Astronomical Units & Solar-System Distances

AU = “astronomical unit.”
Defined as the average distance between the Earth and the Sun.
Serves mainly to express planet–star distances.
- Not typically used for smaller scales such as Earth–Moon; for that we use miles or kilometres.
Essential when describing:
- Distances of planets within our Solar System.
- Orbits of exoplanets around their host stars.

$1\,\text{AU}=93\,000\,000\;\text{miles}$ (approx.).
Convert miles → km (using $1\;\text{mile}=1.6\;\text{km}$ ):
- $93\,000\,000\times1.6\approx150\,000\,000\;\text{km}$ .

Start with $150\,000\,000$ km (six zeroes in “million”).
Move decimal 8 places left → $1.5\times10^{8}\;\text{km}$ .
To convert km → metres, multiply by $10^{3}$ :
- $1.5\times10^{8}\;\text{km}\times10^{3}=1.5\times10^{11}\;\text{m}$ .
Summary of equivalent statements for 1 AU:
- $93\,000\,000\;\text{miles}$
- $150\,000\,000\;\text{km}$
- $1.5\times10^{8}\;\text{km}$
- $1.5\times10^{11}\;\text{m}$

Light requires ≈ 8 minutes to travel 1 AU.
Therefore “8 light-minutes” is an alternative distance unit for Earth → Sun.
More generally, “light-minutes,” “light-hours,” and “light-years” are all distance units defined by the light-travel‐time concept.

(Data sourced from textbook Appendix C-1 plus lecturer additions)

Mercury – $0.38\;\text{AU}$
Venus – $0.72\;\text{AU}$
Earth – $1.00\;\text{AU}$ (definition reference)
Mars – $1.52\;\text{AU}$
Ceres (largest asteroid; first discovered) – $2.76\;\text{AU}$
- Etymology: Ceres, goddess of harvest → modern word “cereal.”
Jupiter – $5.2\;\text{AU}$
Saturn – $9.5\;\text{AU}$
Uranus – ≈ $19\;\text{AU}$ (value implied in lecture when subtracting 10 from Saturn; exact table value ≈19.2)
Neptune – ≈ $30\;\text{AU}$ (lecture notes imply “outside of the room” when drawn to scale)
Pluto (dwarf planet) – $39\;\text{AU}$
- Demoted because its size & dynamical context match many other distant icy bodies (“planet X,” etc.).
Unnamed distant planet (“planet X”) – ≈ $67\;\text{AU}$

Earth → Venus: $|1.00-0.72|=0.28\;\text{AU}.$
Earth → Mars: $|1.00-1.52|=0.52\;\text{AU}.$
- Ratio $\dfrac{0.52}{0.28}\approx2.$
- All else equal, a probe should reach Venus about twice as fast as Mars.
Earth → Mercury: $|1.00-0.38|=0.62\;\text{AU}.$
- Compare with Earth → Mars (0.52 AU): $\dfrac{0.62}{0.52}\approx1.2$ → Mars is ≈ 20 % closer than Mercury.
Caveat: Actual mission durations also depend on orbital positions & transfer‐orbit mechanics.

A simple linear scale model on a classroom board:
1. Place Sun at origin.
2. Mark Earth at 1 unit to the right (1 AU).
3. Mercury at 0.38 AU (38 % of Earth–Sun line).
4. Venus at 0.72 AU.
5. Mars at 1.52 AU (½ AU beyond Earth).
6. Asteroid belt centred on ~2.76 AU (Ceres).
7. Jupiter at 5.2 AU (note growing gaps).
8. Saturn at 9.5 AU (≈4 AU beyond Jupiter).
9. Uranus ≈19 AU, Neptune ≈30 AU, Pluto ≈39 AU, etc. (would extend outside typical classroom perimeter).
Observation: Spacing increases dramatically beyond the asteroid belt; “empty space” dominates outer Solar System.

Frequently published Solar‐System images are not to scale in either distance or planet size.
If true scale were kept:
- Jupiter would need to be placed 5× farther from the Sun than Earth’s position on the same page.
- Outer planets would fall off the page entirely.
Such distortions are tolerated so readers can at least see all planets simultaneously.

AU provides an intuitive yardstick for:
- Comparative planet studies.
- Mission‐planning rough estimates (travel time, fuel budgets).
- Public outreach projects (e.g.
- Poster-board Solar System with scaled distances).
Hands-on classroom suggestion (junior-high level):
- Supply students with AU values.
- Task: draw a scaled linear or circular Solar System on poster board to appreciate true spacing.
Broader relevance:
- Exoplanet catalogues routinely list semi-major axes in AUs.
- Facilitates cross-comparison of foreign systems with our own.