---
# System prepended metadata

title: 行星科學導論 Introduction to Planetary Science

---

# 行星科學導論 Introduction to Planetary Science

:::info
[wingip@astro.ncu.edu.tw](wingip@astro.ncu.edu.tw)
:::

[ToC]

## Lecture 1

### Solar system formation

#### step of solar system formation
![](https://i.imgur.com/1MGfktp.jpg)

1. Interstellar clouds 
    - some dense place in the space
    - consist of gas( most $H$, $He$ ) and dust
    - Interstellar Medium(ISM)
        - gas/dust = 100( mass, average )
2. Molecule clouds
    - some part of interstellar clouds
    - layers of molecule cloud
        - inside: effect by pressure, so it's easier to form molecule
        - outside: effect by radiation, so there are many ion
![](https://i.imgur.com/EaYR4nD.png)
###### 註：Neutral Hydragent($HI$)、Carbon ion(一次電離，$CII$)

3. Dark clouds
    - some information
        - size: $r\sim 50 pc$
        - mass: $\sim 10^6 M_{sun}$
        - temperature: $\sim 20 K$
        - density: $\sim 100\sim 300cm^{-3}$
    - High density dusty-cold cloudlets
    - **evaporating gaseous globules(EGGs)**
    ![](https://i.imgur.com/3EvBLlO.png)
    - bok globules(also dark cloud)
        - some information
            - size: $r\sim 1 pc$
            - mass: $\sim 10\sim 1000 M_{sun}$
            - temperature: $\sim 10 K$
            - density: $\geq 10^4 cm^{-3}$
        - Professor Bok
        - contracting to form protostars
        - *other example*
![](https://i.imgur.com/dEbPXRH.png)
    - most of small particle
    - $H_2$ is difficult to form by collision of two $H$, but it's easier when they collision on the dust
    - some information of hot, dense cores(where stars form)
        - size: $0.05\sim 1 pc$
        - mass: $10\sim 100 M_{sun}$
        - temperature: $100\sim 200 K$
        - density: $10^7\sim 10^9 cm^{-3}$
    - stars do not form isolatedly, but in large group(Open cluster，疏散星團)
    - fragmentation：forming stars blow out the cloud around them, then can be seen
    - collision of molecule generate radiation(能階躍遷)，then cause the temperature of cloud go down, so cloud become denser

4. Gravitational collapse
    - the cloud collapse by self-gravity
    - how long will the giant molecule cloud(GMC) collapse?
    ![](https://i.imgur.com/rjblI6y.png)
    ###### $\rho$ is density
    - GMC collapse rapidly in $4\times 10^5 yr$
5. Solar nebula
    - accretion disks
    ![](https://i.imgur.com/Mc7YUL0.png)
        - the gaps in the disk maybe show the evidence of planet forming or protoplanet and the dust have some angular momentum exchange
        ![](https://i.imgur.com/eHWwSVp.png)
        ![](https://i.imgur.com/Am6Kmwp.jpg)
        - **why accretion disk is a disk?**：
        塵埃的碰撞速度小，通常是非彈性碰撞，越來越大，為維持角動量守恆，造成垂直於盤面的能量散失，垂直速度減小，變成扁盤
        - there is a thin layer of dust in the disk

6. Protostars
![](https://i.imgur.com/OtWlDjL.png)

7. [T Tauri Star(TTS)](https://bit.ly/3AiO8hB)
    ![](https://i.imgur.com/Awn0jc8.png)
    ###### $dm/dt$, $dt$ is year
    - accretion inflow
        - most of the mass are blow out by the wind
    ![](https://i.imgur.com/Rqh8hSC.png)
    ###### 透過磁場跟吸積盤互動，靠近恆星時，物質沿磁力線移動
    - jet
    ![](https://i.imgur.com/aXOY6gV.jpg)
    ###### HH object
    ![](https://i.imgur.com/Lnqyxgj.jpg)
    ###### some example
    - TTSs and protostars also are pre-main sequence stars

8. Debris disks
    ![](https://i.imgur.com/SFyNlsD.png)
    ###### Stelar spectrum + disk spectrum (IR)
    - Class 0: cloud collapse, only the cloud spectrum(紅外線)
    - Class 1: disk and jet form, plus star specturm
    - Class 2(classic TTS): jet disappear, disk spectrum almost disappear
    - Class 3(weak-lined TTS): protostar
    - some timeline
        - from 0 ~ 3 cost 1 ~ 10 Ma(jupiter must be formed between this duration(some Ma))
    ![](https://i.imgur.com/LCfsT7s.png)
    ###### 內部可能有行星形成
9. Proto-planets


### Summary
![](https://i.imgur.com/z4zN4Cw.png)
![](https://i.imgur.com/nukJulO.png)


## Lecture 2

### Planet formation and evolution

#### Collisional accumulation

![](https://i.imgur.com/IOTqKWS.png)
- Geometrical collision
![](https://i.imgur.com/bVWR4Qv.png)
###### $\pi R^2$ is collision area

#### Gravitational focusing
![](https://i.imgur.com/7kM8M48.png)
- a planetary embryo has enough gravity so it can extend its collision area to let it grow faster
- **How to compute the collision area**
    - Energy conservation
    $$\frac{1}{2}mv_0^2 = \frac{1}{2}mv_{max}^2 - \frac{GM_em}{r_{min}}$$
    (總能 ＝ 動能 ＋ 位能(為負))
    ($M_e$ is the mass of embryo, $r_{min}$ is the minimal distance to the center of embryo)
    - Conservation of angular momentum
    $$L = mbv_0$$
    ($b$ is impact parameter, $v_0$ 離開物體的相對速度)
    (since $L = m\omega r^2$ and $v = \omega r$ in general)
    - **Gravitational focusing factor**
    $$v_{max} = \frac{bv_0}{r_{min}}$$
    $$b^2 = r_{min}^2(1+\frac{2GM_e}{v_0^2r_{min}}) = R_e^2(1+(\frac{v_{\infty}}{v_0})^2)$$
    $$F_g = 1 + \frac{2GM_e}{R_ev^2}$$
- no gravitational focusing
$$\frac{dM_e}{dt} = \pi R_e^2\rho_sv$$
$$\frac{1}{M_e}\frac{dM_e}{dt}\propto M_e^{-1/3}$$
($\rho_s$，接近物質的平均質量密度)
無重力聚焦現象時，質量越大，質量增加速度越慢

- strong gravitational focusing
$$\frac{dM_e}{dt} = \pi R_e^2(1 + \frac{2GM_e}{R_ev^2})\rho_sv$$
$$\frac{1}{M_e}\frac{dM_e}{dt}\propto M_e^{1/3}$$
有重力聚焦現象時，質量越大，質量增加速度越快

- mass accretion
    - Weak gravitational focusing
    $$\frac{dM_e}{dt}=\frac{dR_e}{dt}\cdot 4\pi R_e^2\rho_e$$
    - Size growth rate independent of size
    $$\frac{dR_e}{dt} = \frac{\rho_s}{4\rho_e}v$$

#### Coagulation
- happen to similar size of objects
- evidence
![](https://i.imgur.com/72dPOYU.png)
- **Coagulation equation**
$$\frac{dn_k}{dt} = \frac{1}{2}\sum_{i+j=k}A_{ij}n_in_j-n_k\sum_{i=1}A_{ki}n_i$$
($i$, $j$, $k$ 代表幾單位，$A$為碰撞機率)

![](https://i.imgur.com/2KwgSNi.png)
###### 質量1單位物體越來越少，大單位物體較晚形成

#### Runaway growth
- the $F_g$ of a embryo is larger than 1, and it won't stop to grow

#### Oligarchy
![](https://i.imgur.com/rzBT5NW.png)

- few large objects(4)
- growth are leading by some large object
![](https://i.imgur.com/YYo2fmc.png)
- terrestrial planet took 10 ~ 100 Ma to form

#### Feeding zone
![](https://i.imgur.com/IAYzRio.png)

##### Hill sphere
![](https://i.imgur.com/AFLYvem.png)
- the area that the object inside will **only influence by the planet**, not the star it orbit
- radius
    $$R_H = a_e(\frac{M_e}{3M_*})^{1/3}$$
    $a_e$ is the distance between two object, $M_e$ is small object(**Earth**), and $M_*$ is the biggest one(**sun**)
    
- Hills sphere determines the width of feeding  zone, and width of feeding zone is about $2\sim 4R_H$

- **Isolated planetoid mass**
$$M_e^{iso} = 2\pi a_e\times 2BR_H\times \sigma$$
$B\sim (2\sim 4)$
$$R_H = a_e(\frac{M_e}{3M_*})^{1/3}$$
$$M_e^{iso} = \frac{(4\pi Ba_e^2\sigma)^{3/2}}{(3M_*)^{1/2}}$$
    - 可能有大概300個月亮大小物體形成地球
    - by feeding zone, we can know the mass of the object

#### Summary
![](https://i.imgur.com/Bi7q32p.png)

#### Minimum solar nebula model (MMSN)
- Pro. Weidenschilling 
- want to slove the problem that the total mass of asteroid belt is too small
- surface density
    ![](https://i.imgur.com/bATSX9j.png)
    $\sigma =$ planetary mass / area(grey)

    ![](https://i.imgur.com/n6ZD4rI.png)

    ###### no asteroid blet on left graph
    - distribution of solar mass(refill the gas(gas/dust = 100))
    $$\sigma_{MMSN}(r) = \sigma_0(\frac{r}{r_0})^{-n}$$
    ,for our solar system
    $$\sigma_{MMSN}(r) = 1700(\frac{r}{1AU})^{-3/2}g\cdot cm^{-2}$$
    - dust and gas density distribution
    $$\Sigma_d = 10 \times f_d\eta_{ice}(\frac{r}{1AU})^{-3/2}g\cdot cm^{-2}$$
    $$\Sigma_g = 2400 \times f_g(\frac{r}{1AU})^{-3/2}g\cdot cm^{-2}$$

- disk temperature(center)
$$\frac{dP}{dz} = -\rho g_z$$
gas pressure and gravity balance to keep the thickness, $g_z$ is the sun gravity on z-axis
$$g_z = \frac{GM_*}{r^2}(\frac{z}{r}) = \omega^2z$$
$$\frac{dP}{dz}\sim\frac{P_{surface}-P_{center}}{z_{surface}-0}\sim\frac{-P_{center}}{z_{surface}}$$

$$T_{center}\propto r^{-3/2}$$

#### Snow line
![](https://i.imgur.com/ZyNRneT.png)
###### water ice condensation temperature ~ 153K in the solar nebula, isn't fit to other system
![](https://i.imgur.com/OmBl3da.png)
- snow line in solar system is on **2.7 AU**, just the place of **asteriod belt**
![](https://i.imgur.com/qkym0kk.png)
###### outside the snow line, water became ice(dust), so we have more material to form planet

#### Gravitational instability 
- **Problem: Pebbles don't stick to each other**
- when the disk become thicker, there are some parts of it will be denser than other, then cause gravitational instablity so that can form planetasimals
- also happen in molecule clouds

#### Gas-dust interaction 
- more problem: we have gas in the disk(Weidenschilling)
    - from solid body orbit motion
    $$\frac{d^2r}{dt^2} = \frac{GM}{r^2} = 0$$
    $$\frac{GM}{r^2} = \omega^2r$$
    - to plus gas motion
    $$\frac{d^2r}{dt^2} = \frac{1}{\rho}\frac{dP}{dr}+\frac{GM}{r^2} = 0$$
    $$\frac{1}{\rho}\frac{dP}{dr}+\frac{GM}{r^2} = \omega^2r$$
- head wind: $\frac{1}{\rho}\frac{dP}{dr}$
**gas slow the speed of orbit**

![](https://i.imgur.com/4G0al1n.png)
###### 氣體產生渦流，分散塵埃，造成塵埃盤加厚，破壞重力不穩定性

#### Two-stream instability
![](https://i.imgur.com/o6nFXLW.png)
- 渦流聚集塵埃，再次形成重力不穩定性

![](https://i.imgur.com/zAitqJl.png)

#### Pebble accretion
- accretion disk inner boundary: few star radius
outer boundary: 100 star radius
- 吸積盤面光致蒸發（phonic-evaporation）->disk wind(10% mass)
- 吸積盤塵埃溫度$\propto r^\alpha,\alpha\approx \frac{1}{2}$
- circum-stellar disk

#### Summary

![](https://i.imgur.com/ZD3qf1E.png)

## Lecture 3

### The Earth-Moon system

#### questions
1. What is the different between the hill sphere and the Roche limit
2. How to explain the formation of saturnian rings in terms of Roche limit
3. Can yo describe the impact theory of the lunar origin
4. What is the compositional difference between the Moon and the Earth
5. What is the structure of a synestia
6. What is the origin of the lunar magma ocean
7. How long did it last
8. Can you sketch the solidification sequence of the lunar interior

#### Co-rotation

#### Synchronous rotation(Tidal locking)

#### [Lagrangian points](https://bit.ly/3Dp520i)

- definition：
- [Roche lobe(洛希瓣)](https://bit.ly/3ljJU5h)
- L1 for solar space telescopes
- L2 for astronomical and lunar missions

#### Hill sphere

- = **sphere of influence**
- $R_H = a(\frac{m}{3M})^{\frac{1}{3}}$，a是m的軌道半長軸
- lunar orbit in a fixed frame

#### [Roche limit](https://bit.ly/3ais649)

- $d_R=2.44\times R_M\times (\frac{\rho_m}{\rho_M})$, $\rho$ is density
- 小星體質量和放射性物質不夠，產生熱度不足以造成熔融狀態，因此多為碎塊聚合

#### some theory of lunar formation
1. fission from earth
2. **giant impact(mainstream)**
3. capture theory

#### Giant impact
- Dr. Robin Canup
- Mars-sized impactor
- Lunar formation in an accretion disk
- object inside it become magma
- outside roch limit
- moon is leaving earth because of tidal power and cause the rotatation speed of earth and moon change

#### Lunar magma ocean(LMO)
- Crustal solidification:
magma->form crystal(Olivine/pyroxene)->form crust->layering(pyroxene->Olivine->magma->anorthorsite crust)
![](https://i.imgur.com/9DZMYEr.jpg)
![](https://i.imgur.com/knAuh3M.jpg)
- anorthorsite crust slow the speed of lunar cooling
- LMO cooling time scale:200 Myr
- Anorthosite
- Olivine/pyroxene

#### Compositional analysis
- most: oxygen
- rotation speed of earth is fast at that time, so that causes the consist of earth and moon are resemble
- bulk silicate Earth

#### The synestia theory
- new theory
- in giant impact, earth and moon form seperately
- in this theory, after impact they become a synestia(like donuts without hole)

![](https://i.imgur.com/ZK1M9D3.jpg)

#### Near side/far side
- tow side extremely not symmetric
- MOLA(Moob Orbiter LiDAR Altimater)
- SPA(South Pole Atkin)

#### Maria/highlands
![](https://i.imgur.com/8gpoFEh.png)
![](https://i.imgur.com/q6s0H2D.png)
- albedo 反光率(0~1)

#### Simple craters/complex craters 
![](https://i.imgur.com/jvF2XI1.jpg)
![](https://i.imgur.com/oDRH6UN.jpg)
- central peek
- Ejection 彈射物：隕石撞擊時被彈射出來堆積在隕坑周圍的物質
- 超過10km的隕石才能形成complex craters
![](https://i.imgur.com/y5Xl6sI.png)


#### Crater impact process
![](https://i.imgur.com/gJjhbJw.jpg)
![](https://i.imgur.com/Pcw9JCb.png)
###### ka(千年前, 'a' means ago)
- $\frac{dN}{dD}\propto D^{-\gamma}$

![](https://i.imgur.com/I0Tzrrm.jpg)
- the red line in graph is call the production curve or source curve

#### Crustal fracture/mega-regolith 
- space weathering
![](https://i.imgur.com/RAa9zz7.png)
- megeregolith format by deep impact
![](https://i.imgur.com/tWN964w.png)

#### Regolith
- 月球的石頭樣本都年份都在37~38億年前，可能原因：
late heavy bombardment event、拾取範圍是在該時候形成

#### Breccia

## Lecture 4

#### Questions
1. Why there is a very strong surface temperature of the number densities of He and Ne
2. Why Ar has a different behavior
3. What are the possible source mechanisms of the lunar exosphere
4. Which atomic species has strong optical emission


1. Around its orbital motion, the Moon will interact with different types of plasma flows and charged particle populations. Can you give examples?
2. Can you please sketch the plasma environment of the Moon including its upstream and downstream (wake) regions?
3. Does the Moon have an ionosphere?

### Moonquakes
- Apollo seismic stations
![](https://i.imgur.com/DRpGfI4.png)
- source
    - shallow 
    - deep

#### Deep moonquakes

#### lunar atmosphere
- The NASA LADEE(Lunar Atmosphere and Dust Environment Expolorar) mission
``` mermaid
pie
title lunar soli consist
"O" : 42
"Si" : 21
"Fe" : 13
"Ca" : 8
"Al": 7
"Mg": 6
"Other": 3
```
- atmosphere: H:22.6%, Ar:19.4%, He4:25.8%, Ne:25.8%
![](https://i.imgur.com/vBQsNgr.png)
- He and Ne is increasing in morning, reaching top at night
![](https://i.imgur.com/A5F76Be.png)
- the temparature of moon at night will not down to zero because it will keep some heat inside
- Ar is opposite to He and Ne
![](https://i.imgur.com/mE5IbdX.png)
- He and Ar36 is from solar wind
![](https://i.imgur.com/kXVq81E.jpg)
- ar40 is from moonquake
- pickup: the molecule become ion and be effected by the magnetice field of sun then escape
- reason:ballistic motion(causes lunar exosphere)
- $t_b = \sqrt2(V/g)$
$t_b = (2/g)(kT/ m)^{1/2}$
![](https://i.imgur.com/ChUdqN9.png)
- random walk
    - scala height $H=kT/mg$
    - random walk step size $\Delta s\approx H_1$
- transport time scale
    - $t_m = t_bn_{rw}\propto T^{-3/2}$
    - $n_0H/t_m = constant$
    - $n_0 \propto T^{-5/2}$
- lunar sphere is cause by molecule hit
- density of He, Ne, Ar in lunar atomsphere $n \propto\frac{1}{T^{\frac{5}{2}}}$
![](https://i.imgur.com/jdgd9vp.jpg)
- Na in lunar atmosphere extend to about 8~10 lunar radius, there is a sunken on the opposite side because there is no sunlight
- lunar sodium tail
- photon momentum $p = \frac{hv}{c}$
- Radiation Pressure accumulation
![](https://i.imgur.com/AdM3kAh.jpg)
###### PSR(Permanently Shadowal Regions)
- ISRU(In-Situ Resource Utilization)

#### Creustal asymmetry
#### Core

## Lecture 5
### The terrestrial planets: Mercury, Venus, and Mars

#### Mars

##### Introduction
- Radius $= 3396 km$
- Mass $= 6.42\times 10^{26}g$
- Density $= 3.96 g/cc$
- Suface temperature
    - day：$293K$
    - night：$150K$(release the heat **kept in the daytime**)
- Crustal magnetic field
    - residue 4 billion years ago
    - **most in the south**

##### Surface geomorphology
- consist of atomsphere：$CO_2$、$N_2$
- pressure：$0.7 mb$($< 0.1\%$)
- **LiDAR** 

##### Mars exploration
- early
    - Mariner 6/7：$CO_2$ ice cap
    - Viking Lander(1976)：global map
    - Soviet Phobos Mission
- Odyessy(2001)：GRS(**Gamma ray spectrometer**)
    - graph here(cosmic ray porduction of gamma rays)
    - another graph here(nuclear physics right)
    - from the quantity of fast neutron and slow neutron, we can know the **particle size** in an area
        - FN > SN：most bigger particle
        - FN < SN：most same size particle(many hydragen, **find ice underground**)
        - Lunar gamma ray spectroscopy：Lunar Thorium map(in lunar sea and south pole atkins(SPA) are abundent in Thorium(from inside magma))
- diurnal surface temperature variation of Mars
    - the temperature go down at Mars 4 billion years ago
    - a theorem：4 billion years ago, a meteroids impact the surface and then cause the core of Mars stop flow, then the solar wind blows out the water on the surface(recording 1:35:57)
    - depth distribution of water ice on Mars(graph here)

- Near Earth Objects，NEOs


### The gas giants: Jupiter and Saturn

### The icy giants: Uranus and Neptune

### The small bodies: Asteroids and comets

### The Kuiper belt objects