16.4 An extrasolar planet has a small moon, which orbits the planet in 336 hours. The semimajor axis of the moon's orbit is
1.94e+9 m. What is the mass of the planet?
kg16.5 Jupiter's moon Callisto orbits the planet at a distance of 1.88×10^9 m from the center of the planet. Jupiter's mass is
1.90×10^27 kg. What is the period of Callisto's orbit, in hours?
hours16.6 The Trans-Neptunian object Sedna has an extremely large semimajor axis. In the year 2004, it was estimated to be 480 AU.
What is the period of Sedna's orbit, measured in Earth years?
years
Section 17 - Orbits and energy
17.1 The Hubble Space Telescope orbits the Earth at an altitude of approximately 612 km. Its mass is 11,100 kg and the mass of
the Earth is 5.97×10^24 kg. The Earth's radius is 6.38×10^6 m. Assume the Hubble's orbit is circular. (a) What is the gravitational
potential energy of the Earth-Hubble system? (Assume that it is zero when their separation is infinite.) (b) What is the
Hubble's KE? (c) What is the Hubble's total energy?
(a) J
(b) J
(c) J17.2 What is the least amount of energy it takes to send a spacecraft of mass 3.50×10^4 kg from Earth's orbit to that of Mars?
(Neglect the gravitational influence of the planets themselves.) Assume that both planetary orbits are circular, the radius of
Earth's orbit is 1.50×10^11 meters, and that of Mars' orbit is 2.28×10^11 meters. The Sun's mass is 1.99×10^30 kg.
J
17.3 How much work is required to send a spacecraft from Earth's orbit to Saturn's orbit around the sun? The semimajor axis of
Earth's orbit is 1.50×10^11 meters and that of Saturn's orbit is 1.43×10^12 meters. The spacecraft has a mass of 3.71e+4 kg and
the Sun's mass is 1.99×10^30 kg.
J17.4 You wish to boost a 9,550 kg Earth satellite from a circular orbit with an altitude of 359 km to a much higher circular orbit with
an altitude of 35,800 km. What is the difference in energy between the two orbits, that is, how much energy will it take to
accomplish the orbit change? Earth's radius is 6.38×10^6 m and its mass is 5.97×10^24 kg.
J
17.5 A satellite is put in a circular orbit 485 km above the surface of the Earth. After some time, friction with the Earth's
atmosphere causes the satellite to fall to the Earth's surface. The 375 kg satellite hits the Pacific Ocean with a speed of
2,500 m/s. What is the change in the satellite's mechanical energy? (Watch the sign of your answer.) In this situation,
mechanical energy is transformed into heat and sound. The Earth's mass is 5.97×10^24 kg, and its radius is 6.38×10^6 m.
J17.6 You launch an engine-less space capsule from the surface of the Earth and it travels into space until it experiences
essentially zero gravitational force from the Earth. The initial speed of the capsule is 18,500 m/s. What is its final speed?
Assume no significant gravitational influence from other solar system bodies. The Earth's mass is 5.97×10^24 kg, and its radius
is 6.38×10^6 m.
m/s
Section 18 - Escape speed
18.1 Calculate the escape speed from the surface of Venus, whose radius is 6.05×10^6 m and mass is 4.87×10^24 kg. Neglect the
influence of the Sun's gravity.
m/s18.2 The escape speed of a particular planet with a radius of 7.60e+6 m is 14,500 m/s. What is the mass of the planet?
kg18.3 A planet has a mass of 5.69×10^26 kg. The planet is not a perfect sphere, instead it is somewhat flattened. At the equator, its
radius is 6.03×10^7 m, and at the poles, the radius is 5.38×10^7 m. (a) What is the escape speed from the surface of the planet
at the equator? (b) What is the escape speed at the poles?
(a) m/s
(b) m/s