Raising the ascendant by hand, the gist

Raising the ascendant by hand

The rising sign on a chart is the answer to one sum, and this essay does that sum for a real place and a real minute, in the open, then checks it twice.

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

Finding the rising degree takes one idea and nine lines of arithmetic. The idea is that a point is on your horizon when it sits exactly ninety degrees away from straight overhead. Everything else is multiplication.

The rising degree, the lagna, is the point of the sun's yearly track that is climbing over the eastern horizon at a given moment, and the whole of finding it rests on one sentence: a point is on your horizon when it sits ninety degrees from straight overhead. So start with the horizon.

Stand on flat ground and the sky seems to end in a line. Astronomy makes that exact. A plumb line points down; straight up is the zenith. Take every direction at a right angle to the plumb line. Together they make a flat plane through you, and where it meets the sky it draws a circle: the horizon. As the earth turns, the sky is carried up one side and down the other.

The sun travels the same track through the sky every year, and the twelve signs are marked along it. That track is the ecliptic.

Two circles of that kind on a ball always cross in exactly two places. So the ecliptic meets the horizon at two points, one going up and one going down. The one going up is the rising degree, the lagna.

Finding it needs three numbers: which way the sky was facing, how far north the place is, and how much the earth's axis is tilted. The essay takes a hypothetical birth at 9:12 in the morning on 22 July 2009 at Ujjain, and writes the calculation out in words before touching a number.

Then the sum: five values from a trigonometry table, two multiplications, one addition, one division, and out comes an angle. There are two possible answers, half a circle apart, and the essay shows which is rising and which is setting. The answer is 162° 52′ 07″, which is 12° 52′ of Virgo counted from the spring equinox.

The old Indian method, which uses the rising times of the signs, gives the same figure to the last digit. The sky gives a second check: the sun stood 43° 22′ above the horizon that morning, and 43° 23′ along the ecliptic from the rising point.

Last, what can go wrong. A latitude wrong by one arcminute moves the answer eight arcseconds. A clock wrong by one minute moves it nearly fourteen arcminutes. It then subtracts the offset Indian tradition uses and arrives at 18° 52′ of Leo, which is where the computation stops, because what that degree is supposed to mean is not in the arithmetic. The last thing the essay does is hand the sum back: run it again for your own place, and do the check that proves the answer.

Words decoded

horizon: the circle where the sky meets the flat plane through you at right angles to a plumb line
zenith: the point straight overhead
ecliptic: the track the sun follows through the sky across a year; the signs are marked along it
lagna (लग्न), or ascendant: the point of that track coming up over the eastern horizon at a given moment
latitude: how far north or south of the equator a place is
obliquity: the angle between the sun's track and the equator, about 23 degrees 26 minutes; it is the tilt of the earth's axis seen another way
sidereal time: a clock reading that tells you which part of the sky is facing you
degree, arcminute, arcsecond: a degree is a 360th of a circle, an arcminute a 60th of a degree, an arcsecond a 60th of that
tangent, arctangent: a ratio worked out from an angle, and the reverse operation that gets the angle back from the ratio
ascensional difference: the correction that says how much earlier or later a point rises because it is north or south of the equator
ayanamsha (अयनांश): the gap between counting the signs from the spring equinox and counting them from the stars, now about 24 degrees

Why anyone should careThe rising sign sits at the top of every chart anybody has ever been handed, and almost nobody is shown where it comes from. It comes from a clock reading, a latitude, an angle of tilt, and less arithmetic than a school exam question. Seeing the whole of it does two things. It removes the mystery, and it shows you exactly which input is fragile: not the constants, which are known to fractions of an arcsecond, but the minute somebody wrote down in a register.

Read it properly, 8 min Raising the ascendant by hand