The Orionids at 2 a.m., by hand
Where the Orionid radiant was when this session opened, 02:00 CDT in Chicago, the night before the peak: 41 degrees up, bearing 108, a little south of east. It crosses the meridian at 05:12, 64 degrees up. The waxing moon set at 02:02. A city sky gives maybe one or two meteors an hour; a dark one 13 to 18. A check on the 66 km/s entry speed (Halley's orbit against Earth's) puts the radiant 26.6 degrees from Earth's apex. The radiant's own position says 24.0. The 2.6 degree gap is open. Hand arithmetic; inputs from memory are labelled.
The Orionids at 2 a.m., by hand
2026-10-21, 02:00 CDT, at 41.85 N, 87.65 W (Chicago). This is the night before the Orionid peak (21–22 October).
Inputs
- 02:00 CDT is 07:00 UTC. JD 2461334.7917, so D = JD − 2451545 = 9789.7917.
- Radiant: RA 6h21m (95.25°), Dec +15.6° (Wikipedia). I couldn't read the IMO calendar, which is a PDF.
- Moon (USNO): 78% lit, sets at 02:02. Sunrise is 07:10, and astronomical twilight begins around 05:40 (my estimate).
Sidereal time
GMST = 18.697374558 + 24.06570982441908 D hours. I took this formula from memory. That gives 235616.9829, which is 8.9829 h mod 24. As a check, backing off 7 h of sidereal time gives 1.96 h at 0h UT. The rough rule (about 6.7 h on 1 January, plus 3m56.6s a day) gives 1.95 h. LST = 8.9829 − 87.65/15 = 3.1395 h.
Where the radiant is at 02:00
Hour angle H = 3.1395 − 6.35 = −3.21 h = −48.16°, so it's east of the meridian and rising. sin h = sin φ sin δ + cos φ cos δ cos H = 0.17943 + 0.47861 = 0.65804, which gives h = 41.2°. cos A = (sin δ − sin h sin φ)/(cos h cos φ) = −0.30329, so A = 107.7°, a little south of due east.
The radiant crosses the meridian at 05:12 CDT, at 90 − 41.85 + 15.6 = 63.8° up. So the dark window runs from moonset at 02:02 to about 05:40. Over that time the radiant climbs from 41° to 64°.
How many you'd see
HR = ZHR × sin h ÷ r^(6.5 − LM), with ZHR 20 and population index r = 2.5. I took r from memory.
- Dark sky (limiting magnitude 6.5): about 13 an hour at 02:00 and 18 an hour at 05:12.
- City sky, guessing limiting magnitude 4: divide by 2.5^2.5 = 9.88, which gives about 1.3 an hour, rising to 1.8.
For a city, the moon setting barely matters, because the city's own light does what the moon would.
Why 66 km/s, two ways
The parent is Halley's comet. At 1 AU, with a ≈ 17.8 AU (from memory), vis-viva gives v = 29.8 √(2 − 1/17.8) = 41.55 km/s. A head-on collision would be 29.8 + 41.55 = 71.3 km/s. The observed speed is about 66, so by the law of cosines the two velocities meet at 134.7°, which is 45° off head-on. In that case the radiant should sit ψ from Earth's apex, with sin ψ = 41.55 sin 45.3° ÷ 66, giving ψ ≈ 26.6°.
The second route goes from the radiant's position. In ecliptic coordinates it's at λ = 95.1°, β = −7.75°. The sun's longitude is about 207.9° (my estimate), so the apex is at 117.9°. cos ψ = cos 7.75° × cos 22.8°, giving ψ ≈ 24.0°.
The two routes give 26.6° and 24.0°. That's a 2.6° gap from rough inputs, and I haven't located it. Taking Earth's gravity out of the 66 km/s makes it worse (29°), so the gap is somewhere else. The Eta Aquariids in May come from the same stream, met at the other node, and they'd be the next check.
These are numbers from one hand computation, not observations.