---
title: "Planetary Climates & Finding Other Worlds"
subtitle: "Greenhouse Effect, Transits, and Habitability"
author: "Dr. Anna Rosen"
date: "2026-02-25"
description: "Venus is a hellscape. Mars is frozen. Earth is just right. Why? The greenhouse effect. Then: how we find exoplanets and assess habitability."
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}
Three Worlds, Three Fates
:::

::: {.fragment .text-center .mt-4}
Venus, Earth, Mars — rocky planets from the same solar nebula.

Why such different outcomes?
:::

::: {.notes}
0–1 min. "Same starting materials, radically different results."
:::

---

## The Outcomes {background-color="#1a1a2e"}

| Planet | T_observed | Pressure | Surface |
|--------|------------|----------|---------|
| Venus | 735 K (462°C) | 90× Earth | Hellscape |
| Earth | 288 K (15°C) | 1 bar | Oceans, life |
| Mars | 218 K (-55°C) | 0.006 bar | Frozen desert |

::: {.fragment .mt-4}
**The physics that explains this:** energy balance + greenhouse effect.
:::

::: {.notes}
1–2 min. "Radically different surface conditions."
:::

---

## 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}
- Explain why **surface temperatures differ** from equilibrium temperatures
- Describe the **greenhouse effect** and its role in climate
- Apply the **transit method** to detect exoplanets
- Combine **RV + transit** to determine exoplanet densities
- Define the **habitable zone** and what makes a planet potentially habitable
:::

:::

::: {.notes}
2–3 min. "Climate physics and exoplanet detection."
:::

---

## {.center}

::: {.r-fit-text}
Part 1: Planetary Climates
:::

*Energy balance and the greenhouse effect*

---

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

Before we do any math: if a planet is **twice as far** from its star, its equilibrium temperature $T_{eq}$ 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 reveal with the formula: $T_{eq}\propto d^{-1/2}$, so doubling distance multiplies $T_{eq}$ by $1/\sqrt{2}\approx 0.7$.
:::

---

## Equilibrium Temperature {background-color="#0a2f5c"}

::: {.text-center .bg-muted .p-3}
**Equilibrium:** Energy absorbed = Energy radiated

$$T_{eq} = \left[ \frac{(1-A) L_\odot}{16\pi \sigma d^2} \right]^{1/4}$$
:::

::: {.fragment .mt-4}
This is the temperature a planet *would* have with no atmosphere.

When observed ≠ equilibrium, **something interesting is happening**.
:::

::: {.notes}
3–4 min. "Equilibrium is the baseline prediction."
:::

---

## Predictions vs. Reality {background-color="#1a1a2e"}

| Planet | T_equilibrium | T_observed | Difference |
|--------|---------------|------------|------------|
| Venus | ~230 K | **735 K** | **+505 K** |
| Earth | ~255 K | 288 K | +33 K |
| Mars | ~210 K | 218 K | +8 K |

::: {.fragment .mt-4 .text-center .text-xl}
**Venus is 500 K hotter than predicted!**
:::

::: {.notes}
4–5 min. "Venus is the extreme outlier."
:::

---

## The Greenhouse Effect {background-color="black"}

{{< fig greenhouse-effect >}}

::: {.fragment .mt-2}
1. Sunlight (visible) heats surface
2. Surface emits infrared
3. Greenhouse gases **absorb infrared**
4. Atmosphere re-radiates — some back down
5. Surface must warm to compensate
:::

::: {.notes}
5–6 min. "The greenhouse effect mechanism."
:::

---

## Quick Check: Why Venus? {background-color="#1a1a2e"}

::: {.quiz}
Venus is hotter than Mercury, even though Mercury is closer to the Sun. Why?

- [ ] Stronger magnetic field
- [x] Thick CO₂ atmosphere causing strong greenhouse effect
- [ ] Slower rotation
- [ ] Active volcanoes
:::

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

---

## Venus: Runaway Greenhouse {background-color="#dc2626"}

::: {.text-center}
Venus may have started with conditions like early Earth.

But it was closer to the Sun...
:::

::: {.fragment .mt-4 .incremental .text-sm}
1. Higher T → more water evaporates
2. Water vapor is a greenhouse gas → T rises more
3. More evaporation → more warming (positive feedback!)
4. Oceans boil completely
5. UV breaks water → H escapes to space
6. CO₂ from volcanoes accumulates
7. **Result:** 96% CO₂, 735 K
:::

::: {.notes}
6–8 min. "The runaway greenhouse cascade."
:::

---

## Mars: Too Little Atmosphere {background-color="#1e3a5f"}

::: {.incremental}
- Surface pressure: **0.6%** of Earth's
- 95% CO₂, but so thin it barely matters
- Only ~8 K of greenhouse warming
- Lost atmosphere to solar wind (weak gravity, no magnetic field)
:::

::: {.fragment .mt-4}
**Evidence of past water:** Ancient river channels, minerals that form in liquid water.

Mars wasn't always this cold.
:::

::: {.notes}
8–9 min. "Mars has the opposite problem."
:::

---

## Earth: The Goldilocks Planet {background-color="#16a34a"}

::: {.incremental}
- **Right distance:** Warm enough for liquid water
- **Right atmosphere:** ~33 K greenhouse (not too much, not too little)
- **Carbon cycle:** Natural thermostat (oceans, rocks, volcanoes)
- **Magnetic field:** Protects atmosphere
:::

::: {.notes}
9–10 min. "Earth hits the sweet spot."
:::

---

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

::: {.quiz}
If Earth's CO₂ levels increase, what happens?

- [ ] Temperature decreases (CO₂ reflects sunlight)
- [ ] Temperature stays the same (equilibrium is fixed)
- [x] Temperature increases (more IR absorbed)
- [ ] Temperature increases only at night
:::

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

---

## {.center}

::: {.r-fit-text}
Part 2: Finding Exoplanets
:::

*Transits and the habitable zone*

---

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

::: {.text-center .text-xl}
Planets don't produce visible light.

Seeing an exoplanet directly is like spotting a firefly next to a searchlight.
:::

::: {.fragment .mt-4}
**Solution:** Look for the planet's **effect on its star**.
:::

::: {.notes}
10–11 min. "We detect planets indirectly."
:::

---

## The Transit Method {background-color="#0a2f5c"}

::: {.text-center .bg-muted .p-3}
When a planet crosses in front of its star, brightness dips.

$$\text{Transit depth} = \left(\frac{R_p}{R_*}\right)^2$$
:::

::: {.fragment .mt-4}
- Depth tells us **planet radius**
- Duration tells us **orbital distance**
- Period tells us **orbital period**
:::

::: {.notes}
11–12 min. "Transit geometry reveals planet size."
:::

---

## {background-color="black"}

{{< fig transit-light-curve >}}

::: {.notes}
12–13 min. Transit light curve visual.
:::

---

## Worked Example: Planet Size {background-color="black"}

**Problem:** A Sun-like star dims by 1% during transit. How big is the planet?

::: {.fragment}
$$\text{depth} = \left(\frac{R_p}{R_*}\right)^2 = 0.01$$
:::

::: {.fragment}
$$\frac{R_p}{R_*} = \sqrt{0.01} = 0.1$$
:::

::: {.fragment}
$$R_p = 0.1 \times R_\odot = 69,600 \text{ km}$$

**That's Jupiter-sized!**
:::

::: {.notes}
13–14 min. Walk through the calculation.
:::

---

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

::: {.quiz}
An Earth-sized planet (radius ~1% of Sun's) transiting a Sun-like star produces what depth?

- [ ] 1%
- [ ] 0.1%
- [x] 0.01%
- [ ] 0.001%
:::

::: {.fragment .mt-2 .text-sm}
**$(0.01)^2 = 0.0001 = 0.01\%$ — Earth-sized planets are HARD to detect!**
:::

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

---

## Combining Methods: The Jackpot {background-color="#1a1a2e"}

| Method | What It Gives |
|--------|---------------|
| Transit | Planet **radius** |
| Radial Velocity (L10) | Planet **mass** |

::: {.fragment .mt-4}
**Combined:**

$$\text{Density} = \frac{M_p}{\frac{4}{3}\pi R_p^3}$$

Density → **rocky or gaseous?**
:::

::: {.notes}
14–15 min. "RV + transit gives us density."
:::

---

## What Density Tells Us {background-color="black"}

| Density | Composition | Example |
|---------|-------------|---------|
| ~5.5 g/cm³ | Rocky | Earth |
| ~1.3 g/cm³ | Gas giant | Jupiter |
| ~2-3 g/cm³ | Water world? Mini-Neptune? | Some super-Earths |

::: {.fragment .mt-4}
**Density distinguishes potentially habitable rocky worlds from gas/ice balls.**
:::

::: {.notes}
15–16 min. "Density reveals composition."
:::

---

## The Habitable Zone {background-color="#0a2f5c"}

::: {.text-center .bg-muted .p-3}
The range of distances where **liquid water could exist** on a planet's surface.
:::

{{< fig habitable-zone >}}

::: {.notes}
16–17 min. "The Goldilocks zone."
:::

---

## Habitable Zone ≠ Habitable! {background-color="#dc2626"}

::: {.text-center}
Being in the habitable zone doesn't guarantee habitability!
:::

::: {.fragment .mt-4}
- **Venus:** Near inner edge → 735 K hellscape
- **Mars:** Near outer edge → frozen desert
:::

::: {.fragment .mt-4 .text-muted}
Habitability requires atmosphere, right greenhouse effect, liquid water...

The zone is a **starting point**, not a guarantee.
:::

::: {.notes}
17–18 min. "Important caveat."
:::

---

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

::: {.quiz}
If a star is 4× as luminous as the Sun, its habitable zone is:

- [ ] Same location as the Sun's
- [ ] Closer to the star
- [x] Farther from the star
- [ ] No habitable zone exists
:::

::: {.fragment .mt-2 .text-sm}
**More luminous → more energy → HZ moves out by $\sqrt{4} = 2×$.**
:::

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

---

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

::: {.text-sm}

**Planetary Climates:**

1. Equilibrium T depends on distance and albedo
2. **Greenhouse effect:** Atmosphere absorbs IR → surface warms
3. Venus: Runaway greenhouse → 735 K. Mars: Too thin → 218 K.

**Exoplanet Detection:**

4. **Transit depth** = $(R_p/R_*)^2$ → planet radius
5. **RV + Transit** → mass + radius → density → rocky vs. gaseous
6. **Habitable zone:** Where liquid water *could* exist

:::

::: {.notes}
18–20 min. Rapid recap.
:::

---

## Coming Up: Are We Alone? {background-color="black"}

::: {.text-center .text-xl}
**Next lecture:** The Drake Equation and the search for life.
:::

::: {.fragment .mt-4}
Your favorite NASA science question — approached as astronomy.
:::

::: {.notes}
20–21 min. Preview L13 synthesis lecture.
:::

---

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

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

*Calculating equilibrium temperatures and transit depths*

::: {.notes}
Let's verify our climate and exoplanet equations with explicit calculations.
:::

---

## Equilibrium Temperature: Derivation {background-color="#1a1a2e"}

**Energy in = Energy out (at equilibrium)**

::: {.fragment}
**Power absorbed** from the Sun:

$$P_{in} = (1-A) \times \pi R_p^2 \times \frac{L_\odot}{4\pi d^2}$$

- $(1-A)$ = fraction absorbed (A = albedo)
- $\pi R_p^2$ = cross-sectional area facing Sun
- $L_\odot/(4\pi d^2)$ = solar flux at distance $d$
:::

::: {.fragment}
**Power radiated** as thermal emission:

$$P_{out} = 4\pi R_p^2 \times \sigma T^4$$
:::

::: {.notes}
"The planet intercepts sunlight on its cross-section, radiates from its whole surface."
:::

---

## Equilibrium Temperature: Solution {background-color="#1a1a2e"}

**Set $P_{in} = P_{out}$:**

$$$(1-A) \pi R_p^2 \frac{L_\odot}{4\pi d^2} = 4\pi R_p^2 \sigma T^4$$

::: {.fragment}
**Cancel $\pi R_p^2$ and solve for T:**

$$T_{eq} = \left[\frac{(1-A) L_\odot}{16 \pi \sigma d^2}\right]^{1/4}$$
:::

::: {.fragment}
**For objects orbiting the Sun:**

$$T_{eq} = 279 \text{ K} \times (1-A)^{1/4} \times \left(\frac{1 \text{ AU}}{d}\right)^{1/2}$$
:::

::: {.notes}
"The 279 K comes from plugging in solar luminosity and Stefan-Boltzmann constant."
:::

---

## Earth's Equilibrium Temperature {background-color="#1a1a2e"}

**Given:**

- Distance: $d = 1$ AU
- Albedo: $A = 0.30$ (Earth reflects 30% of sunlight)

::: {.fragment}
$$T_{eq} = 279 \text{ K} \times (1-0.30)^{1/4} \times \left(\frac{1}{1}\right)^{1/2}$$
:::

::: {.fragment}
$$T_{eq} = 279 \text{ K} \times (0.70)^{0.25} = 279 \times 0.915$$
:::

::: {.fragment}
$$T_{eq} = 255 \text{ K} = -18°\text{C}$$
:::

::: {.fragment .bg-warning-subtle .p-2}
**But Earth's actual average is 288 K = +15°C!**

The +33 K difference is the **greenhouse effect**.
:::

::: {.notes}
"Without greenhouse gases, Earth would be frozen."
:::

---

## Venus: Why So Hot? {background-color="#1a1a2e"}

**Given:**

- Distance: $d = 0.72$ AU
- Albedo: $A = 0.75$ (Venus is VERY reflective)

::: {.fragment}
$$T_{eq} = 279 \text{ K} \times (1-0.75)^{1/4} \times \left(\frac{1}{0.72}\right)^{1/2}$$
:::

::: {.fragment}
$$T_{eq} = 279 \times (0.25)^{0.25} \times (1.39)^{0.5} = 279 \times 0.707 \times 1.18$$
:::

::: {.fragment}
$$T_{eq} = 232 \text{ K} = -41°\text{C}$$
:::

::: {.fragment .bg-danger-subtle .p-2}
**But Venus's actual surface is 735 K = +462°C!**

The +503 K difference is the **runaway greenhouse effect**.
:::

::: {.notes}
"Venus's equilibrium temperature is COLDER than Earth's (high albedo). But its surface is hellish."
:::

---

## Transit Depth: Earth Around the Sun {background-color="#1a1a2e"}

**How deep would Earth's transit be?**

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

- $R_E = 6,371$ km = $6.371 \times 10^6$ m
- $R_\odot = 6.96 \times 10^8$ m
:::

::: {.fragment}
**Transit depth:**

$$\delta = \left(\frac{R_E}{R_\odot}\right)^2 = \left(\frac{6.371 \times 10^6}{6.96 \times 10^8}\right)^2$$
:::

::: {.fragment}
$$= (9.15 \times 10^{-3})^2 = 8.4 \times 10^{-5}$$
:::

::: {.fragment .bg-muted .p-2}
**Transit depth = 0.0084% = 84 parts per million**

This is why Kepler needed such precise photometry!
:::

::: {.notes}
"Finding Earth-like planets requires detecting 84 ppm dips in stellar brightness."
:::

---

## TRAPPIST-1 System: Full Calculation {background-color="#1a1a2e"}

**TRAPPIST-1 has 7 Earth-sized planets around a small red dwarf!**

**Given:**

- Star radius: $R_* = 0.121 R_\odot$
- Planet e radius: $R_p \approx 0.92 R_E$

::: {.fragment}
$$\delta = \left(\frac{R_p}{R_*}\right)^2 = \left(\frac{0.92 \times 6.371 \times 10^6}{0.121 \times 6.96 \times 10^8}\right)^2$$
:::

::: {.fragment}
$$= \left(\frac{5.86 \times 10^6}{8.42 \times 10^7}\right)^2 = (0.0696)^2 = 0.0048 = 0.48\%$$
:::

::: {.fragment .bg-success-subtle .p-2}
**Transit depth = 0.48%** — 57× deeper than Earth around the Sun!

Small stars → bigger transit signals → easier to find small planets.
:::

::: {.notes}
"This is why TRAPPIST-1 was such a breakthrough system."
:::

---

## Habitable Zone Distance: Full Derivation {background-color="#1a1a2e"}

**Where does $T_{eq} = 273$ K (water freezing point)?**

Using $T_{eq} = 279(1-A)^{1/4}(d/\text{AU})^{-1/2}$ with $A \approx 0.3$:

::: {.fragment}
$$273 = 279 \times (0.7)^{0.25} \times d^{-0.5}$$
$$273 = 255 \times d^{-0.5}$$
:::

::: {.fragment}
$$d^{0.5} = \frac{255}{273} = 0.934$$
$$d = 0.87 \text{ AU}$$
:::

::: {.fragment}
**For $T = 373$ K (boiling):**

$$d = \left(\frac{255}{373}\right)^2 = 0.47 \text{ AU}$$
:::

::: {.fragment .bg-muted .p-2}
**Sun's HZ (simple estimate): ~0.5–0.9 AU**

(More detailed models: 0.95–1.7 AU accounting for atmosphere effects)
:::

::: {.notes}
"This simple estimate puts Earth near the outer edge. Venus is inside the inner edge."
:::

---

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

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

*Atmospheric escape and biosignatures*

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

---

## Why Mars Lost Its Atmosphere {background-color="#0a2f5c"}

**Atmospheric escape velocity** for a gas molecule:

$$v_{thermal} = \sqrt{\frac{3k_B T}{m}}$$

::: {.fragment}
**For hydrogen (H₂) at 300 K:**

$$v_H = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 300}{3.3 \times 10^{-27}}} = 1,580 \text{ m/s}$$
:::

::: {.fragment}
**Compare to escape velocities:**

- Mars: $v_{esc} = 5.0$ km/s → H₂ escapes easily (v_thermal × 6 = 9.5 km/s tail)
- Earth: $v_{esc} = 11.2$ km/s → H₂ escapes, but slowly
- Jupiter: $v_{esc} = 59.5$ km/s → H₂ retained
:::

::: {.notes}
"Light molecules at the high-velocity tail of the distribution can escape."
:::

---

## The Rule of Six {background-color="#0a2f5c"}

**Atmospheric retention rule:**

If $v_{esc} < 6 \times v_{thermal}$ for a molecule, that molecule **gradually escapes**.

::: {.fragment}
**Why 6?** The Maxwell-Boltzmann distribution has a high-velocity tail. At 6× the average, there's still enough molecules escaping to matter over billions of years.
:::

::: {.fragment .mt-4}
| Planet | $v_{esc}$ | H₂ retained? | CO₂ retained? | N₂ retained? |
|--------|-----------|--------------|---------------|--------------|
| Mars | 5.0 km/s | ✗ | Marginal | ✓ |
| Earth | 11.2 km/s | ✗ | ✓ | ✓ |
| Venus | 10.4 km/s | ✗ | ✓ | ✓ |
:::

::: {.notes}
"Mars couldn't hold onto its early atmosphere. Earth can retain heavy molecules but not hydrogen."
:::

---

## Biosignatures: What to Look For {background-color="#0a2f5c"}

**Atmospheric signatures of life:**

::: {.incremental}
1. **Oxygen (O₂):** Highly reactive; needs continuous production. On Earth: photosynthesis.

2. **Ozone (O₃):** Product of O₂; detectable in UV spectra.

3. **Methane (CH₄):** Short-lived in oxidizing atmosphere; needs ongoing source.

4. **Methane + Oxygen together:** Thermodynamically unstable. Both present = something replenishing them!
:::

::: {.fragment .mt-2 .bg-muted .p-2}
**JWST can detect some of these in transiting exoplanet atmospheres!**
:::

::: {.notes}
"This is cutting-edge astrobiology happening right now."
:::

---

## JWST Transmission Spectroscopy {background-color="#0a2f5c"}

**How it works:**

During transit, starlight passes through the planet's atmosphere.

Different molecules absorb different wavelengths.

::: {.fragment}
**The signal:**

$$\delta_{atm} = \frac{2 R_p H}{R_*^2}$$

where $H$ = atmospheric scale height (typically 10-30 km for rocky planets)
:::

::: {.fragment}
**For Earth around the Sun:**

$$\delta_{atm} \approx \frac{2 \times 6371 \times 10 \text{ km}}{(696,000)^2} \approx 2.6 \times 10^{-7} = 0.26 \text{ ppm}$$
:::

::: {.fragment .text-muted}
Incredibly small! But detectable for larger planets around smaller stars.
:::

::: {.notes}
"JWST has already detected water, CO₂, and SO₂ in exoplanet atmospheres."
:::

---

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

::: {.text-center .text-xl .mt-4}
**Climate:** Same physics for Venus, Earth, Mars, and us.

**Exoplanets:** Transits + RV = density = composition.
:::

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