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maximum speed of 125 000 km/h on its way to photograph Jupiter. Beyond what
distance from the Sun is this speed sufficient to escape the solar system?
45. A satellite of mass 200 kg is placed into Earth orbit at a height of 200 km above
the surface. (a) Assuming a circular orbit, how long does the satellite take to
complete one orbit? (b) What is the satellite’s speed? (c) Starting from the satellite
on the Earth’s surface, what is the minimum energy input necessary to place this
satellite in orbit? Ignore air resistance but include the effect of the planet’s daily
rotation.
46. A satellite of mass m, originally on the surface of the Earth, is placed into Earth
orbit at an altitude h. (a) Assuming a circular orbit, how long does the satellite
take to complete one orbit? (b) What is the satellite’s speed? (c) What is the
minimum energy input necessary to place this satellite in orbit? Ignore air
resistance but include the effect of the planet’s daily rotation. Represent the mass
and radius of the Earth as ME and RE, respectively.
47. Ganymede is the largest of Jupiter’s moons. Consider a rocket on the surface of
Ganymede, at the point farthest from the planet (Fig. P13.47). Model the rocket as
a particle. (a) Does the presence of Ganymede make Jupiter exert a larger, smaller,
or same size force on the rocket compared with the force it would exert if
Ganymede were not interposed? (b) Determine the escape speed for the rocket
from the planet–satellite system. The radius of Ganymede is 2.64 × 106 m, and its
mass is 1.495 × 1023 kg. The distance between Jupiter and Ganymede is 1.071 ×
109 m, and the mass of Jupiter is 1.90 × 1027 kg. Ignore the motion of Jupiter and
Ganymede as they revolve about their center of mass.