Ground Truth · a schoolroom fact, re-derived from the orbits

The Closest Neighbour You'll Never Meet

Ask which planet is closest to Earth and the answer comes back fast: Venus. It's the planet that swings nearest to us. But "nearest" hides a second question — nearest right now, or nearest on average, across all the years? Average it over time and the winner is not Venus. It's Mercury — the little one that hugs the Sun and so never strays far from anyone.

Assumption: circular, coplanar orbits, with the relative orbital phase uniform over long times. Real orbits are slightly eccentric and tilted — small corrections named at the foot of the page. Everything below is computed from one number per planet: its distance from the Sun (semi-major axis, in AU).

Compare Earth with —

Distance right now

— AU

— M km

Time-average (counting…)

— AU

over — simulated yr

Closed-form mean

— AU

(2/π)(r₁+r₂)·E(m)

Closest approach

— AU

= |r₁ − r₂|

Loading the orbits…

Compared planet's orbit — 0.723 AU

Slide it in toward the Sun and its time-average drops — proximity to the Sun, not to Earth, is what makes a planet a close neighbour.

Earth's orbit (the reference) — 1.000 AU

You can move the reference planet too. The method is the same for any pair — that's how we get Mercury's distance to Neptune.

Watch the middle readout. The distance right now swings between a closest approach of |r₁ − r₂| and a far side of r₁ + r₂ as the planets lap each other. But the time-average — the number your intuition should actually use for "closest" — climbs to a fixed value and stays there. That value is the same whether you average over time or over every possible arrangement of the two planets, because over the long run the relative angle between them is spread evenly around the circle. The simulator's running tally is converging onto the exact closed-form mean beside it.

The ranking flips depending on what "closest" means

Both columns are computed live from the same orbits (Earth = 1.000 AU, standard NASA semi-major axes). Only the question differs.

Closest on average

metric: mean distance over time

Comes closest

metric: minimum separation

The familiar "Venus" answer is the right answer to the right-hand question: at closest approach Venus comes within about 0.28 AU (~41 million km) — the circular-orbit value this page recomputes; real eccentricity pulls the true minimum a little lower, to ~38 M km (≈ 0.25 AU), closer than any other planet ever gets. It's simply the wrong answer to "which planet is nearest to us, on average" — that's Mercury.

The check — every number recomputed in front of you

Two independent engines compute the mean distance. If the closed form and the brute-force average ever disagreed, one of them would be wrong — they agree to machine precision:

Earth & —	closed form E(m)	numeric ∫dθ	\|Δ\|	Physics Today

—

And the striking part: because Mercury sits closest to the Sun, it's the nearest planet — on average — to every other planet, not just Earth. Even to Neptune, thirty times farther out, where the gaps are tiny but real:

planet	mean distance to Neptune

Run it yourself: node research/closest-planet-to-earth/verify-closest-planet-to-earth.mjs (32/32 checks).

What's proven, what's assumed, and the one number I couldn't source

Proven here, from scratch. The closed-form point-circle mean d = (2/π)(r₁+r₂)·E(m) equals the brute-force numeric average of √(r₁²+r₂²−2r₁r₂cos θ) to ~10⁻¹⁴ AU; a time-stepping simulation at the planets' true Keplerian rates converges to the same value. Mercury has the smallest time-averaged distance to Earth (1.038 < 1.136 < 1.693 AU for Mercury/Venus/Mars), and to every other planet. The two metrics genuinely rank differently.

Assumed / idealised. Orbits are treated as circular and coplanar, with relative phase uniformly distributed. Real orbits are eccentric and inclined; these are small corrections. The authors' own full simulation over 10,000 years (with the PyEphem library) reproduced the point-circle values to within about 1%, whereas a naïve "average of closest approaches" was off by up to about 300% — this ~1% vs ~300% comparison is stated in the primary Physics Today column itself ("the simulation results differ from the flawed numbers by up to 300%, but they deviate from the PCM figures by less than 1%"); it is the authors' own measurement, not this page's. "Time-average equals configuration-average" holds because the orbital periods are incommensurate, so over long times the relative phase equidistributes — which is exactly what the running tally demonstrates.

The number I couldn't source to the paper. The widely-quoted split — Mercury is Earth's nearest planet ~47% of the time, Venus ~36%, Mars ~17% — appears only in secondary summaries; I could not find it in the primary Physics Today column, which says only that Mercury has the smallest average distance and is Earth's nearest planet "most frequently." So this page does not cite those percentages to the paper; it recomputes them live in the verifier (~46.5% / 36.7% / 16.8%) and labels them as the page's own output.

Closest-approach caveat. The 0.28 AU (~41 M km) Venus minimum is the circular-orbit value, the one this page can recompute. Accounting for real eccentricity, the theoretical minimum is a little smaller (~38 M km ≈ 0.25 AU). Semi-major axes (Mercury 0.387, Venus 0.723, Earth 1.000, Mars 1.524, Neptune 30.07 AU) are standard NASA fact-sheet values; the ~1.04 / ~1.14 AU results are insensitive to their last digit.