Astronomical Unit (AU) - Unit Information & Conversion

Quick Answer

1 AU = 149,597,870,700 meters (EXACT) ≈ 150 million km ≈ 93 million miles

The astronomical unit represents the average Earth-Sun distance. It's the fundamental ruler for measuring our Solar System. When we say Mercury orbits at 0.39 AU, we mean it's about 39% of Earth's distance from the Sun. Light from the Sun takes 8 minutes 19 seconds to reach Earth—that's the light travel time for one AU.

Why it matters: AU makes planetary distances intuitive. Instead of saying "Mars is 228 million kilometers away," astronomers say "Mars orbits at 1.52 AU"—immediately conveying it's about 50% farther from the Sun than Earth.

Quick Comparison Table

Object	Distance from Sun	Context
Mercury	0.39 AU (58M km)	Closest planet, scorching surface
Venus	0.72 AU (108M km)	Hottest planet, runaway greenhouse
Earth	1.00 AU (150M km)	Habitable zone, liquid water
Mars	1.52 AU (228M km)	Red planet, potential colonization
Asteroid Belt	2.2-3.2 AU	Rocky debris between Mars/Jupiter
Jupiter	5.20 AU (778M km)	Gas giant, 318× Earth's mass
Saturn	9.58 AU (1.43B km)	Ringed planet, Cassini mission
Uranus	19.2 AU (2.87B km)	Ice giant, tilted 98° axis
Neptune	30.1 AU (4.50B km)	Outermost planet, supersonic winds
Kuiper Belt	30-50 AU	Icy objects, Pluto (39.5 AU)
Voyager 1 (2024)	164 AU	Farthest human-made object

Definition

1 astronomical unit (AU) = 149,597,870,700 meters (EXACT)

The astronomical unit is a unit of length in astronomy and planetary science, representing the mean distance from Earth to the Sun. Since 2012, the AU has been a defined constant—exactly 149,597,870,700 m—rather than a measured quantity.

Why Not Just Use Kilometers?

Scale problem: Solar System distances in kilometers become unwieldy:

• Earth to Sun: 149,597,871 km (hard to grasp)
• Jupiter to Sun: 778,500,000 km (increasingly meaningless)
• Neptune to Sun: 4,500,000,000 km (just a big number)

AU makes it intuitive:

• Earth: 1.00 AU (baseline)
• Jupiter: 5.20 AU (5× farther than Earth)
• Neptune: 30.1 AU (30× Earth's distance)

The human brain handles ratios better than absolute numbers. "Neptune is 30 times farther from the Sun than Earth" is far more comprehensible than "Neptune is 4.5 billion kilometers from the Sun."

Light Travel Time

The AU has a natural time component:

1 AU = 8 minutes 19 seconds at the speed of light

• Light from the Sun takes 8m 19s to reach Earth
• If the Sun suddenly vanished, we wouldn't know for 8+ minutes
• Solar flares and coronal mass ejections take this long to arrive
• Real-time communication with spacecraft: Earth-Mars = 4-24 minutes one-way delay (depending on orbital positions)

AU vs. Light-Year vs. Parsec

Three different distance scales for different contexts:

Unit	Meters	Use Case
Astronomical Unit (AU)	1.496 × 10¹¹ m	Solar System (planets, asteroids, comets)
Light-year (ly)	9.461 × 10¹⁵ m (63,241 AU)	Interstellar distances (nearest stars)
Parsec (pc)	3.086 × 10¹⁶ m (206,265 AU)	Galactic/extragalactic distances (parallax-based)

Why each exists:

• AU: Human-scale for our cosmic neighborhood
• Light-year: Intuitive (distance light travels in a year)
• Parsec: Technical (distance at which 1 AU subtends 1 arcsecond)

History

Ancient Underestimates (300 BCE - 1500 CE)

Aristarchus of Samos (3rd century BCE): The first known attempt to measure the Earth-Sun distance. Using lunar phases and geometry, Aristarchus estimated the Sun was 18-20 times farther than the Moon. His method was sound, but observational limitations led to severe underestimation.

Actual ratio: Sun is ~400× farther than the Moon, not 20×.

Ptolemy's geocentric model (2nd century CE): Ptolemy's Almagest placed the Sun relatively close—around 1,200 Earth radii (~7.6 million km), about 5% of the true distance. This underestimation persisted for 1,400 years during the geocentric era.

Copernican Revolution (1543-1600s)

Nicolaus Copernicus (1543): De revolutionibus orbium coelestium established the heliocentric model. While Copernicus correctly ordered the planets, his distance estimates were still too small—placing the Sun about 20 million km away (13% of the actual distance).

Johannes Kepler (1609-1619): Kepler's laws of planetary motion (published in Astronomia Nova and Harmonices Mundi) enabled calculation of relative planetary distances. If Earth's orbit is 1 AU, then:

• Venus: 0.72 AU
• Mars: 1.52 AU
• Jupiter: 5.20 AU

Problem: Kepler knew the proportions, but not the absolute scale. What was the AU in meters or kilometers?

The Transit of Venus Method (1761-1769)

Edmond Halley's proposal (1716): Halley realized that observing Venus crossing the Sun's face (a "transit") from different Earth locations would create a parallax effect, enabling triangulation of the Earth-Sun distance.

1761 Transit of Venus: International expeditions to Siberia, South Africa, India, and the South Pacific. Observations were complicated by:

• The "black drop effect" (Venus appearing to stick to the Sun's edge)
• Cloudy weather disrupting measurements
• Imprecise timekeeping

1769 Transit of Venus: More extensive global coordination:

• Captain James Cook: Observed from Tahiti (Point Venus)
• Charles Mason & Jeremiah Dixon: Observed from the Cape of Good Hope
• Russian expeditions: Observed from Siberia

Result: Combined data yielded an Earth-Sun distance of approximately 153 million km, within 2% of the modern value (150M km). This was the first accurate measurement of the AU.

Why transits work: Observers at different latitudes see Venus cross the Sun along slightly different paths. The timing difference creates a parallax angle:

tan(parallax) = (Earth baseline) / (Earth-Sun distance)

With a known Earth baseline (distance between observation sites) and measured parallax, the AU could be calculated.

19th Century Refinement (1800-1900)

1874 and 1882 Transits of Venus: Equipped with photography and telegraph time-synchronization, astronomers improved AU measurements to ~149.5 million km.

Asteroid parallax (1898-1900): The asteroid 433 Eros passes closer to Earth than Venus, providing better parallax measurements. During Eros's 1900-1901 opposition, global observatories measured its position, refining the AU to 149.53 million km (±0.03%).

Term standardization: The phrase "astronomical unit" became standard in the late 19th century, replacing earlier terms like "solar distance" or "Earth's mean distance."

20th Century Precision (1961-2012)

Radar ranging to Venus (1961): The Goldstone Observatory and Jodrell Bank transmitted radar signals to Venus and measured the round-trip time. Since radio waves travel at the speed of light (c), the distance calculation was straightforward:

Distance = (c × round-trip time) / 2

Result: The AU was refined to 149,597,870 km (±1 km precision).

Radar ranging to Mars (1965-1976): Mariner and Viking spacecraft provided radar measurements, cross-verifying the Venus-based AU.

Viking landers (1976): Precise radio tracking of the Viking landers on Mars enabled AU measurements to sub-kilometer precision.

Jet Propulsion Laboratory ephemerides: JPL's Development Ephemeris (DE) models incorporated radar, spacecraft tracking, and lunar laser ranging. By 2000, the AU was known to meter-level precision.

IAU 2012 Redefinition

The problem: The AU was previously defined as "the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.01720209895 radians per day (the Gaussian gravitational constant)."

This definition was:

1. Circular (tied to a theoretical model, not measurable)
2. Dependent on the solar mass (which itself was measured in AU-based units)
3. Subject to revision as measurements improved

The solution (IAU Resolution B2, 2012): The International Astronomical Union redefined the AU as a fixed constant:

1 AU = 149,597,870,700 meters (EXACT)

Why this matters:

• Consistency: The AU no longer changes with better measurements of solar mass
• Spacecraft navigation: JPL's navigation software uses this exact constant
• Parallels SI units: Like the meter (defined via the speed of light), the AU is now a defined standard, not a derived quantity

Fun fact: The chosen value (149,597,870,700 m) was the best measurement available in 2012, now frozen as the definition.

Cultural and Scientific Impact

The AU represents humanity's growing comprehension of cosmic scale:

• Ancient world: Sun thought to be ~10 million km away
• Kepler era: Relative distances known, absolute scale uncertain
• 1769: First accurate measurement (153M km, 2% error)
• 1961: Radar precision (±1 km)
• 2012: Defined as exact constant (no error—it IS the standard)

This progression mirrors the scientific method: hypothesis → observation → refinement → standardization.

Real-World Examples

1. Planetary Orbits

Inner Planets (Terrestrial Worlds):

Mercury:

• Semi-major axis: 0.387 AU (57.9 million km)
• Orbital period: 88 Earth days
• Sunlight intensity: 6.7× stronger than Earth (inverse square law: 1/0.387² ≈ 6.7)
• Surface temperature: -173°C to 427°C

Venus:

• Distance: 0.723 AU (108.2 million km)
• Orbital period: 225 Earth days
• Runaway greenhouse effect: 465°C surface (hottest planet)
• Thick CO₂ atmosphere: 92 bar pressure

Earth:

• Distance: 1.000 AU (149.6 million km) — the definition
• Orbital period: 365.25 days
• Habitable zone: Liquid water, temperate climate
• Eccentricity: 0.0167 (nearly circular orbit)

Mars:

• Distance: 1.524 AU (227.9 million km)
• Orbital period: 687 Earth days
• Thin atmosphere: 0.6% Earth's pressure
• Potential for human colonization (SpaceX, NASA Artemis follow-on)

Outer Planets (Gas and Ice Giants):

Jupiter:

• Distance: 5.203 AU (778.5 million km)
• Orbital period: 11.86 Earth years
• Mass: 318× Earth (dominates asteroid belt dynamics)
• Moons: 95+ known (Galilean moons: Io, Europa, Ganymede, Callisto)

Saturn:

• Distance: 9.537 AU (1.427 billion km)
• Orbital period: 29.46 Earth years
• Rings: Icy particles from <1 cm to 10 m
• Cassini mission (1997-2017): 13 years orbiting Saturn

Uranus:

• Distance: 19.19 AU (2.871 billion km)
• Orbital period: 84.02 Earth years
• Axial tilt: 98° (rolls on its side)
• Discovery: 1781 (William Herschel)

Neptune:

• Distance: 30.07 AU (4.495 billion km)
• Orbital period: 164.8 Earth years
• Supersonic winds: 2,100 km/h (fastest in Solar System)
• Discovery: 1846 (mathematical prediction → observation)

2. Small Bodies

Asteroid Belt:

• Location: 2.2 to 3.2 AU (between Mars and Jupiter)
• Largest object: Ceres (dwarf planet, 2.77 AU)
• Total mass: ~3% of Moon's mass (not a "failed planet")

Near-Earth Asteroids (NEAs):

• Perihelion: <1.3 AU (come close to Earth)
• Example: Apophis (0.922 AU) — will pass 31,000 km from Earth in 2029
• Planetary defense: NASA DART mission (2022) successfully deflected Dimorphos

Comets:

• Short-period comets: 5-20 AU aphelion (Jupiter-family)
  • Halley's Comet: 0.586 AU (perihelion) to 35.1 AU (aphelion)
• Long-period comets: 1,000-50,000 AU aphelion (Oort Cloud origin)

Kuiper Belt:

• Region: 30-50 AU
• Objects: Icy dwarf planets, comets
• Pluto: 39.5 AU (39× farther than Earth, 5.9 billion km)
• Eris: 67.7 AU (most distant known dwarf planet in eccentric orbit)

3. Spacecraft Missions

Voyager 1 (launched 1977):

• Current distance: ~164 AU (24.5 billion km, as of 2024)
• Speed: 3.6 AU/year (17 km/s relative to the Sun)
• Entered interstellar space: August 2012 (121 AU)
• Power: Decaying RTGs (radioisotope thermoelectric generators)
• Last contact expected: ~2025-2030

Voyager 2 (launched 1977):

• Current distance: ~136 AU (20.4 billion km)
• Only spacecraft to visit Uranus (1986) and Neptune (1989)
• Entered interstellar space: November 2018 (119 AU)

New Horizons (launched 2006):

• Pluto flyby: July 2015 (32.9 AU)
• Arrokoth flyby: January 2019 (43.4 AU, Kuiper Belt object)
• Current distance: ~59 AU (as of 2024)
• Speed: 3.1 AU/year

Parker Solar Probe (launched 2018):

• Mission: Study the Sun's corona
• Perihelion: 0.046 AU (6.9 million km) — closest approach to the Sun
• Speed at perihelion: 192 km/s (0.064% speed of light!)
• Temperature: Heat shield endures 1,377°C

Mars missions:

• Earth-Mars distance: 0.52 AU (closest) to 2.52 AU (farthest)
• Travel time: 6-9 months (depending on launch window)
• Communication delay: 4-24 minutes one-way

4. Habitable Zone

Goldilocks Zone: The habitable zone (HZ) is the orbital distance where liquid water can exist on a planet's surface.

Our Solar System:

• Inner edge: ~0.95 AU (too hot, runaway greenhouse like Venus)
• Outer edge: ~1.37 AU (too cold, frozen surface)
• Earth: 1.00 AU (perfect!)
• Mars: 1.52 AU (marginally habitable, thin atmosphere)

Other star systems: Habitable zone depends on star luminosity:

Proxima Centauri (red dwarf, 12% Sun's luminosity):

• HZ: 0.05-0.10 AU
• Proxima b: 0.0485 AU (within HZ!)

Sirius A (blue-white star, 25× Sun's luminosity):

• HZ: 4-8 AU (Jupiter's distance)

Formula:

HZ distance (AU) = √(Star luminosity / Sun luminosity)

5. Parallax and Stellar Distances

How parallax works: As Earth orbits the Sun (2 AU baseline diameter), nearby stars appear to shift position against distant background stars. This angular shift is the parallax angle.

1 AU baseline → parallax measurements:

• 1 parsec (pc) = distance at which 1 AU subtends 1 arcsecond
• 1 parsec = 206,265 AU = 3.26 light-years

Example: Proxima Centauri

• Parallax angle: 0.7687 arcseconds
• Distance: 1 / 0.7687 = 1.301 parsecs = 4.24 light-years = 268,000 AU

Why AU matters for parallax: The AU is the "ruler" for measuring stellar distances. Without an accurate AU, all stellar distance measurements would be wrong.

6. Light Travel Times

Within the Solar System:

Distance	Light Travel Time
Sun to Earth (1 AU)	8 min 19 sec
Sun to Mars (1.52 AU)	12 min 40 sec
Sun to Jupiter (5.20 AU)	43 min 16 sec
Sun to Neptune (30.1 AU)	4 hr 10 min
Sun to Voyager 1 (164 AU)	22 hr 42 min

Spacecraft communication:

• Mars rovers: 4-24 minute delay (depending on orbital positions)
• Voyager 1: 22+ hours round-trip communication
• New Horizons (Pluto): 9+ hours round-trip (during 2015 flyby)

Why real-time control is impossible: Commands to Mars rovers take 4-24 minutes to arrive, plus 4-24 minutes for confirmation. Total: 8-48 minute delay. Rovers must be semi-autonomous.

7. Inverse Square Law (Sunlight Intensity)

Solar energy decreases with the square of distance:

Intensity = (1 AU / distance)²

Planet	Distance	Sunlight Intensity
Mercury	0.39 AU	6.67× Earth
Venus	0.72 AU	1.91× Earth
Earth	1.00 AU	1.00× (baseline)
Mars	1.52 AU	0.43× Earth (43%)
Jupiter	5.20 AU	0.037× Earth (3.7%)
Neptune	30.1 AU	0.0011× Earth (0.11%)

Why this matters:

• Mars: Solar panels receive 43% of Earth's sunlight (need 2.3× larger panels)
• Jupiter: Solar power becomes marginal (NASA Juno uses solar panels, but just barely)
• Saturn/Neptune: Nuclear RTGs required (Cassini, Voyager use plutonium-238)

Common Uses

1. Planetary Science and Orbital Mechanics

The AU is the natural unit for describing planetary orbits using Kepler's laws.

Kepler's Third Law:

P² = a³

Where:

• P = orbital period (Earth years)
• a = semi-major axis (AU)

Example: Mars

• Semi-major axis: 1.524 AU
• Predicted period: √(1.524³) = √(3.540) = 1.881 Earth years
• Actual period: 1.881 years (687 days) ✓

Why AU simplifies this: In SI units, Kepler's Third Law requires the gravitational constant G and solar mass M☉:

P² = (4π² / GM☉) × a³

Using AU and years, the constants vanish!

2. Asteroid and Comet Tracking

Orbital elements use AU:

• Semi-major axis (a): Average orbital distance (AU)
• Perihelion distance (q): Closest approach to Sun (AU)
• Aphelion distance (Q): Farthest point from Sun (AU)

Example: Halley's Comet

• Semi-major axis: 17.8 AU
• Perihelion: 0.586 AU (inside Venus's orbit)
• Aphelion: 35.1 AU (beyond Neptune)
• Orbital period: 75-76 years

Near-Earth Object (NEO) classification:

• Atens: Semi-major axis <1.0 AU, perihelion >0.983 AU
• Apollos: Semi-major axis >1.0 AU, perihelion <1.017 AU
• Amors: Semi-major axis >1.0 AU, perihelion 1.017-1.3 AU

3. Exoplanet Characterization

When astronomers discover exoplanets, they report orbital distances in AU for comparison with our Solar System.

Kepler-452b ("Earth's cousin"):

• Star: G-type (Sun-like)
• Distance from star: 1.05 AU
• Orbital period: 385 days
• Size: 1.6× Earth diameter
• In habitable zone (liquid water possible)

TRAPPIST-1 system:

• Star: Ultra-cool red dwarf (9% Sun's mass)
• 7 planets: 0.011 to 0.063 AU (all closer than Mercury!)
• 3 in habitable zone (TRAPPIST-1e, f, g)
• Why so close? Red dwarf is dim, HZ is much nearer

Proxima Centauri b:

• Distance from star: 0.0485 AU (7.3 million km)
• Orbital period: 11.2 days
• In habitable zone (red dwarf is faint)
• Nearest potentially habitable exoplanet (4.24 light-years)

4. Mission Planning and Spacecraft Navigation

Delta-v budgets: Spacecraft missions calculate fuel requirements based on AU distances.

Hohmann transfer orbit (Earth to Mars):

• Earth orbit: 1.00 AU (circular approximation)
• Mars orbit: 1.52 AU
• Transfer orbit semi-major axis: (1.00 + 1.52) / 2 = 1.26 AU
• Travel time: Half the transfer orbit period ≈ 259 days (8.5 months)

Launch windows: Earth and Mars align favorably every 26 months (synodic period). Missing a window means waiting 2+ years.

Example: Perseverance rover

• Launch: July 30, 2020
• Landing: February 18, 2021
• Distance traveled: ~480 million km (depends on orbital path, not straight-line)

5. Solar Wind and Space Weather

Heliosphere: The Sun's influence extends well beyond planetary orbits, measured in AU.

Termination shock: ~90 AU

• Solar wind slows below sound speed
• Voyager 1 crossed: 94 AU (2004)

Heliopause: ~120 AU

• Boundary where solar wind meets interstellar medium
• Voyager 1 crossed: 121 AU (2012)

Bow shock: ~150 AU

• Where interstellar medium piles up against heliosphere

Oort Cloud: 2,000-100,000 AU

• Spherical shell of icy comets surrounding Solar System
• Gravitationally bound to the Sun, but barely

6. Educational and Outreach

The AU provides an intuitive scale for teaching Solar System structure.

Scale models: If Earth = 1 cm diameter:

• Sun: 109 cm (1.09 m) diameter
• Earth-Sun distance: 117 m (1 AU scale)
• Jupiter: 11 cm diameter, 608 m from Sun
• Neptune: 4 cm diameter, 3.5 km from Sun!

The "Voyage" scale model (Washington, D.C.):

• 1:10 billion scale
• Sun (Smithsonian): 1.39 m diameter sphere
• Earth: 1.3 cm (grain of rice), 15 m away
• Pluto: 0.2 cm, 590 m away

7. Historical Astronomy

Pre-AU era challenges: Before the AU was accurately measured, astronomers knew relative planetary positions but not absolute distances.

Example: Kepler knew...

• Venus is 0.72× Earth's distance
• Mars is 1.52× Earth's distance
• Jupiter is 5.20× Earth's distance

...but NOT the actual Earth-Sun distance!

The AU filled this gap, providing the absolute scale.

Conversion Guide

Basic Conversions

Astronomical Unit to Metric:

1 AU = 149,597,870,700 meters (EXACT)
1 AU = 149,597,870.7 kilometers
1 AU ≈ 150 million km (rounded)

Astronomical Unit to Imperial:

1 AU = 92,955,807.3 miles
1 AU ≈ 93 million miles (rounded)

Astronomical Unit to Light Units:

1 AU = 499.004783836 light-seconds (8 min 19 sec)
1 AU = 0.00001581 light-years

Astronomical Unit to Other Astronomical Units:

1 light-year = 63,241.1 AU
1 parsec = 206,264.8 AU
1 AU = 0.0000158 light-years
1 AU = 0.00000485 parsecs

Conversion Tables

Astronomical Units → Kilometers

AU	Kilometers
0.1 AU	15 million km
0.39 AU (Mercury)	58 million km
0.72 AU (Venus)	108 million km
1.00 AU (Earth)	150 million km
1.52 AU (Mars)	228 million km
5.20 AU (Jupiter)	778 million km
9.54 AU (Saturn)	1.43 billion km
19.2 AU (Uranus)	2.87 billion km
30.1 AU (Neptune)	4.50 billion km
39.5 AU (Pluto)	5.91 billion km

Kilometers → Astronomical Units

Kilometers	AU
1 million km	0.00668 AU
10 million km	0.0668 AU
100 million km	0.668 AU
150 million km	1.002 AU
500 million km	3.342 AU
1 billion km	6.684 AU
5 billion km	33.42 AU

AU → Miles

AU	Miles
0.1 AU	9.3 million mi
1 AU	93 million mi
5 AU	465 million mi
10 AU	930 million mi
30 AU	2.79 billion mi
100 AU	9.30 billion mi

Practical Conversion Examples

Example 1: Mars distance Mars is 1.524 AU from the Sun. What is this in kilometers?

1.524 AU × 149,597,870.7 km/AU = 227,987,155 km ≈ 228 million km

Example 2: Voyager 1 distance Voyager 1 is 164 AU from the Sun. How many light-years is that?

164 AU ÷ 63,241.1 AU/ly = 0.00259 light-years

(Voyager 1 has traveled only 0.26% of a light-year in 47 years!)

Example 3: Light travel time to Jupiter Jupiter orbits at 5.203 AU. How long does sunlight take to reach Jupiter?

5.203 AU × 499 light-seconds/AU = 2,596 seconds = 43 minutes 16 seconds

Example 4: Exoplanet comparison An exoplanet orbits its star at 0.85 AU. If the star is Sun-like, is it in the habitable zone?

Habitable zone: 0.95-1.37 AU (for Sun-like stars)
0.85 AU < 0.95 AU → Too close! (likely too hot, like Venus)

Common Conversion Mistakes

1. Confusing AU with Light-Years

The mistake: Using AU and light-years interchangeably.

Reality:

• 1 AU = Earth-Sun distance = 150 million km
• 1 light-year = Distance light travels in a year = 9.46 trillion km
• 1 light-year = 63,241 AU (63,000× larger!)

Example error: "Proxima Centauri is 4.24 AU away" (WRONG!)

• Correct: Proxima Centauri is 4.24 light-years = 268,000 AU

How to avoid:

• Use AU for Solar System distances (planets, asteroids)
• Use light-years for interstellar distances (nearest stars)

2. Using AU for Interstellar Distances

The mistake: Saying "Alpha Centauri is 276,000 AU away" in casual conversation.

Why it's awkward: While technically correct, it's like measuring the distance from New York to Tokyo in millimeters (11 trillion mm)—accurate but unwieldy.

Better: "Alpha Centauri is 4.37 light-years away" (or 1.34 parsecs for technical work)

When AU is appropriate for stars: Scientific papers sometimes use AU for very nearby objects:

• "Proxima Centauri is 268,000 AU distant" (shows Solar System scale comparison)

3. Forgetting the IAU 2012 Redefinition

The mistake: Treating the AU as a measured quantity that changes with better observations.

Reality (pre-2012): The AU was defined via the Gaussian gravitational constant and solar mass, so it shifted slightly as measurements improved.

Reality (post-2012): The AU is now a defined constant (exactly 149,597,870,700 m), like the speed of light. It will never change.

Why this matters: Old textbooks may list slightly different AU values (149,597,870.691 km in some sources). The modern, official value is exact: 149,597,870.700 km.

4. Mixing Up Orbital Distance and Travel Distance

The mistake: Assuming a spacecraft travels exactly the AU distance to reach a planet.

Reality: Planets orbit the Sun, so the straight-line distance from Earth to Mars varies:

• Closest approach (opposition): 0.52 AU (78 million km)
• Farthest (conjunction): 2.52 AU (377 million km)

Spacecraft don't fly straight:

• Hohmann transfer orbits curve through space
• Mars missions travel ~480 million km (3.2 AU path length) despite Mars orbiting at only 1.52 AU

How to avoid:

• Orbital distance: How far the planet is from the Sun (fixed)
• Opposition distance: How close Earth and the planet get
• Transfer orbit: The curved path spacecraft take

5. Incorrect Sunlight Intensity Calculations

The mistake: Thinking sunlight at 2 AU is half as bright as at 1 AU.

Reality: Light intensity follows the inverse square law:

Intensity = (1/distance)²

At 2 AU:

Intensity = (1/2)² = 1/4 = 25% (NOT 50%!)

Example:

• Mars (1.52 AU): Intensity = (1/1.52)² = 0.43 (43% of Earth's sunlight)
• Jupiter (5.2 AU): Intensity = (1/5.2)² = 0.037 (3.7%)

6. Assuming AU = Average Distance for Elliptical Orbits

The mistake: Thinking the semi-major axis (AU) is the average distance.

Reality: For elliptical orbits, the semi-major axis is the average of perihelion and aphelion:

a = (perihelion + aphelion) / 2

But time-averaged distance ≠ semi-major axis due to Kepler's second law (planets move faster near perihelion).

Example: Earth

• Semi-major axis: 1.000 AU (definition)
• Perihelion: 0.983 AU (early January)
• Aphelion: 1.017 AU (early July)
• Earth spends more time near aphelion (slower orbital speed)

Why this matters: When calculating light travel time or radiation dosage, use the instantaneous distance, not the semi-major axis.