---
title: "Are We Alone?"
subtitle: "Module 1 Synthesis — The Drake Equation"
author: "Dr. Anna Rosen"
date: "2026-02-27"
description: "Your favorite NASA science question — approached as astronomy. The Drake Equation organizes what we know and don't know about cosmic company."
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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}
Your Favorite Question
:::

::: {.fragment .text-center .mt-4 .text-xl}
"Are we alone in the universe?"
:::

::: {.fragment .mt-4 .text-muted}
Today: Not philosophy. Not science fiction.

**Astronomy.**
:::

::: {.notes}
0–1 min. "We'll approach this as scientists."
:::

---

## Today's 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 the **Drake Equation** and identify which terms we know vs. don't know
- Describe why **heavy elements** are necessary for rocky planets and life
- Connect **Module 1 concepts** to the search for life
- **Synthesize** all Module 1 tools: gravity, orbits, light, spectra, Doppler
:::

:::

::: {.notes}
1–2 min. "This is the Module 1 synthesis lecture."
:::

---

## {.center}

::: {.r-fit-text}
Part 1: The Drake Equation
:::

*A framework for the question*

---

## The Drake Equation (1961) {background-color="#0a2f5c"}

::: {.text-center .bg-muted .p-3}
$$N = R_* \times f_p \times n_e \times f_l \times f_i \times f_c \times L$$

$N$ = number of communicating civilizations in our galaxy
:::

::: {.fragment .mt-4 .text-muted}
Frank Drake didn't expect to calculate an exact answer.

The equation is a **framework** — it organizes what we need to know.
:::

::: {.notes}
2–3 min. "Drake's equation organizes the question."
:::

---

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

::: {.text-sm}
| Symbol | Meaning |
|--------|---------|
| $R_*$ | Star formation rate (new stars/year) |
| $f_p$ | Fraction of stars with planets |
| $n_e$ | Habitable planets per system |
| $f_l$ | Fraction that develop life |
| $f_i$ | Fraction with intelligence |
| $f_c$ | Fraction that communicate |
| $L$ | Civilization lifetime (years) |
:::

::: {.notes}
3–4 min. "Seven terms to estimate."
:::

---

## What We Know (Terms 1-3) {background-color="#16a34a"}

| Term | Value | How We Know |
|------|-------|-------------|
| $R_*$ | ~2-7/year | Star counts, luminosity |
| $f_p$ | ~1 | **Kepler mission!** (L12) |
| $n_e$ | ~0.1-0.5 | Kepler + habitable zone (L12) |

::: {.fragment .mt-4}
**Major progress:** Before Kepler (2009), we didn't know if planets were common.

Now we know: **at least one planet per star on average.**
:::

::: {.notes}
4–5 min. "The first three terms are now reasonably constrained."
:::

---

## Quick Check: What Kepler Told Us {background-color="#1a1a2e"}

::: {.quiz}
Which Drake Equation term became MUCH better constrained thanks to the Kepler mission?

- [ ] $f_l$ (fraction that develop life)
- [x] $f_p$ (fraction of stars with planets)
- [ ] $L$ (civilization lifetime)
- [ ] $f_i$ (fraction with intelligence)
:::

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

---

## What We Don't Know (Terms 4-7) {background-color="#dc2626"}

| Term | Value | Status |
|------|-------|--------|
| $f_l$ | ? | **Unknown** — 1 data point (Earth) |
| $f_i$ | ? | **Unknown** |
| $f_c$ | ? | **Unknown** |
| $L$ | ? | **The most sobering term** |

::: {.fragment .mt-4 .text-muted}
These four terms span our ignorance — and swing $N$ by **billions**.
:::

::: {.notes}
5–6 min. "The last four terms are completely uncertain."
:::

---

## Three Scenarios {background-color="#1a1a2e"}

::: {.text-sm}
| Scenario | Known terms | $f_l \times f_i \times f_c$ | $L$ | **N** |
|----------|-------------|---------------------------|-----|-------|
| Pessimistic | 0.6 | 0.000001 | 100 | ~0.00006 |
| Middle | 0.6 | 0.001 | 10,000 | ~6 |
| Optimistic | 0.6 | 0.125 | 1,000,000 | ~75,000 |
:::

::: {.fragment .mt-4 .text-center}
**Same first three terms — result swings by 9 orders of magnitude!**
:::

::: {.notes}
6–7 min. "The uncertainty is enormous."
:::

---

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

In the pessimistic scenario, $N \approx 0.00006$. What does $N \ll 1$ mean?

:::: {.columns .mt-4}
::: {.column width="50%"}
A) There are definitely zero civilizations.
:::

::: {.column width="50%"}
B) The *expected value* is far below 1 — probably zero, but not guaranteed.
:::
::::

::: {.notes}
30–45 s. Commit first, then emphasize: $N$ is an expected value (a statistical mean), not a guarantee.
:::

---

## The Staggering Numbers {background-color="black"}

::: {.text-center}
The Drake Equation applies to the **Milky Way**.

But zoom out...
:::

::: {.fragment .mt-4}
| Scale | Number |
|-------|--------|
| Stars in Milky Way | ~10¹¹ (100-400 billion) |
| Galaxies in observable universe | ~10¹¹-10¹² |
| **Total stars** | up to ~10²⁴ |
:::

::: {.fragment .mt-4 .text-muted}
More stars than grains of sand on all of Earth's beaches.
:::

::: {.notes}
7–8 min. "The scale is incomprehensible."
:::

---

## The Fermi Paradox {background-color="#1a1a2e"}

::: {.text-center .text-xl}
"Where is everybody?" — Enrico Fermi (1950)
:::

::: {.fragment .mt-4}
If numbers are so large, why no signs of extraterrestrial intelligence?

**Possible answers:**

- Life is extremely rare ($f_l \times f_i \ll 1$)
- Civilizations don't last long ($L$ is small)
- They're not interested in communicating
- We haven't looked hard enough yet
:::

::: {.notes}
8–9 min. "The Fermi Paradox remains unsolved."
:::

---

## {.center}

::: {.r-fit-text}
Part 2: The Missing Ingredients
:::

*Why the early universe was metal-poor*

---

## Stars Made the Ingredients {background-color="black"}

::: {.text-center}
The early universe was **almost entirely hydrogen and helium**.

No carbon. No oxygen. No iron.
:::

::: {.fragment .mt-4}
**Rocky planets require heavy elements.**

Life requires carbon, oxygen, nitrogen...

**Where did they come from?**
:::

::: {.fragment .mt-4 .text-xl}
**Stars made them.**
:::

::: {.notes}
9–10 min. "Heavy elements came from stars."
:::

---

## Stars as Element Factories {background-color="#1a1a2e"}

::: {.incremental}
- **H → He:** Main sequence stars (like the Sun)
- **He → C, O:** Red giant stars
- **C, O → ... → Fe:** Massive stars
- **Beyond Fe:** Supernovae, neutron star mergers
:::

::: {.fragment .mt-4}
When stars die, they scatter elements into space.

Next generation of stars (and planets) forms from enriched material.
:::

::: {.notes}
10–11 min. "Stellar nucleosynthesis."
:::

---

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

::: {.quiz}
Why were Earth-like rocky planets unlikely in the early universe?

- [ ] It was too hot
- [ ] There were no galaxies yet
- [x] Heavy elements (metals) hadn't been created yet
- [ ] Gravity was weaker
:::

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

---

## {.center}

::: {.r-fit-text}
Part 3: Module 1 Synthesis
:::

*The toolkit, complete*

---

## Your Module 1 Toolkit {background-color="#0a2f5c"}

::: {.text-sm}
| Lecture | Tool | What It Reveals |
|---------|------|-----------------|
| L5 | Kepler's Laws | Orbits, periods, distances |
| L6 | Newton's Gravity | **Mass from motion** |
| L7-L8 | Blackbody/Wien | **Temperature from light** |
| L9 | Spectral Lines | **Composition from light** |
| L10 | Doppler Effect | **Motion from light** |
| L11-12 | Applications | Solar system, exoplanets, climate |
:::

::: {.notes}
11–12 min. "All the tools you've learned."
:::

---

## Quick Check: Toolkit → Inference {background-color="#1a1a2e"}

::: {.quiz}
Which measurement most directly lets you infer a planet’s **radius**?

- [ ] Doppler shift of stellar lines
- [x] Transit depth
- [ ] Spectral line pattern
- [ ] Orbital period alone
:::

::: {.notes}
1 min. Retrieval practice: connect each “tool” to what it reveals.
:::

---

## How Everything Connects {background-color="black"}

**LIGHT (L7-L10):**

- Continuous spectrum → Temperature (Wien, Stefan-Boltzmann)
- Spectral lines → Composition
- Doppler shift → Radial velocity

**GRAVITY (L5-L6):**

- Kepler → Orbits
- Newton → Mass from motion

**TOGETHER → Exoplanets, climate, search for life**

::: {.notes}
12–13 min. "Everything connects."
:::

---

## Key Equations {background-color="#1a1a2e"}

::: {.text-sm}
| Equation | What It Does |
|----------|--------------|
| $(P/1\,\text{yr})^2 = (a/1\,\text{AU})^3$ | Kepler III (Sun-only scaling) — periods & distances |
| $M = 4\pi^2 a^3/(GP^2)$ | Mass from orbits |
| $\lambda_{peak} = 2.9 \times 10^6/T$ | Wien — temperature |
| $L = 4\pi R^2 \sigma T^4$ | Stefan-Boltzmann — luminosity |
| $\Delta\lambda/\lambda_0 = v/c$ | Doppler — velocity |
| depth = $(R_p/R_*)^2$ | Transit — planet size |
:::

::: {.notes}
13–14 min. "Key equations for the exam."
:::

---

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

::: {.text-sm}

**Drake Equation:**

1. Framework for "Are we alone?" — terms 1-3 known, 4-7 unknown
2. Numbers are staggering: up to ~10²⁴ stars
3. Fermi Paradox: If life is common, where is everybody?

**Cosmic Context:**

4. Early universe metal-poor → rocky planets unlikely at first
5. Stars create heavy elements → dispersed via supernovae
6. Life requires stellar evolution (Module 2 preview)

**Module 1 Synthesis:**

7. Light reveals temperature, composition, motion
8. Gravity + orbits reveal mass
9. All tools work together

:::

::: {.notes}
14–15 min. Rapid recap.
:::

---

## Module 1 Exam Prep {background-color="#1a1a2e"}

::: {.text-sm}
**Can you...**

☐ Use Kepler III to find periods/distances?

☐ Apply Newton to find mass from orbits?

☐ Use Wien's Law for temperature?

☐ Explain Kirchhoff's Laws (3 spectrum types)?

☐ Apply Doppler to find radial velocity?

☐ Explain transit depth and what it measures?

☐ Describe greenhouse effect (Venus vs. Earth vs. Mars)?

☐ Explain why early universe couldn't form rocky planets?
:::

::: {.notes}
15–16 min. "Self-assessment for the exam."
:::

---

## What's Next {background-color="black"}

::: {.text-center .text-xl}
**Monday: Module 1 Exam**
:::

::: {.fragment .mt-4}
Then: **Module 2 — Stars!**

- How stars are born
- How they live and die
- Where the elements in your body came from
:::

::: {.notes}
16–17 min. "After the exam, we study stars."
:::

---

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

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

*Drake Equation calculations and unit checks*

::: {.notes}
Let's work through Drake Equation scenarios with explicit numbers.
:::

---

## Drake Equation: Explicit Calculation {background-color="#1a1a2e"}

$$N = R_* \times f_p \times n_e \times f_l \times f_i \times f_c \times L$$

**Using the same “optimistic” scenario as the reading:**

::: {.text-sm}
| Term | Value | Reasoning |
|------|-------|-----------|
| $R_*$ | 3 yr⁻¹ | Star formation rate in Milky Way |
| $f_p$ | 1 | Fraction of stars with planets (evidence-informed) |
| $n_e$ | 0.2 | Habitable planets per system (order-of-magnitude) |
| $f_l$ | 0.5 | Fraction that develop life (optimistic) |
| $f_i$ | 0.5 | Fraction that develop intelligence (optimistic) |
| $f_c$ | 0.5 | Fraction that communicate (optimistic) |
| $L$ | 1,000,000 yr | Civilization lifetime (optimistic) |
:::

::: {.notes}
"These numbers span huge uncertainties. Let's see what they give."
:::

---

## Drake Calculation: Step by Step {background-color="#1a1a2e"}

$$N = 3 \times 1 \times 0.2 \times 0.5 \times 0.5 \times 0.5 \times 1{,}000{,}000$$

::: {.fragment}
**Step by step:**

$$= 3 \times 1 \times 0.2 = 0.6 \text{ (habitable planets per year)}$$
$$= 0.6 \times 0.5 \times 0.5 \times 0.5 = 0.075 \text{ (communicating per year)}$$
:::

::: {.fragment}
$$= 0.075 \times 1{,}000{,}000 = 75{,}000$$
:::

::: {.fragment .bg-muted .p-2}
**N ≈ 75,000 communicating civilizations** in the Milky Way right now.

Now compare to the pessimistic scenario: $N \ll 1$ (probably zero, but not guaranteed).
:::

::: {.notes}
"The result depends HUGELY on the unknown factors."
:::

---

## Unit Analysis: Drake Equation {background-color="#1a1a2e"}

**Check that units work out to "number of civilizations":**

$$N = \underbrace{R_*}_{\text{yr}^{-1}} \times \underbrace{f_p}_{\text{dimensionless}} \times \underbrace{n_e}_{\text{planets/system}} \times \underbrace{f_l}_{\text{dimensionless}} \times \underbrace{f_i}_{\text{dimensionless}} \times \underbrace{f_c}_{\text{dimensionless}} \times \underbrace{L}_{\text{yr}}$$

::: {.fragment}
$$[N] = \frac{1}{\text{yr}} \times \text{yr} = \text{dimensionless}$$

**Units cancel to give a pure number!** ✓
:::

::: {.fragment .mt-2}
**Physical interpretation:**

$R_* \times L$ = total stars formed during a civilization's lifetime

The $f$ factors filter down to those currently communicating.
:::

::: {.notes}
"The units make sense: stars per year times years gives a number."
:::

---

## Number of Stars: Scale Calculation {background-color="#1a1a2e"}

**How many stars are in the observable universe?**

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

- Stars in the Milky Way: order $10^{11}$ (roughly 100–400 billion)
- Galaxies in the observable universe: hundreds of billions to ~2 trillion (order $10^{11}$–$10^{12}$)
:::

::: {.fragment}
**Total stars (order-of-magnitude):**

Up to about $10^{24}$ (a septillion).
:::

::: {.fragment}
More stars than grains of sand on all Earth's beaches.
:::

::: {.notes}
"The numbers are staggering. Even with tiny probabilities, the outcomes could be large."
:::

---

## Number of Potentially Habitable Planets {background-color="#1a1a2e"}

Some studies suggest **~22%** of Sun-like stars host Earth-sized planets in the habitable zone — but published estimates vary because “Earth-sized” and “habitable zone” depend on definitions and star type.

::: {.fragment .bg-muted .p-2}
**Takeaway:** Kepler (and follow-on surveys) tell us that planets are common and that “potentially habitable” worlds are not absurdly rare — but the exact number is uncertain.
:::

::: {.notes}
"Kepler revolutionized our estimates of f_p and n_e."
:::

---

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

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

*The Fermi Paradox and information theory*

::: {.notes}
Optional advanced content on SETI and the paradox.
:::

---

## The Fermi Paradox: Timeline {background-color="#0a2f5c"}

**Galaxy crossing time:**

At 1% of light speed (achievable with current-concept technology):

$$t_{cross} = \frac{100,000 \text{ ly}}{0.01c} = 10^7 \text{ years}$$

::: {.fragment}
**The Milky Way is ~10 billion years old.**

Even with slow ships, a colonizing civilization could have crossed the galaxy **1000 times**.
:::

::: {.fragment .mt-2 .bg-warning-subtle .p-2}
**Fermi's question:** If life is common and civilizations spread, the galaxy should be FULL of them by now.

**Where is everybody?**
:::

::: {.notes}
"The timescales work against us being alone unless something stops civilizations."
:::

---

## Possible Resolutions {background-color="#0a2f5c"}

**Why might we not see evidence of other civilizations?**

::: {.incremental}
1. **We ARE rare:** Life or intelligence might be incredibly improbable
2. **The Great Filter:** Something wipes out civilizations (before or after us?)
3. **They're quiet:** Advanced civilizations go "dark" (energy efficiency, hiding)
4. **We're not looking right:** Wrong frequencies, wrong modalities
5. **Zoo hypothesis:** They're watching but not contacting
6. **We're first:** Someone has to be first in the galaxy
:::

::: {.notes}
"Each possibility has profound implications."
:::

---

## The Great Filter {background-color="#0a2f5c"}

**Somewhere between dead matter and galaxy-spanning civilizations, something is very rare.**

::: {.fragment}
**If the filter is behind us:** We're lucky survivors of something improbable.

(Life? Multicellular life? Intelligence? Civilization?)
:::

::: {.fragment}
**If the filter is ahead of us:** Civilizations destroy themselves.

(Nuclear war? Climate? AI? Biotech?)
:::

::: {.fragment .mt-2 .bg-warning-subtle .p-2}
**Finding microbial life on Mars would be BAD news!**

It would mean the filter isn't "life arising" — it must be ahead of us.
:::

::: {.notes}
"This is why finding life elsewhere has philosophical implications."
:::

---

## SETI Signal Detection {background-color="#0a2f5c"}

**How would we recognize an artificial signal?**

::: {.fragment}
**Natural sources are broadband** (emit across many frequencies).

**Artificial signals could be:**

- Narrowband (concentrated at one frequency)
- Pulsed with regular patterns
- Carrying encoded information
:::

::: {.fragment}
**The "water hole":**

Frequencies between H (1420 MHz) and OH (1665 MHz) are quiet in the galaxy.

Water = H + OH → maybe aliens use this band too?
:::

::: {.notes}
"SETI looks for signals that don't fit natural explanations."
:::

---

## How Far Have Our Signals Reached? {background-color="#0a2f5c"}

**First powerful radio transmissions:** about a century ago

::: {.fragment}
Our signals have traveled: order $\sim 100$ light-years

**Volume covered:**

$$V = \frac{4}{3}\pi r^3 \sim \frac{4}{3}\pi (100)^3 \approx \text{few} \times 10^6 \text{ ly}^3$$
:::

::: {.fragment}
Even if that sphere contains many nearby stars, it is still a **tiny fraction** of the Milky Way.
:::

::: {.fragment .text-muted}
The key idea: our signals are spreading and weakening — only nearby stars could plausibly detect them.
:::

::: {.notes}
"Our radio bubble is tiny compared to the galaxy."
:::

---

## Module 1 Synthesis: Final Checklist {background-color="#0a2f5c"}

::: {.text-sm}
**Can you calculate these?**

☐ Orbital period from distance (Sun-only scaling): $\left(\frac{P}{1\,\text{yr}}\right)^2 = \left(\frac{a}{1\,\text{AU}}\right)^3$

☐ Mass from orbital data: $M = 4\pi^2 a^3 / GP^2$ (SI units!)

☐ Temperature from peak wavelength: $T = 2.9 \times 10^6 / \lambda_{peak}$ (nm, K)

☐ Luminosity from T and R: $L = 4\pi R^2 \sigma T^4$

☐ Radial velocity from Doppler: $v = c \times \Delta\lambda/\lambda_0$

☐ Planet radius from transit: $R_p = R_* \sqrt{\text{depth}}$

☐ Equilibrium temperature: $T_{eq} = 279(1-A)^{1/4}(d/\text{AU})^{-1/2}$

**Do you track units at every step?** This is the key to not making mistakes!
:::

::: {.notes}
"If you can do all of these with proper units, you're ready for the exam."
:::

---

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

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

Motion → mass. Light → everything else.

Now: **Are we alone?**
:::

::: {.notes}
Remaining time for questions and exam prep discussion.
:::
