The tilt that sets the seasons, the gist

The tilt that sets the seasons

The earth's axis leans by 23 degrees 26 minutes and 9 seconds of arc, that lean is slowly shrinking, and this essay takes one birth chart and works out exactly what would change if the lean were different.

This is the short way in. The essay has the working, the sources and the sky.

The lean is one of only three numbers behind the rising sign printed at the top of every chart. Give it the value the old Sanskrit textbooks use, half a degree too big, and for one worked birth the rising degree moves by 6 seconds of arc.

The earth spins about an axis, and travels round the sun in a flat path. The two are not lined up. The angle between them is called the obliquity, and this year it is 23 degrees, 26 minutes and 9 seconds of arc. This lean is why a year has seasons in it.

The lean is shrinking, by about 47 seconds of arc every hundred years. Two slow movements get confused here. The first is precession: the sun and moon pull on the earth's bulging middle, and the axis swings round in a wide cone, one turn in about 26,000 years. That changes which way the axis points, not how far it leans. The shrinking has a different cause. The other planets pull on the earth's path round the sun, and that path slowly tips. The angle changes because the floor is moving, not the pole.

It does not shrink forever. Over long spans the lean swings between about 22.1 and 24.5 degrees, taking roughly 41,000 years to go and come back. The last widest lean was around 8700 BCE and the next narrowest falls near the year 11,800. The swing stays small because of the moon.

The lean is used in four places when a chart is built: turning star-table positions into chart coordinates, finding the point directly overhead, finding the degree rising in the east, and working out how far the sun gets from the equator.

Then the test. The essay takes a birth it already computed for Ujjain and runs the sum again with 24 degrees, the value Indian astronomy used for centuries. The rising degree moves 6 seconds of arc. Two parts of the formula shift in opposite directions and almost cancel, and twice in every turn of the sky they cancel exactly. At other hours the same change is worth up to 22 minutes of arc, which is what a minute and a half of doubt about the birth time would cost.

Words decoded

obliquity: the angle between the earth's equator and the flat path it travels round the sun; about 23 and a half degrees
ecliptic: that flat path seen from here as a line across the sky, the line the sun appears to walk through the year
degree, minute of arc, second of arc: a degree is a 360th of a circle, a minute of arc a 60th of a degree, a second of arc a 60th of that
precession: the slow cone-shaped swing of the earth's axis, one turn in about 26,000 years
lagna (लग्न), or ascendant, or rising degree: the point of the ecliptic climbing over the eastern horizon at a given moment
midheaven: the point of the ecliptic directly overhead at that moment
declination: how far north or south of the equator a body stands
paramakranti (परमक्रान्ति): the Sanskrit name for the same angle, meaning the greatest declination the sun reaches in a year
sidereal time: a clock reading that says which part of the sky is facing you
ephemeris: a printed or computed table of where the sun, moon and planets are, day by day
Surya Siddhanta: one of the standard old Sanskrit textbooks of astronomy
ecliptic latitude: how far a body sits above or below the ecliptic; a chart prints longitude along that line but not this

Why anyone should carePeople are told that a chart is delicate, that everything in it hangs on getting every input exactly right. Here is one input where that is not true, and the essay shows the arithmetic instead of asserting it. Half a degree of error in the tilt leaves nine of the ten numbers on a chart untouched and moves the tenth by less than the birth time already does. Knowing which inputs are fragile, and which are not, is what separates checking a chart from worrying about one.

Read it properly, 7 min The tilt that sets the seasons