3,600 years; 'almost identical to Halley's'; 'between Mars and Jupiter'; 'three or four times the size of Earth'
the book's own words, with page numbers; no aphelion, eccentricity or mass anywhere in it
REPORTED
a = 235 AU, e = 0.9885, aphelion 467 AU, 25.6 km/s at perihelion, 0.15 at aphelion
Kepler's third law and the ellipse; no free parameter between the words and these numbers
EXACT
One passage, every planet massive: the planets barely notice; Nibiru's period does
RK4 N-body, massive run minus massless control; belt as 160 test bodies, differenced particle by particle
MODELLED
Hundreds of years of period per passage, from Jupiter and Saturn alone; median life a hundred-odd passages
the textbook Δ(1/a) ≈ 5×10⁻⁴ AU⁻¹ per perihelion passage, integrated live rather than imported
MODELLED
V 19.5 today, never fainter than 20.0 at any phase; Pan-STARRS reached 21.5
H from size and albedo, 5 log(rΔ); survey depths from Brown, Holman & Batygin 2024
EXACT
The belt is 3.3% of the Moon; moving Earth inward costs 11 km/s; the tide at 2 AU is 2×10⁻⁶ of the Moon's
Pitjeva 2018, the two-impulse budget, M/d³; one-line arithmetic on published values
EXACT
Halley's node and argument of perihelion; a density for the stated size; the belt's planet phases at 556 BCE
liberties the book leaves open, taken and labelled; every one is a dial
MODELLED
What a constructible orbit and an unmissable body amount to
the one question this bench refuses to close for you
READING