AS101ps5 - J.I AS101 Problem Set#5 37 The Importance of...

J.I.
AS101
Problem Set #5
6/26/07
37. The Importance of Rotation. Suppose the material that formed Jupiter came together without any rotation so that no
“jovian nebula” formed and the planet today wasn’t spinning. How else would the jovian system be different? Think of as
many effects as you can, and explain each in a sentence.
Jupiter’s speed of rotation is a key to the history of the way in which the planet and its
surrounding part of the solar system was formed. There are many key features to the planet and
the area that are due in part to the way in which Jupiter was formed. If there was no ‘jovian
nebula’ one important difference would be the difference of Jupiter’s satellites. Instead of many
very small moons there may be only a few major moons. Jupiter would not have the tidal forces
to rip large moons apart into smaller moons.
39. Comparing Jovian Planets. You can do comparative planetology armed only with telescopes and an understanding of
gravity.
a. The small moon Amalthea orbits Jupiter at about the same distance in kilometers at which Mimas orbits Saturn, yet
Mimas takes almost twice as long to orbit. From this observation, what can you conclude about how Jupiter and Saturn
differ? Explain.
b. Jupiter and Saturn are not very different in radius. When you combine this information with your answer to part (a),
what can you conclude? Explain.
(a) Jupiter is a much more massive planet than Saturn. A moon that is orbiting at the same
distance could be affected by that difference in mass. Saturn’s moon at this distance orbits almost
twice as long to orbit. From this simple observation we can use Keplarian orbit concepts to
determine how different Saturn’s mass is from Jupiter.
(b) Using the same model, if the radius is also the same then it is true that it is the mass that is the
only major difference that would affect the moons and the way they orbit. So if the moon around
Jupiter orbits two times as fast as the one that orbits Saturn then Jupiter must be more massive to
cause that moon to move faster.
50. Orbital Resonances. Using the data in Appendix E, identify the orbital resonance relationship between Titan and
Hyperion. (Hint: If the orbital period of one were 1.5 times the other, we would say that they are in a 3:2 resonance.)
Which medium-size moon is in a 2:1 resonance with Enceladus?
Titan Orbital Period = 15.9 days 21.3 / 15.9 = 1.33 / 1
Hyperion Orbital Period = 21.3 days Hyperion and Titan are in a 4:3 resonance
Enceladus Orbital Period = 1.4 days 2:1 resonance with Enceladus
Either .7 days or 2.8 days
Dione Orbital Period = 2.7 days Dione and Enceladus are in a 2:1 resonance

52. Titan’s Evolving Atmosphere. Titan’s exosphere lies nearly 1,400 kilometers above its surface. What is the escape
velocity from this altitude? What is the thermal speed of a hydrogen atom at the exospheric temperature of about 200 K?