Download Homework #3

Homework #3
Astronomy 101 – Fall 2010
Due: October 21, 2010
1. What produces Jupiter’s strong magnetic field? Describe its source.
Jupiter’s magnetic field is generated by moving charges in the liquid metallic
hydrogen region of its interior. This region (an also the rest of Jupiter) is composed
mostly of hydrogen, which, because of the very high temperatures and pressure, shares
properties similar to metals although it is still in the liquid phase. One of the most
important properties of this metallic hydrogen is that it is a good conductor and therefore
allows more movement of electrons than, for example, Earth’s molten iron mantle. More
movement of electrons will create a stronger magnetic field. Since Jupiter is also very
large and has a correspondingly large liquid layer (much thicker than Earth’s outer core),
there are more electrons to generate an even stronger magnetic field.
2. Page 111 #16
Asteroids vs Comets. Contrast the compositions and locations of comets and
asteroids, and explain in your own words why they turned out differently.
Both comets and asteroids contain rocky material, but comets contain ices with a
smaller rocky component, whereas asteroids are mostly rock and sometimes metal.
Comets are located in the outer solar system, beyond the planets, whereas asteroids are
found much closer to the Sun, between the orbits of Mars and Jupiter. Both types of
objects were formed by condensation. Because asteroids are closer to the Sun (within the
frost line) and thus at a higher temperature, they cannot contain much ice. However,
comets formed far enough away from the Sun (beyond the frost line) and were able to
condense ices.
3. Why do some planets have rings? Explain.
Rings are found within a planet’s Roche Limit. In this region, any sizeable body
would be sheared apart by the planet’s gravity. Thus, rings are formed from the many
small bodies (moonlets) that collide with each other as they orbit a planet. Minor
collisions (less forceful) cause the moonlets to lose a small amount of their matter in the
form of dust, whereas more major collisions cause the moonlets to break into chunks the
size of boulders. These results of moonlet collisions and these moonlets themselves
make up the rings. The jovian planets are more massive and have stronger gravity. They
were able to draw in more material during and after formation to be available for moons,
moonlets, and rings.
4. Which outer solar system moons are considered to be “active” and explain the
source of their geological activity.
Some geologically “active” moons include Io, Europa, Ganymede, and Callisto
(Jupiter), Titan and Enceladus (Saturn), Miranda (Uranus), and Triton (Neptune). In spite
of their small size, these satellites still seem to have geological activity, meaning that
their surfaces are changing due to internal forces.
The key to geological activity is heat: if a planet or body is hot enough inside, it will
have a liquid component to its interior, and convection cycles in the liquid interior can
then affect the surface features of the planet.
The “active” moons in the solar system are composed of much more ice than rock or
metal, and since ice melts at much lower temperatures than rocks or metals do, the moons
can still have liquid interiors at much lower temperatures than Earth’s moon, for
example, which contains much more rock than ice, which allows these small and far
objects to be active.
But the moons still need a source of heat to generate the convection currents that
cause geological activity. This comes from tidal forces that are being exerted on the
moon by its planet (and surrounding moons). The force of gravity decreases with
distance, so a moon orbiting a planet will feel less gravity on the side of it farther away
from the planet and more gravity on the side of it closer to the planet; the change in force
causes distortions in the objects, making the moon flex and bulge. But the moon is also
rotating about its own axis and orbiting around the planet, so the side of the moon closer
and the side farther away will change, causing different parts of the moon to bulge.
These changes create friction, which will heat up the moon’s interior and thus support
continued geological activity.
5. Problems:
(a) Compare the intensity of sunlight at Earth’s distance from the Sun to that at
Uranus. (b) -- to that at the dwarf planet Eris. See p. 58
(a) Intensity is proportional to 1/(distance)2. We are only asked to compare the intensity
of the Sun at each planet’s distance, so we can just take the ratio of the intensities:
IEarth / IUranus = 1 / (dEarth2)
1 / (dUranus2)
= dUranus2 / dEarth2
From the table on page 58, we know the distance from the Sun to Earth (1 AU) and from
the Sun to Uranus (19.2 AU), so:
IEarth / IUranus = (19.2 AU)2 / (1 AU)2
= 19.2 x 19.2=368.64
= 369
So the Sun’s light at Earth is 369 times more intense than at Uranus.
(b) We know the average distance to Eris (67.7 AU), so we can use the same
method to compare Earth and Eris as we used for Earth and Uranus, so:
IEarth / IEris = dEris2 / dEarth2
= (67.7 AU)2 / (1 AU)2
= 67.7 x 67.7 =4583.29
= 4580
So the Sun’s light at Earth is 4580 times more intense than at Eris!