Math
To ensure measurement consistency, a theoretical, perfectly manufactured regulation men’s basketball (Size 7) serves as the sole physical reference. Earth’s mean diameter is adopted as the primary scaling anchor, while equatorial and polar diameters are included for geometric context.
Show the math: Basketball diameter & model consistency
The model initiates with a regulation men’s basketball (Size 7) as a familiar physical reference for representing Earth.
Step 1 — Regulation basketball circumference:
- Official men’s basketball circumference: 29.5 inches
- Convert inches to centimeters:
29.5 in × 2.54 = 74.93 cm
Step 2 — Derive basketball diameter using circle geometry:
Diameter = Circumference ÷ π
74.93 cm ÷ π = 23.85095977 cm
Note: Use the Excel pi function 3.14159265358979 for the mathematical constant pi, accurate to 15 digits
This value corresponds to the geometric diameter derived from the official circumference of a regulation men’s basketball.
Step 3 — Model consistency with Earth’s geometry:
NASA/JPL defines Earth’s radii using the mean radius rather than the equatorial or polar values. To maintain consistency with this standard, the scale model employs Earth’s mean diameter as the authoritative reference for all conversions, while equatorial and polar diameters are provided to illustrate Earth’s slight oblateness.
To ensure internal consistency, the scale model disregards variations in retail basketball tolerances (e.g., inflation pressure differences). All distances are anchored to Earth’s mean diameter, and identical geometric relationships to the theoretical, perfectly manufactured regulation men’s basketball (Size 7) are applied throughout.
Earth's equatorial diameter:
12,756.3 km
Earth's mean diameter:
12,742.0 km
Earth's polar diameter:
12,713.6 km
Scale factor (using Earth's mean diameter):23.85095977 cm ÷ 12,742 km = 0.001871837998097 cm per km
Derived model Earth values:Model Earth radius:
11.92547989 cm
Model Earth diameter:
23.85095977 cm
Model Earth circumference:
75.479794 cm
Although regulation basketballs may vary slightly by manufacturer and inflation, this model is based on a perfectly manufactured regulation men’s basketball with a circumference of 29.5 inches. Employing Earth’s mean geometry ensures that all scale distances remain mathematically consistent and reproducible.
Anchor: Earth (Mean) diameter = 12,742.0 km = 23.85095977 cm (model).
Scale factor: 23.85095977 cm ÷ 12,742 km = 0.001871837998097 cm per km.
1 AU in the model: 149,597,870.7 km × 0.001871837998097 cm/km = 280,022.9788 cm = 2,800.229788 m (≈ 2.800229788 km).
Formulas used
- Convert inches to centimeters: 29.5 in × 2.54 = 74.9300 cm
- Excel Pi function ≈ 3.14159265358979... accurate to 15 digits
- Earth Model Diameter cm = Circumference (cm) ÷ π
- Scaled length (cm) = real length (km) × (Earth_model_diameter_cm ÷ Earth_mean_diameter_km)
- Scaled distance (m) = scaled length (cm) ÷ 100
- Scaled distance (miles) = scaled distance (m) ÷ 1609.344
- AU conversion: km = AU × 149,597,870.7 km
Lunar perihelion, aphelion, and eccentricity are Earth-centered and are not part of the Sun-centered planetary orbit table used here.
For readability, scaled orbital distances are shown in meters for inner planets and kilometers for outer planets.
Sun
Physical size
| Quantity | km | miles | AU | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|---|
| Sun Radius | 695,508.00 | 432,168.64 | 0.004649 | 109.046268 | 1,348.052920 | 13.480529 | 44.227458 |
| Sun Diameter | 1,391,016.00 | 864,337.27 | 0.009298 | 218.092535 | 2,696.105839 | 26.961058 | 88.454916 |
| Sun Circumference | 4,370,005.65 | 2,715,395.62 | 0.029212 | 685.157907 | 8,470.066297 | 84.700663 | 277.889314 |
No orbital elements for this body in this workbook tab (the Sun is the reference center).
Mercury
Physical size
| Quantity | km | miles | AU | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|---|
| Mercury Radius | 2,439.70 | 1,515.96 | 0.000016 | 0.382512 | 4.605845 | 0.046058 | 0.151108 |
| Mercury Diameter | 4,879.40 | 3,031.92 | 0.000033 | 0.765024 | 9.211690 | 0.092117 | 0.302216 |
| Mercury Circumference | 15,329.09 | 9,525.05 | 0.000102 | 2.403394 | 28.946940 | 0.289469 | 0.949895 |
Mercury Orbit (Sun-centered)
| Parameter | Real (AU) | Real (km) | Model (km) | Model (miles) |
|---|---|---|---|---|
| Perihelion | 0.3075 | 46,001,200 | 0.861 | 0.535 |
| Semimajor Axis (a) | 0.3871 | 57,909,050 | 1.084 | 0.674 |
| Aphelion | 0.4667 | 69,816,900 | 1.307 | 0.812 |
| Eccentricity (e) | 0.2056 | |||
Venus
Physical size
| Quantity | km | miles | AU | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|---|
| Venus Radius | 6,051.80 | 3,760.41 | 0.000040 | 0.948841 | 11.416983 | 0.114170 | 0.374574 |
| Venus Diameter | 12,103.60 | 7,520.83 | 0.000081 | 1.897681 | 22.833967 | 0.228340 | 0.749148 |
| Venus Circumference | 38,024.58 | 23,627.38 | 0.000254 | 5.961741 | 71.727441 | 0.717274 | 2.353919 |
Venus Orbit (Sun-centered)
| Parameter | Real (AU) | Real (km) | Model (km) | Model (miles) |
|---|---|---|---|---|
| Perihelion | 0.7184 | 107,476,000 | 2.012 | 1.250 |
| Semimajor Axis (a) | 0.7233 | 108,208,000 | 2.025 | 1.259 |
| Aphelion | 0.7282 | 108,939,000 | 2.038 | 1.266 |
| Eccentricity (e) | 0.0068 | |||
Earth
Physical size
| Quantity | km | miles | AU | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|---|
| Earth (Equatorial) radius | 6,378.10 | 3,963.17 | 0.000043 | 1.000000 | 12.031431 | 0.120314 | 0.394767 |
| Earth (Polar) diameter | 12,713.6 | 7,899.83 | 0.000085 | 1.99376 | 23.8049 | 0.238049 | 0.78099 |
| Earth (Mean) diameter | 12,742.0 | 7,917.51 | 0.000085 | 2.000000 | 23.85095977 | 0.2385096 | 0.78252 |
| Earth (Equatorial) diameter | 12,756.3 | 7,926.34 | 0.000085 | 2.00224 | 23.8767 | 0.238767 | 0.78335 |
Earth Orbit (Sun-centered)
| Parameter | Real (AU) | Real (km) | Model (km) | Model (miles) |
|---|---|---|---|---|
| Perihelion | 0.98327 | 147,098,074 | 2.753 | 1.711 |
| Semimajor Axis (a) | 1.00000 | 149,597,870.7 | 2.800 | 1.740 |
| Aphelion | 1.01671 | 152,097,701 | 2.847 | 1.769 |
| Eccentricity (e) | 0.0167 | |||
Moon
Physical size
| Quantity | km | miles | AU | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|---|
| Moon Equatorial radius | 1,738.10 | 1,080.01 | 0.000012 | 0.272511 | 3.277699 | 0.032777 | 0.107538 |
| Moon Equatorial Diameter | 3,476.20 | 2,160.01 | 0.000023 | 0.545021 | 6.555398 | 0.065554 | 0.215076 |
| Moon Equatorial Circumference | 10,920.80 | 6,785.87 | 0.000073 | 1.712235 | 20.595699 | 0.205957 | 0.675725 |
Moon Orbit distances (Earth-centered)
| Quantity | km | miles | Model (m) | Model (ft) |
|---|---|---|---|---|
| Moon Perigee (closest) | 363,300 | 225,623 | 6.85 | 22.5 |
| Moon Semimajor Axis (mean distance) | 384,400 | 238,855 | 7.25 | 23.8 |
| Moon Apogee (farthest) | 405,500 | 252,088 | 7.65 | 25.1 |
| Moon Eccentricity | 0.0549 | |||
The Moon’s orbital distances are measured relative to Earth rather than the Sun. At this scale, where Earth is represented by a basketball, the Moon orbits at a distance of approximately 7 to 8 meters.
Mars
Physical size
| Quantity | km | miles | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|
| Mars Radius | 3,396.20 | 2,110.30 | 0.53248 | 6.4039 | 0.06404 | 0.21010 |
| Mars Diameter | 6,792.40 | 4,220.60 | 1.06496 | 12.8077 | 0.12808 | 0.42020 |
| Mars Circumference | 21,338.95 | 13,259.41 | 3.34566 | 40.2367 | 0.40237 | 1.32010 |
Mars Orbit (Sun-centered)
| Parameter | Real (AU) | Real (km) | Model (km) | Model (miles) |
|---|---|---|---|---|
| Perihelion | 1.3814 | 206,700,000 | 3.870 | 2.405 |
| Semimajor Axis (a) | 1.5237 | 227,939,200 | 4.267 | 2.652 |
| Aphelion | 1.6660 | 249,228,730 | 4.666 | 2.899 |
| Eccentricity (e) | 0.0934 | |||
Jupiter
Physical size
| Quantity | km | miles | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|
| Jupiter Radius | 71,492.00 | 44,423.07 | 11.20898 | 134.8053 | 1.34805 | 4.42275 |
| Jupiter Diameter | 142,984.00 | 88,846.14 | 22.41796 | 269.6106 | 2.69611 | 8.84549 |
| Jupiter Circumference | 449,197.48 | 279,118.38 | 70.42810 | 847.0066 | 8.47007 | 27.78893 |
Jupiter Orbit (Sun-centered)
| Parameter | Real (AU) | Real (km) | Model (km) | Model (miles) |
|---|---|---|---|---|
| Perihelion | 4.9501 | 740,573,600 | 13.86 | 8.61 |
| Semimajor Axis (a) | 5.2044 | 778,340,800 | 14.57 | 9.06 |
| Aphelion | 5.4588 | 816,107,200 | 15.28 | 9.49 |
| Eccentricity (e) | 0.0489 | |||
Saturn
Physical size
| Quantity | km | miles | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|
| Saturn Radius | 60,268.00 | 37,448.80 | 9.44921 | 113.6413 | 1.13641 | 3.72839 |
| Saturn Diameter | 120,536.00 | 74,897.60 | 18.89842 | 227.2826 | 2.27283 | 7.45678 |
| Saturn Circumference | 378,675.01 | 235,297.74 | 59.37113 | 714.0295 | 7.14029 | 23.42616 |
Saturn Orbit (Sun-centered)
| Parameter | Real (AU) | Real (km) | Model (km) | Model (miles) |
|---|---|---|---|---|
| Perihelion | 9.0412 | 1,352,550,000 | 25.32 | 15.74 |
| Semimajor Axis (a) | 9.5826 | 1,433,449,370 | 26.82 | 16.67 |
| Aphelion | 10.1238 | 1,514,500,000 | 28.34 | 17.61 |
| Eccentricity (e) | 0.0565 | |||
Uranus
Physical size
| Quantity | km | miles | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|
| Uranus Radius | 25,559.00 | 15,881.63 | 4.00731 | 48.1940 | 0.48194 | 1.58117 |
| Uranus Diameter | 51,118.00 | 31,763.25 | 8.01461 | 96.3881 | 0.96388 | 3.16234 |
| Uranus Circumference | 160,591.93 | 99,787.20 | 25.17865 | 302.8121 | 3.02812 | 9.93478 |
Uranus Orbit (Sun-centered)
| Parameter | Real (AU) | Real (km) | Model (km) | Model (miles) |
|---|---|---|---|---|
| Perihelion | 18.3755 | 2,741,300,000 | 51.34 | 31.91 |
| Semimajor Axis (a) | 19.1913 | 2,870,658,186 | 53.74 | 33.40 |
| Aphelion | 20.0063 | 3,002,000,000 | 56.20 | 34.92 |
| Eccentricity (e) | 0.0472 | |||
Neptune
Physical size
| Quantity | km | miles | Earth radii | Model (cm) | Model (m) | Model (ft) |
|---|---|---|---|---|---|---|
| Neptune Radius | 24,764.00 | 15,387.64 | 3.88266 | 46.6950 | 0.46695 | 1.53199 |
| Neptune Diameter | 49,528.00 | 30,775.27 | 7.76532 | 93.3900 | 0.93390 | 3.06398 |
| Neptune Circumference | 155,596.80 | 96,683.37 | 24.39548 | 293.3933 | 2.93393 | 9.62576 |
Neptune Orbit (Sun-centered)
| Parameter | Real (AU) | Real (km) | Model (km) | Model (miles) |
|---|---|---|---|---|
| Perihelion | 29.7661 | 4,444,450,000 | 83.16 | 51.68 |
| Semimajor Axis (a) | 30.0689 | 4,503,443,661 | 84.25 | 52.34 |
| Aphelion | 30.3717 | 4,564,600,000 | 85.42 | 53.07 |
| Eccentricity (e) | 0.0086 | |||
Pluto
Physical size
| Quantity | Real value (km) | Model (cm) | Model (mm) |
|---|---|---|---|
| Pluto Mean Radius | 1,188.3 | 2.22 | 22.4 |
| Pluto Mean Diameter | 2,376.6 | 4.45 | 44.8 |
| Pluto Circumference | 7,466.9 | 13.98 | 140.8 |
At this scale, with Earth represented as a basketball, Pluto’s physical size is comparable to that of a large marble or a small ping-pong ball. In the outer Solar System, Pluto’s orbit is its most visually prominent feature, rather than its size.
Pluto Orbit (Sun-centered)
| Parameter | Real (AU) | Real (km) | Model (km) | Model (miles) |
|---|---|---|---|---|
| Perihelion | 29.658 | 4,437,000,000 | 83.03 | 51.60 |
| Semimajor Axis (a) | 39.482 | 5,906,440,000 | 110.51 | 68.67 |
| Aphelion | 49.305 | 7,375,930,000 | 137.98 | 85.75 |
| Eccentricity (e) | 0.2488 | |||
Works Cited
- NASA National Space Science Data Center. “Planetary Fact Sheet.” NASA, Goddard Space Flight Center, https://nssdc.gsfc.nasa.gov/planetary/factsheet/index.html. Accessed 26 Jan. 2026.
- Cain, Fraser. “How Far Is Mercury from the Sun?” Universe Today, https://www.universetoday.com/14163/how-far-is-mercury-from-the-sun/. Accessed 26 Jan. 2026.
- Ridgway, Ross. “Planets.” Department of Meteorology, University of Reading, http://www.met.rdg.ac.uk/~ross/Astronomy/Planets.html. Accessed 26 Jan. 2026.
- European Space Education Resource Office (ESERO). Astronomy and Football Activity. ESERO Ireland, Jan. 2015, https://esero.ie/wp-content/uploads/2015/01/astronomy_and_football_activity.pdf. Accessed 26 Jan. 2026.
- “Astronomical Unit to Light Second Conversion.” Conversion-Website.com, http://www.conversion-website.com/length/astronomical-unit-to-light-second.html. Accessed 26 Jan. 2026.