The Asteroid News

This scale model of the Solar System uses a basketball to represent Earth, providing comparative sizes and Sun-centered orbital distances for major celestial bodies, with all calculations detailed.

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

Physical size of the Sun, showing real dimensions and scaled model equivalents using the basketball–Earth scale.
QuantitykmmilesAUEarth radiiModel (cm)Model (m)Model (ft)
Sun Radius695,508.00432,168.640.004649109.0462681,348.05292013.48052944.227458
Sun Diameter1,391,016.00864,337.270.009298218.0925352,696.10583926.96105888.454916
Sun Circumference4,370,005.652,715,395.620.029212685.1579078,470.06629784.700663277.889314

No orbital elements for this body in this workbook tab (the Sun is the reference center).

Mercury

Physical size

Physical size of Mercury, showing real dimensions and scaled model equivalents using the basketball–Earth scale.
QuantitykmmilesAUEarth radiiModel (cm)Model (m)Model (ft)
Mercury Radius2,439.701,515.960.0000160.3825124.6058450.0460580.151108
Mercury Diameter4,879.403,031.920.0000330.7650249.2116900.0921170.302216
Mercury Circumference15,329.099,525.050.0001022.40339428.9469400.2894690.949895

Mercury Orbit (Sun-centered)

Sun-centered orbital distances of Mercury, including perihelion, semimajor axis, and aphelion, shown in AU, real kilometers, and scaled model distances.
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

Physical size of Venus, showing real dimensions and scaled model equivalents using the basketball–Earth scale.
QuantitykmmilesAUEarth radiiModel (cm)Model (m)Model (ft)
Venus Radius6,051.803,760.410.0000400.94884111.4169830.1141700.374574
Venus Diameter12,103.607,520.830.0000811.89768122.8339670.2283400.749148
Venus Circumference38,024.5823,627.380.0002545.96174171.7274410.7172742.353919

Venus Orbit (Sun-centered)

Sun-centered orbital distances of Venus, including perihelion, semimajor axis, and aphelion, shown in AU, real kilometers, and scaled model distances.
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

Physical size of Earth, including mean, equatorial, and polar diameters, with scaled model equivalents used to anchor the basketball scale.
QuantitykmmilesAUEarth radiiModel (cm)Model (m)Model (ft)
Earth (Equatorial) radius6,378.103,963.170.0000431.00000012.0314310.1203140.394767
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)

Sun-centered orbital distances of Earth, including perihelion, semimajor axis (1 AU), and aphelion, shown in AU, real kilometers, and scaled model distances.
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

Physical size of the Moon, showing real dimensions and scaled model equivalents using the basketball–Earth scale.
QuantitykmmilesAUEarth radiiModel (cm)Model (m)Model (ft)
Moon Equatorial radius1,738.101,080.010.0000120.2725113.2776990.0327770.107538
Moon Equatorial Diameter3,476.202,160.010.0000230.5450216.5553980.0655540.215076
Moon Equatorial Circumference10,920.806,785.870.0000731.71223520.5956990.2059570.675725

Moon Orbit distances (Earth-centered)

Earth-centered orbital distances of the Moon, including perigee, semimajor axis, and apogee, shown in real kilometers and scaled model distances.
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

Physical size of Mars, showing real dimensions and scaled model equivalents using the basketball–Earth scale.
QuantitykmmilesEarth radiiModel (cm)Model (m)Model (ft)
Mars Radius3,396.202,110.300.532486.40390.064040.21010
Mars Diameter6,792.404,220.601.0649612.80770.128080.42020
Mars Circumference21,338.9513,259.413.3456640.23670.402371.32010

Mars Orbit (Sun-centered)

Sun-centered orbital distances of Mars, including perihelion, semimajor axis, and aphelion, shown in AU, real kilometers, and scaled model distances.
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

Physical size of Jupiter, showing real dimensions and scaled model equivalents using the basketball–Earth scale.
QuantitykmmilesEarth radiiModel (cm)Model (m)Model (ft)
Jupiter Radius71,492.0044,423.0711.20898134.80531.348054.42275
Jupiter Diameter142,984.0088,846.1422.41796269.61062.696118.84549
Jupiter Circumference449,197.48279,118.3870.42810847.00668.4700727.78893

Jupiter Orbit (Sun-centered)

Sun-centered orbital distances of Jupiter, including perihelion, semimajor axis, and aphelion, shown in AU, real kilometers, and scaled model distances.
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

Physical size of Saturn, showing real dimensions and scaled model equivalents using the basketball–Earth scale.
QuantitykmmilesEarth radiiModel (cm)Model (m)Model (ft)
Saturn Radius60,268.0037,448.809.44921113.64131.136413.72839
Saturn Diameter120,536.0074,897.6018.89842227.28262.272837.45678
Saturn Circumference378,675.01235,297.7459.37113714.02957.1402923.42616

Saturn Orbit (Sun-centered)

Sun-centered orbital distances of Saturn, including perihelion, semimajor axis, and aphelion, shown in AU, real kilometers, and scaled model distances.
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

Physical size of Uranus, showing real dimensions and scaled model equivalents using the basketball–Earth scale.
QuantitykmmilesEarth radiiModel (cm)Model (m)Model (ft)
Uranus Radius25,559.0015,881.634.0073148.19400.481941.58117
Uranus Diameter51,118.0031,763.258.0146196.38810.963883.16234
Uranus Circumference160,591.9399,787.2025.17865302.81213.028129.93478

Uranus Orbit (Sun-centered)

Sun-centered orbital distances of Uranus, including perihelion, semimajor axis, and aphelion, shown in AU, real kilometers, and scaled model distances.
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

Physical size of Neptune, showing real dimensions and scaled model equivalents using the basketball–Earth scale.
QuantitykmmilesEarth radiiModel (cm)Model (m)Model (ft)
Neptune Radius24,764.0015,387.643.8826646.69500.466951.53199
Neptune Diameter49,528.0030,775.277.7653293.39000.933903.06398
Neptune Circumference155,596.8096,683.3724.39548293.39332.933939.62576

Neptune Orbit (Sun-centered)

Sun-centered orbital distances of Neptune, including perihelion, semimajor axis, and aphelion, shown in AU, real kilometers, and scaled model distances.
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

Physical size of Pluto, showing real dimensions and scaled model equivalents for context within the basketball–Earth scale.
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)

Sun-centered orbital distances of Pluto, including perihelion, semimajor axis, and aphelion, shown in AU, real kilometers, and scaled model distances.
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
This webpage is an expansion of the webmasters' spreadsheets done in 2018. Drafting and coding were done with the aid of ChatGPT, Gemini, Copilot, and Grammarly, under the direction and guidance of the webmaster.

Works Cited

  1. 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.
  2. 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.
  3. Ridgway, Ross. “Planets.” Department of Meteorology, University of Reading, http://www.met.rdg.ac.uk/~ross/Astronomy/Planets.html. Accessed 26 Jan. 2026.
  4. 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.
  5. “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.