Download Homework #5 Chapter 3: Solar System Due

Homework #5
Chapter 3: Solar System
Due: 26 Sept 2013
Review and Discussion:
RD.1 Name three important differences between terrestrial and Jovian planets.
Answer:
First, the terrestrial planets are all in the inner 1.5 AU of the solar
system, while the jovian planets are scattered from 5 to 30 AU. Second, the
jovian planets are substantially larger in both mass and radius. Finally, the
terrestrial planets are mostly made of rock and metal, with a much higher
density than the jovian planets, which are made mostly of light gases and
liquid.
.
RD.2 Why are asteroids and meteoroids important to planetary scientists?.
Answer:
Asteroids and meteoroids are important because they often contain material
that has undergone little change since the solar system formed. In many
cases, they contain the original material that formed the solar system. The
surface material of the Earth and Moon, by contrast, has greatly changed over
time. Thus, the surface material gives us little insight into the original
conditions under which these objects formed.
RD.6 Why can comets approach the Sun from any direction but asteroids generally orbit close to the
plane of the elliptic?.
Answer:
The Oort Cloud of comets, considered the source of most comets, is like a
large, spherical halo around the solar system. Comets enter the inner solar
system with a large range of orbital inclinations. Asteroids are mostly
confined to the ecliptic. Their position indicates they are the product,
perhaps leftovers, of planet formation. The comets, from their distribution
and composition, may date from an earlier period in the solar
RD.11 Why are jovian planets so much larger than terrestrial plane
Answer:
In the position in the solar nebula where the jovian planets are now found,
the temperatures were sufficiently low for ices of water, ammonia, and
methane to form. This provided much more material for the early accretion
that occurred, and it proceeded rapidly. The planetesimals that formed could
then also attract hydrogen and helium, and the jovian planets grew to a large
size. In the region of the inner solar nebula, temperatures were sufficiently
high that time had to pass before the first rocky particles could condense
and start the accretion process. There was less material to accrete because
it was too hot for the icy material to exist. Finally, hydrogen and helium
could not be accreted because of the jovian planets’ low gravity and high
temperatures.
RD.15 In what ways do observed extrasolar planetary systems differ from our own solar system?
Answer:
Many of the newly discovered planetary systems are very different from our
own. Most of the planets are as big as or bigger than Jupiter or Saturn, with
no Earth-like planets found yet. Many of the newly discovered planets have
highly elliptical orbits. Many of these worlds are very close to their stars,
some within 0.1 AU, even planets massive enough to be "gas giants." It is
possible, however, that planetary systems such as our own would not produce
enough motion in their stars to detect from Earth. The effects of such
systems would be impossible to detect with current techniques and technology.
Conceptual Self Test:
CST.1
The largest planets also have the largest densities..
FALSE
CST.3
The asteroids were recently formed from the collision and breakup of an object orbiting within the
asteroid belt.
FALSE
CST.9 In the leading theory of solar system formation, the planets
formed from the same flattened, swirling gas cloud that formed the Sun (b)
CST.11 Water on Earth was
transported here by comets (b)
CST.15 According to Figure 4.28 in the textbook, the temperature in the solar nebula at the location
now at the center of the asteroid belt is
400 K (a)
Problems:
P4.01: Suppose the average mass of each of 20000 asteroids in the solar system is 10^17 (kg). (a)
Compare the total mass of these asteroids to the mass of Earth. (b) Assuming a spherical shape and a
density of rho, estimate the diameter of an asteroid
ANSWER:
The total mass of all asteroids would be 20,000 1017 kg = 2 1021 kg. The mass of Earth is 6 1024 kg.
Comparing these, 2 1021 kg /6 1024 kg / = 0.0003. Thus, the mass of all the asteroids combined is
0.03% of the mass of Earth. As we see them today, the asteroids would not make up much of a
planet! A single body would have the following size. Use the formula for density:
3000 
1017
(4 / 3) πR 3
R = 20,000 m or 20 km, so the diameter would be 40 km.
P4.05: (a) Using the version of Kepler's laws of planetary motion from Section 1.5 in the textbook,
calculate the orbital period of an Oort cloud comet if the semimajor axis of the comet's orbit is 50,000
AU. (b) What is the maximum possible aphelion?
(a) Use Kepler’s third law, P2 = a3:
P  a 3  50,000 3 = 11 million years.
(b) Use Kepler’s third law to find the semi-major axis:
a  3 P 2  3 125 2 = 25 AU
Twice this distance is the major axis, 50 AU. The maximum aphelion distance cannot be any larger than
this.
P4.07: a) Given the data provided in the text, calculate the gravitational acceleration at the surfaces
of the two transiting super-Earths (CoRoT 7b and GJ 1214B) discussed in Section 4.4 in the textbook.
Acceleration due to gravity on the surface of the planet is proportional to the mass of the planet and
inversely proportional to the square of the radius. Comparing a planet to Earth gives
gplanet = [M/r2 ] gearth
For CoRoT 7b: gplanet = [4.8/1.72 ] gearth = 1.7 gearth
For GJ 1214B: gplanet = [5.7/2.72 ] gearth = 0.8 gearth
P4.10: The amount of energy reaching a planet's surface per unit time is proportional to the
luminosity of its parent star divided by the square of the planet's distance from the star. If the
luminosity is proportional to the fourth power of the star's mass, estimate the orbital distance (in AU) at
which an Earth-like exoplanet orbiting a 0.5 solar mass star would receive the same amount of energy
from its star as Earth does from the Sun.
Energy is proportional to L/r2 or to M4/r2. Using Earth/Sun units and solving for r:
r  M 4  .54  0.25 AU