---
title: "Our Cosmic Backyard"
subtitle: "Solar System Architecture & Formation"
author: "Dr. Anna Rosen"
date: "2026-02-23"
description: "The solar system is where we apply everything we've learned. Kepler's Laws, Newton's gravity, blackbody radiation, spectroscopy — all used to understand our cosmic neighborhood."
draft: true

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---

## Join iClicker {background-color="black"}

::: {.text-center}
{{< img iclicker-qr-astr101 width="36%" class="img-center" >}}

::: {.text-xl .font-semibold .mt-2}
[join.iclicker.com/ASES](https://join.iclicker.com/ASES)
:::
:::

::: {.notes}
30–60 sec. Get everyone connected before starting.
:::

---

## {background-color="black"}

::: {.r-fit-text}
Worlds We've Never Stood On
:::

::: {.fragment .text-center .mt-4}
We know the mass of Jupiter.

We didn't weigh it. We watched how things **move around it**.
:::

::: {.notes}
0–1 min. "We can measure worlds we will never touch."
:::

---

## The Power of Remote Sensing {background-image="../../../assets/images/common/cosmic-cliffs-jwst.png" background-opacity="0.2"}

From billions of kilometers away, we can measure:

::: {.incremental}
- **Mass** from orbits (Newton, L6)
- **Temperature** from infrared glow (Wien, L8)
- **Composition** from spectral lines (L9)
- **Motion** from Doppler shifts (L10)
:::

::: {.fragment .mt-4}
Today: **Apply the entire Module 1 toolkit** to our solar system.
:::

::: {.notes}
1–2 min. "Everything we've learned comes together today."
:::

---

## Today's Learning Objectives {background-image="../../../assets/images/common/cosmic-cliffs-jwst.png" background-opacity="0.2"}

::: {.bg-muted .p-2}

By the end of today, you'll be able to:

::: {.incremental .text-sm}
- Describe the **architecture** of the solar system (rocky, gas giants, ice giants, small bodies)
- Explain the **nebular hypothesis** for solar system formation
- Apply **Kepler, Newton, spectroscopy** to determine planetary properties
- Explain why **rocky planets formed close** and **gas giants formed far**
:::

:::

::: {.notes}
2–3 min. "This is a capstone lecture — applying everything."
:::

---

## {.center}

::: {.r-fit-text}
Part 1: Solar System Architecture
:::

*The grand tour*

---

## The Zones {background-color="black"}

{{< fig solar-system-architecture >}}

::: {.notes}
3–4 min. "The solar system has a clear structure."
:::

---

## Rocky Planets (0.4–1.5 AU) {background-color="#1a1a2e"}

::: {.text-sm}
| Planet | Distance | Size | Surface |
|--------|----------|------|---------|
| Mercury | 0.39 AU | 0.38 R⊕ | Cratered, no atmosphere |
| Venus | 0.72 AU | 0.95 R⊕ | Hellscape, 735 K |
| Earth | 1.0 AU | 1.0 R⊕ | Oceans, life |
| Mars | 1.52 AU | 0.53 R⊕ | Cold desert |
:::

::: {.fragment .mt-2}
**Common features:** Small, dense (4-5 g/cm³), solid surfaces
:::

::: {.notes}
4–5 min. "Rocky planets are small and dense."
:::

---

## Gas Giants (5–10 AU) {background-color="#1a1a2e"}

::: {.text-sm}
| Planet | Distance | Size | Composition |
|--------|----------|------|-------------|
| Jupiter | 5.2 AU | 11 R⊕ | H/He dominated |
| Saturn | 9.5 AU | 9.4 R⊕ | H/He, famous rings |
:::

::: {.fragment .mt-2}
**Key facts:**

- Jupiter has **318 Earth masses** (more than all other planets combined!)
- Saturn would **float in water** (density 0.69 g/cm³)
- **No solid surface** — just deeper and denser gas/liquid
:::

::: {.notes}
5–6 min. "Gas giants are dominated by hydrogen and helium."
:::

---

## Ice Giants (19–30 AU) {background-color="#1a1a2e"}

::: {.text-sm}
| Planet | Distance | Size | Composition |
|--------|----------|------|-------------|
| Uranus | 19.2 AU | 4.0 R⊕ | H/He + ices |
| Neptune | 30.1 AU | 3.9 R⊕ | H/He + ices |
:::

::: {.fragment .mt-2}
**Different from gas giants:**

- More water, ammonia, methane **ices**
- Blue-green from **methane absorbing red light**
- Smaller but still massive (~15-17 M⊕)
:::

::: {.notes}
6–7 min. "Ice giants are distinct from gas giants."
:::

---

## Two Families of Planets {background-color="black"}

| Property | Rocky | Giants |
|----------|------:|-------:|
| Size | Small | Large |
| Mass | Low | High |
| Density | High (4-5 g/cm³) | Low (0.7-1.6 g/cm³) |
| Composition | Rock, metal | H, He, ices |
| Surface | Solid | None |

::: {.fragment .mt-4 .text-center}
**Why this pattern?** Formation explains everything.
:::

::: {.notes}
7–8 min. "Two families with different properties."
:::

---

## Quick Check: Planet Classification {background-color="#1a1a2e"}

::: {.quiz}
Saturn has density 0.69 g/cm³ — less than water. What does this tell you about its composition?

- [ ] Rock and metal
- [x] Primarily lightweight gases (hydrogen, helium)
- [ ] No atmosphere
- [ ] Same as Earth
:::

::: {.notes}
1 min. iClicker poll.
:::

---

## {.center}

::: {.r-fit-text}
Part 2: Applying Our Toolkit
:::

*How do we know what we know?*

---

## The Module 1 Toolkit {background-color="#1a1a2e"}

::: {.text-sm}
| What We Measure | The Tool | The Physics |
|-----------------|----------|-------------|
| Distance from Sun | Kepler III | $P^2 \propto a^3$ |
| Mass (with moons) | Moon orbits + Newton | $M = 4\pi^2 a^3/(GP^2)$ |
| Temperature | IR spectrum + Wien | Peak → T |
| Composition | Spectral lines | Fingerprints |
:::

::: {.notes}
8–9 min. "All Module 1 tools applied to planets."
:::

---

## Worked Example: Jupiter's Mass {background-color="black"}

**Problem:** Io orbits Jupiter at a = 422,000 km with P = 1.77 days. Find Jupiter's mass.

::: {.fragment}
Using Newton's form of Kepler III:
$$M = \frac{4\pi^2 a^3}{GP^2}$$
:::

::: {.fragment}
$$M = \frac{4\pi^2 (4.22 \times 10^8 \text{ m})^3}{(6.67 \times 10^{-11})(1.53 \times 10^5 \text{ s})^2}$$
:::

::: {.fragment}
$$M = 1.9 \times 10^{27} \text{ kg} = 318 \text{ Earth masses}$$
:::

::: {.notes}
9–10 min. Walk through the calculation.
:::

---

## Quick Check: Applying Newton {background-color="#1a1a2e"}

::: {.quiz}
If a moon orbits at twice the distance but with the same period, the planet's mass is:

- [ ] The same
- [ ] 2× larger
- [ ] 4× larger
- [x] 8× larger
:::

::: {.fragment .mt-2 .text-sm}
**From $M \propto a^3/P^2$:** if $a$ doubles and $P$ stays same → $M$ increases by $2^3 = 8$.
:::

::: {.notes}
1–2 min. iClicker poll, then explain.
:::

---

## Predict First! {background-color="#1a1a2e"}

Before we look at the numbers: if a planet is **twice as far** from the Sun, its equilibrium temperature $T_{eq}$ (no-atmosphere baseline) should be…

:::: {.columns .mt-4}
::: {.column width="25%"}
A) 2× higher
:::

::: {.column width="25%"}
B) 1/2×
:::

::: {.column width="25%"}
C) ~0.7×
:::

::: {.column width="25%"}
D) 1/4×
:::
::::

::: {.notes}
30 s. Commit first. Then connect: equilibrium temperature scales like distance$^{-1/2}$, so doubling distance multiplies $T_{eq}$ by $1/\sqrt{2}\approx 0.7$ (under the simple radiative-equilibrium model).
:::

---

## Temperature from Wien's Law {background-color="#1a1a2e"}

::: {.text-sm}
| Planet | T_equilibrium | T_observed | Difference |
|--------|---------------|------------|------------|
| Mercury | ~440 K | 90–700 K | Extreme swings |
| Venus | ~230 K | **735 K** | +505 K! |
| Earth | ~255 K | 288 K | +33 K |
| Mars | ~210 K | 218 K | +8 K |
:::

::: {.fragment .mt-2}
**Venus stands out:** 500 K hotter than expected!

**Why?** Greenhouse effect (L12 preview).
:::

::: {.notes}
10–11 min. "Compare equilibrium to observed temperatures."
:::

---

## {.center}

::: {.r-fit-text}
Part 3: Formation
:::

*Why does it look this way?*

---

## The Nebular Hypothesis {background-color="black"}

The solar system formed ~4.6 billion years ago from a collapsing cloud of gas and dust.

::: {.incremental}
1. **Gravity → Collapse**
2. **Collapse → Spin-up** (angular momentum)
3. **Spin-up → Disk** (material settles)
4. **Temperature gradient** → different materials condense
5. **Core growth outside frost line** → gas capture
:::

::: {.notes}
11–13 min. "The causal chain of formation."
:::

---

## {background-color="black"}

{{< fig nebular-hypothesis >}}

::: {.notes}
13–14 min. Visual of nebular formation.
:::

---

## The Frost Line {background-color="#0a2f5c"}

::: {.text-center .text-xl .bg-muted .p-3}
**Frost line:** ~3 AU from young Sun

Where it was cold enough for **ices to form**.
:::

::: {.fragment .mt-4}
| Region | Solid Material | Result |
|--------|----------------|--------|
| Inside frost line | Rock, metal only | **Small rocky planets** |
| Outside frost line | Rock + metal + ices | **Large cores → gas giants** |
:::

::: {.notes}
14–15 min. "The frost line explains the planet distribution."
:::

---

## Quick Check: Formation {background-color="#1a1a2e"}

::: {.quiz}
Why didn't Earth become a gas giant like Jupiter?

- [ ] Earth formed before Jupiter
- [ ] Not enough hydrogen near Earth
- [x] Earth was inside the frost line, so its core stayed small
- [ ] Jupiter stole all the gas
:::

::: {.notes}
1 min. iClicker poll.
:::

---

## Evidence for the Nebular Hypothesis {background-color="#1a1a2e"}

::: {.incremental}
1. All planets orbit in the **same direction** — from the disk's rotation
2. All planets orbit in nearly the **same plane** — the disk was flat
3. **Rocky inside, giants outside** — frost line
4. **We observe protoplanetary disks** around other young stars!
:::

::: {.notes}
15–16 min. "Multiple lines of evidence support the model."
:::

---

## {background-color="black"}

{{< fig protoplanetary-disk >}}

::: {.fragment .text-center .mt-2}
**We see solar systems forming around other stars.**
:::

::: {.notes}
16–17 min. "Protoplanetary disks are observed directly."
:::

---

## Key Takeaways {background-color="#0a2f5c"}

::: {.text-sm}

**Architecture:**

1. Rocky planets inside (~1.5 AU), gas giants (5–10 AU), ice giants (19–30 AU)
2. Two families: small/dense/rocky vs. large/low-density/gaseous

**Toolkit:**

3. Masses from orbits (Newton), temperatures from IR (Wien), compositions from spectra

**Formation:**

4. Nebular hypothesis: collapse → disk → condensation
5. Frost line (~3 AU) explains rocky vs. gas giant distribution

:::

::: {.notes}
17–18 min. Rapid recap.
:::

---

## Coming Up: Planetary Climates {background-color="black"}

::: {.text-center .text-xl}
**Next lecture:** Why Venus is a hellscape, Earth is habitable, and Mars is frozen.
:::

::: {.fragment .mt-4}
Then: Exoplanet detection — finding worlds around other stars.
:::

::: {.notes}
18–19 min. Preview L12.
:::

---

## {.center background-color="#1a1a2e"}

::: {.r-fit-text}
Numerical Verification
:::

*Calculating solar system properties with careful units*

::: {.notes}
Let's apply our toolkit with explicit calculations.
:::

---

## Jupiter's Mass from Io's Orbit {background-color="#1a1a2e"}

**Given:**

- Io's orbital period: $P = 1.77$ days
- Io's orbital radius: $a = 421,700$ km

::: {.fragment}
**Step 1: Convert to SI units**

$$P = 1.77 \text{ days} \times \frac{86,400 \text{ s}}{1 \text{ day}} = 1.53 \times 10^5 \text{ s}$$

$$a = 421,700 \text{ km} \times \frac{1000 \text{ m}}{1 \text{ km}} = 4.217 \times 10^8 \text{ m}$$
:::

::: {.notes}
"Always convert to SI before using Newton's form of Kepler III."
:::

---

## Jupiter's Mass: Calculation {background-color="#1a1a2e"}

**Newton's form of Kepler III:**

$$M = \frac{4\pi^2 a^3}{G P^2}$$

::: {.fragment}
**Substitute values:**

$$M_J = \frac{4\pi^2 \times (4.217 \times 10^8)^3}{(6.674 \times 10^{-11}) \times (1.53 \times 10^5)^2}$$
:::

::: {.fragment}
**Numerator:**

$$4\pi^2 \times (4.217 \times 10^8)^3 = 39.48 \times 7.50 \times 10^{25} = 2.96 \times 10^{27} \text{ m}^3$$
:::

::: {.fragment}
**Denominator:**

$$(6.674 \times 10^{-11}) \times (2.34 \times 10^{10}) = 1.56 \times 10^{0} \text{ m}^3/\text{kg}$$
:::

::: {.notes}
"Let me work through the units carefully."
:::

---

## Jupiter's Mass: Unit Analysis {background-color="#1a1a2e"}

**Check the denominator units:**

$$[G \times P^2] = \frac{\text{N} \cdot \text{m}^2}{\text{kg}^2} \times \text{s}^2 = \frac{\text{kg} \cdot \text{m}}{\text{s}^2} \times \frac{\text{m}^2}{\text{kg}^2} \times \text{s}^2$$

::: {.fragment}
$$= \frac{\text{m}^3}{\text{kg}} \quad \checkmark$$
:::

::: {.fragment}
**Final result:**

$$M_J = \frac{2.96 \times 10^{27} \text{ m}^3}{1.56 \text{ m}^3/\text{kg}} = 1.90 \times 10^{27} \text{ kg}$$
:::

::: {.fragment .bg-success-subtle .p-2}
**Jupiter's mass: $1.9 \times 10^{27}$ kg**
:::

::: {.notes}
"We 'weighed' Jupiter by watching one of its moons orbit."
:::

---

## Frost Line Temperature {background-color="#1a1a2e"}

**Why is the frost line “a few AU”?**

In the early solar nebula, ices could only form where the disk was cold enough — so there was much more solid material (rock + metal + ice) beyond the frost line.

- **Order-of-magnitude for our solar system:** ~3 AU (between Mars and Jupiter)
- **Not a fixed wall:** it shifts over time as the young Sun’s luminosity and disk heating change

::: {.fragment}
**Simple scaling idea (radiative equilibrium):**

$$T \propto L^{1/4}\,r^{-1/2}$$

If the young Sun were more luminous (or the disk were hotter), the frost line would be farther out — and vice versa.
:::

::: {.notes}
Keep the message conceptual: the frost line is an order-of-magnitude location and a moving target. Avoid “exact” derivations from Earth’s present-day climate, because the protoplanetary disk is not the same physical system.
:::

---

## Planetary Density Calculation {background-color="#1a1a2e"}

**Calculate Earth's average density:**

::: {.fragment}
**Given:**

- Mass: $M_E = 5.97 \times 10^{24}$ kg
- Radius: $R_E = 6.371 \times 10^6$ m
:::

::: {.fragment}
**Volume:**

$$V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi (6.371 \times 10^6)^3 = 1.083 \times 10^{21} \text{ m}^3$$
:::

::: {.fragment}
**Density:**

$$\rho = \frac{M}{V} = \frac{5.97 \times 10^{24} \text{ kg}}{1.083 \times 10^{21} \text{ m}^3} = 5,510 \text{ kg/m}^3$$
:::

::: {.fragment}
**Convert to g/cm³:** (water = 1 g/cm³)

$$\rho = 5510 \text{ kg/m}^3 \times \frac{1 \text{ g/cm}^3}{1000 \text{ kg/m}^3} = 5.51 \text{ g/cm}^3$$
:::

::: {.notes}
"Earth is 5.5× denser than water — made of rock and metal."
:::

---

## Density Comparison {background-color="#1a1a2e"}

| Planet | Mass ($M_E$) | Radius ($R_E$) | Density (g/cm³) |
|--------|--------------|----------------|-----------------|
| Mercury | 0.055 | 0.38 | 5.43 |
| Venus | 0.82 | 0.95 | 5.24 |
| Earth | 1.00 | 1.00 | 5.51 |
| Mars | 0.11 | 0.53 | 3.93 |
| Jupiter | 318 | 11.2 | **1.33** |
| Saturn | 95 | 9.4 | **0.69** |

::: {.fragment .mt-2 .bg-warning-subtle .p-2}
**Saturn's density < water!** It would float (if you had a big enough bathtub).

$\rho = \frac{95 M_E}{(9.4 R_E)^3} = \frac{95}{830} \times 5.51 = 0.63$ g/cm³
:::

::: {.notes}
"Low density = lots of gas (H, He). High density = rock and metal."
:::

---

## {.center background-color="#0a2f5c"}

::: {.r-fit-text}
Deeper Dive
:::

*Orbital mechanics and the Roche limit*

::: {.notes}
Optional advanced content.
:::

---

## Orbital Velocity Around the Sun {background-color="#0a2f5c"}

**For a circular orbit:**

$$v = \sqrt{\frac{GM_\odot}{r}}$$

::: {.fragment}
**Earth's orbital velocity:**

$$v_E = \sqrt{\frac{6.674 \times 10^{-11} \times 1.99 \times 10^{30}}{1.496 \times 10^{11}}}$$
:::

::: {.fragment}
$$v_E = \sqrt{\frac{1.33 \times 10^{20}}{1.50 \times 10^{11}}} = \sqrt{8.87 \times 10^{8}} \text{ m}^2/\text{s}^2$$
:::

::: {.fragment}
$$v_E = 29,800 \text{ m/s} = 29.8 \text{ km/s}$$
:::

::: {.fragment .text-muted}
Earth moves at **107,000 km/hr** around the Sun!
:::

::: {.notes}
"We're moving fast, we just don't feel it because everything around us moves too."
:::

---

## Orbital Velocities Across the Solar System {background-color="#0a2f5c"}

Since $v \propto 1/\sqrt{r}$:

| Planet | r (AU) | v (km/s) | Calculation |
|--------|--------|----------|-------------|
| Mercury | 0.39 | 47.4 | $29.8/\sqrt{0.39}$ |
| Venus | 0.72 | 35.0 | $29.8/\sqrt{0.72}$ |
| Earth | 1.00 | 29.8 | (reference) |
| Mars | 1.52 | 24.1 | $29.8/\sqrt{1.52}$ |
| Jupiter | 5.20 | 13.1 | $29.8/\sqrt{5.20}$ |
| Neptune | 30.1 | 5.4 | $29.8/\sqrt{30.1}$ |

::: {.fragment .mt-2}
**Pattern:** Outer planets move slower — both because of longer paths AND lower speeds!
:::

::: {.notes}
"This is Kepler's Second Law in action. Farther = slower."
:::

---

## The Roche Limit {background-color="#0a2f5c"}

**What happens when a moon gets too close?**

Tidal forces (gravity gradient) can tear it apart!

::: {.fragment}
**The Roche limit:**

$$d_{Roche} \approx 2.44 R_p \left(\frac{\rho_p}{\rho_m}\right)^{1/3}$$

where $R_p$ = planet radius, $\rho$ = densities
:::

::: {.fragment}
**For Saturn (using similar densities):**

$$d_{Roche} \approx 2.44 \times 58,232 \text{ km} = 142,000 \text{ km}$$

Saturn's rings extend to ~137,000 km — **inside the Roche limit!**
:::

::: {.notes}
"This is why Saturn has rings instead of a moon at that distance."
:::

---

## Why Rings, Not Moons? {background-color="#0a2f5c"}

**Inside the Roche limit:**

- Material can't coalesce into a moon
- Existing moons would be torn apart
- Only small particles can survive → **rings**

::: {.fragment}
**Outside the Roche limit:**

- Material can gravitationally clump
- Moons form and survive
- Saturn has 146+ moons beyond its rings!
:::

::: {.fragment .mt-2 .bg-muted .p-2}
**Ring systems mark the Roche limit.**

All four giant planets have rings inside their Roche limits.
:::

::: {.notes}
"The ring-moon boundary is the Roche limit in action."
:::

---

## Lagrange Points {background-color="#0a2f5c"}

**Special locations where gravity and orbital motion balance:**

::: {.text-sm}
- **L1:** Between Sun and Earth (~1.5 million km sunward) — solar observatories
- **L2:** Beyond Earth (~1.5 million km away) — JWST location!
- **L3:** Opposite side of Sun — sci-fi "Counter-Earth"
- **L4/L5:** 60° ahead/behind in orbit — trapped asteroids (Trojans)
:::

::: {.fragment .mt-2}
**JWST at L2:**

Always in Earth's shadow, stable orbit, uninterrupted sky view.

Distance: $\approx 1\%$ of Earth-Sun distance toward night side.
:::

::: {.notes}
"Lagrange points are 'parking spots' in the gravitational landscape."
:::

---

## Questions? {background-image="../../../assets/images/common/cosmic-cliffs-jwst.png" background-opacity="0.25"}

::: {.text-center .text-xl .mt-4}
**Module 1 toolkit applied:**

Motion → mass. Light → temperature & composition.

Formation → explains the pattern.
:::

::: {.notes}
Remaining time for questions.
:::
