatorial orbit with an orbital *32. The binary star system PSR 1913 16 consists of two neutron
period of 12 hours. What is the radius of the orbit? What is stars orbiting with a period of 7.75 h about their center of
the orbital speed? How many times a day will the satellite be mass, which is at the midpoint between the stars. Assume
over the same point on the equator if the satellite orbits in the that the stars have equal masses and that their orbits are
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same direction as the Earth’s rotation? If it orbits in the oppo- circular with a radius of 8.67 10 m.
site direction? (a) What are the masses of the stars?
27. An asteroid is in a circular orbit at a distance of two solar (b) What are their speeds?
diameters from the center of the Sun. What is its orbital
*33. Figure 9.32 shows two stars orbiting about their common
period in days?
center of mass in the binary system Krüger 60. The center of
28. The Sun rotates approximately every 26 days. What is the mass is at a point between the stars such that the distances of
radius of a “heliosynchronous” orbit, that is, an orbit that stays the stars from this point are in the inverse ratio of their
over the same spot of the Sun? masses. Measure the sizes of their orbits and determine the
29. The Apollo command module orbited the Moon while the ratio of their masses.
lunar excursion module visited the surface. If the orbit had a
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radius of 2.0 10 m, how many times per (Earth) day did
FIGURE 9.32 The Center
the command module fly over the excursion module? of mass
orbits of the two stars
30. A Jupiter-sized planet orbits the star 55 Cancri with an orbital in the binary system
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radius of 8.2 10 m (see Fig. 9.31). The orbital period of Krüger 60. Each
this planet is 13 yr. What is the mass of the star 55 Cancri? ellipse has its focus at
How does this compare with the mass of the Sun? the center of mass.

FIGURE 9.31 (a) The Solar System and (b) the 55 Cancri system.
(a) Jupiter
Earth

(b)