Reproducible dossier: how date, place and time change the altitude of a direction in the sky

If I always look in the same direction of the sky, at exactly 21:00 local time, how much does its altitude above the horizon change from Rome to London to New York, and from December to February?

The reference direction is defined by two fixed equatorial coordinates: right ascension 6h 00m and declination 0°. It is not a star and does not correspond to a catalogue object: it is a geometric reference point, chosen as a sample to isolate the effect of date, place and time. The variation depends on the coordinates of the chosen direction.

There are six combinations: three cities (Rome, London, New York) for two dates (25 December 2026 and 14 February 2027), always at 21:00 local time in each city, with the time zone in force on that date. For each combination, local time is converted to universal time, from which the local sidereal time and then the hour angle of the reference direction are derived.

The altitude above the horizon is then obtained with the standard formula sin(h) = sin(φ)·sin(δ) + cos(φ)·cos(δ)·cos(H), where φ is the latitude of the place, δ the declination of the direction and H its hour angle. The values in the table are produced by the calculation code already in use on the site, with the inputs given above: anyone who repeats the calculation with the same coordinates and the same time zones gets the same rows.

The same direction in the sky, at the same clock time, appears differently at different latitudes and in different months: this is the combined effect of the Earth's rotation, the position of the place and the passing of the year. It is why “the sky on a date” does not exist in absolute terms, only together with a where and a when: two people looking at the same instant from two cities do not have the same geometry in front of them, and the same city two months apart does not show the same scene at the same time.

It says nothing about the quality of the sky, the number of visible stars or whether one date is better than another: these depend on the weather, artificial lights, the real horizon and the eyesight of the person looking, all outside this calculation. Nor does it affect the value of a date chosen for personal reasons: that value is symbolic and does not depend on the degrees in this table.

The calculation assumes an ideal horizon: it does not take into account atmospheric refraction, the elevation of the place, hills, buildings or trees, the weather or light pollution. It does not consider the Moon or the planets, which appear neither in this calculation nor in the images of the free tool. A positive altitude only means that the direction was above the geometric horizon, not that anything would have been visible.

The figures are calculated, not measured in the field, and their precision is indicative: they serve to show an order of magnitude, not to prepare an observation. The direction used is a sample: these values cannot tell you how many stars are visible in a city or on a date, nor whether one night is better than another. This dossier is an exercise in reproducible documentation, not a validated or peer-reviewed scientific study.