Download The Sun and Planets Exercise 2.

The Sun and Planets
Exercise 2.
Exercise 1.
Spring Semester 2017
Prof Dr Ravit Helled
Planet Formation: Definitions
This exercise is theoretical one. You have to explain some concepts.
1. Once a planet, Pluto was recently demoted to a “dwarf planet”. What is the difference between a planet and dwarf planet?
2. There are two distinct theories regarding how giant planets form. Briefly explain
the differences between the Disk Instability (DI) and Core Accretion (CA) models.
cs Ω
, where a value of Q > 1
3. The Toomre stability criterion is defined as Q = πGσ
g
implies stability. What does this formula tell us about planet formation?
4. Give brief definitions for the following terms in planet formation: ”protoplanetary
disc”, ”surface density”, ”planetesimal” and ”metallicity”.
5. In giant planet formation, what are the three phases in the core accretion (CA)
model? Draw a rough plot to illustrate your answer.
6. Giant planets form very quickly compared to rocky planets. Quickly explain why
this might be.
7. The Solar System is thought to have from a rotating disc of gas and dust. Briefly
explain the “minimum mass solar nebula” and how it relates to planet formation.
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Table 1: Composition of the palnets in
Planet Total Mass (kg) X
Mercury
0.330 × 1024
0
24
Venus
4.867 × 10
0
Earth
5.972 × 1024
0
23
Mars
6.420 × 10
0
27
Jupiter
1.898 × 10
0.70
Saturn
5.684 × 1026
0.66
25
Uranus
8.681 × 10
0.69
26
Neptune
1.024 × 10
0.70
Exercise 2.
Solar
Y
0
0
0
0
0.25
0.25
0.27
0.23
System
Z
1
1
1
1
0.05
0.09
0.04
0.07
The Minimum Mass Solar Nebula
The Minimum Mass Solar Nebula (hereafter MMSN) is the protoplanetary disk of solar
composition containing the amount of metals necessary to build the eight planets of the
Solar System. From the masses and compositions of the planets, a density of solids is
derived at several radial locations of the disk. Thereafter, the solar composition is arrived
at by adding gas. This gives us a smooth denstity profile of the protoplanetary disk which
we call the MMSN. The MMSN can be thought of as the minimum amount of material
needed to form today’s Solar System. We will try to derive it quickly below.
We assume the solar composition to be:
X = 0.734 ; Y = 0.25 ; Z = 0.016,
where X is the Hydrogen fraction, Y is the Helium fraction, and Z is the fraction of heavy
elements (in astonomy this includes all elements not named Hydrogen or Helium).
The hypotheses states the protosolar nebula had the same composition as the Sun. Thus,
to form a planet with 1 M⊕ of heavy elements (Z = 1) the nebula had to be have least of
36.7 M⊕ Hydrogen and 12.5 M⊕ of Helium.
Calculate the minimum mass of the material needed to form all the planets of the Solar
System.
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