(worksheets)=
# Worksheets

The seven worksheet problem sets and their full solutions are collected on this page as the course runs.
Each worksheet covers one two-lecture block and is discussed in the tutorial session for that block.

The worksheets are ungraded, and they have the same shape and level as the final written exam.
Each one is sized for about two hours of work, entirely on paper.
Work each problem through before opening the solutions: the solutions are complete, so reading them first removes most of the benefit.

| # | Covers | Problems | Solutions |
|---|---|---|---|
| 1 | {ref}`Lecture 1 <lecture01>`, {ref}`Lecture 2 <lecture02>` | [Download (PDF)](_static/worksheets/worksheet01.pdf) | [Download (PDF)](_static/worksheets/worksheet01_solutions.pdf) |
| 2 | {ref}`Lecture 3 <lecture03>`, {ref}`Lecture 4 <lecture04>` | [Download (PDF)](_static/worksheets/worksheet02.pdf) | [Download (PDF)](_static/worksheets/worksheet02_solutions.pdf) |
| 3 | {ref}`Lecture 5 <lecture05>`, {ref}`Lecture 6 <lecture06>` | [Download (PDF)](_static/worksheets/worksheet03.pdf) | [Download (PDF)](_static/worksheets/worksheet03_solutions.pdf) |
| 4 | {ref}`Lecture 7 <lecture07>`, {ref}`Lecture 8 <lecture08>` | [Download (PDF)](_static/worksheets/worksheet04.pdf) | [Download (PDF)](_static/worksheets/worksheet04_solutions.pdf) |
| 5 | {ref}`Lecture 9 <lecture09>`, {ref}`Lecture 10 <lecture10>` | [Download (PDF)](_static/worksheets/worksheet05.pdf) | [Download (PDF)](_static/worksheets/worksheet05_solutions.pdf) |
| 6 | {ref}`Lecture 11 <lecture11>`, {ref}`Lecture 12 <lecture12>` | [Download (PDF)](_static/worksheets/worksheet06.pdf) | [Download (PDF)](_static/worksheets/worksheet06_solutions.pdf) |
| 7 | {ref}`Lecture 13 <lecture13>`, {ref}`Lecture 14 <lecture14>` | [Download (PDF)](_static/worksheets/worksheet07.pdf) | [Download (PDF)](_static/worksheets/worksheet07_solutions.pdf) |


## What each worksheet covers

1. **Orbits and formation** ({ref}`lecture01`, {ref}`lecture02`): Kepler's laws, the vis-viva equation, orbital resonances, tides and the Roche limit, gravitational focusing and the growth regimes.
2. **Thermal evolution and differentiation** ({ref}`lecture03`, {ref}`lecture04`): radiogenic heating, cooling timescales and convective regimes, the thermal-evolution energy balance, core formation, dynamo feasibility.
3. **Atmospheres** ({ref}`lecture05`, {ref}`lecture06`): scale heights and column mass, radiative equilibrium and the greenhouse effect, cloud condensation and the lifting condensation level, the faint young Sun and the carbonate-silicate thermostat.
4. **Surfaces and interiors** ({ref}`lecture07`, {ref}`lecture08`): impact energetics, crater chronology, moment of inertia, central pressure.
5. **Terrestrial planets** ({ref}`lecture09`, {ref}`lecture10`): comparative energy balance, water loss from Venus, the Martian volatile inventory, Mercury's spin-orbit resonance.
6. **Giant planets and small bodies** ({ref}`lecture11`, {ref}`lecture12`): interior transitions, ring dynamics, isotopic dating, Kirkwood gaps.
7. **Exoplanets and habitable worlds** ({ref}`lecture13`, {ref}`lecture14`): transit depths and detection bias, radial-velocity masses and bulk density, atmospheric scale heights and transmission spectroscopy, the habitable zone, direct imaging, the Drake equation.