How Cosmos Daily calculates your lines.

Every astrocartography map is the visualization of a small set of spherical-astronomy equations applied to your birth moment. The math is identical across every credible tool — the differences are in the ephemeris each tool uses to compute planetary positions, and in how carefully each tool applies the corrections that bring those positions into the reference frame Western astrology actually uses. This page explains exactly how we do both.

If you want to use the tool, head to the astrocartography calculator. If you want to understand what the lines mean, the four-angles guide is the place to start. This page is for the third kind of reader: the one who wants to verify, audit, or simply understand.

The line math

An astrocartography line connects every place on Earth where a particular planet sat on one of the four chart angles — Midheaven (MC), Imum Coeli (IC), Ascendant (AC), Descendant (DC) — at the exact moment of your birth. There are exactly two kinds of line, and each has a clean closed-form solution.

MC and IC lines (vertical)

A planet is on the Midheaven at a given location when the planet's right ascension (RA) equals the local sidereal time (LST). Local sidereal time is just Greenwich Mean Sidereal Time (GMST) plus your longitude. Solving for longitude:

This produces a single longitude value, which is why MC and IC lines appear as vertical lines on a world map. Every latitude along that meridian had the planet directly overhead (or directly underfoot) at the moment of birth.

AC and DC lines (curved)

A planet is rising on the Ascendant or setting on the Descendant when its altitude in the local sky is exactly zero. Setting altitude to zero in the standard spherical-astronomy equation and solving for the hour angle H₀ gives the textbook horizon formula:

Sweeping latitude from −72° to +72° and solving the equation at each step produces the smooth curves you see on the map. The geometry is a great circle on the celestial sphere projected onto the geographic sphere — which is why AC and DC lines always appear curved.

This is the entirety of the astrocartography line math. Every credible tool computes lines this way; the formulas trace back to the same sources Jim Lewis used when he developed the technique commercially in 1976.

The ephemeris — where planetary positions come from

To run the equations above we need, for each planet, three numbers at the moment of birth: ecliptic longitude (converted to right ascension), declination, and the GMST. Cosmos Daily computes all three client-side — nothing is fetched from a server — using the following sources.

Sun and Moon — Meeus

Jean Meeus's Astronomical Algorithms is the standard reference for compact, high-accuracy planetary calculations in software. We use:

• Sun: Meeus, Chapter 25. Mean longitude, equation of center, nutation correction. Accurate to about 0.01° — roughly half an arcminute.
• Moon: Meeus, Chapter 47. Mean longitude plus periodic terms in longitude and latitude, with the standard Earth-Moon distance correction. Accurate to about 0.02–0.05°.

Meeus formulas reference the equinox of date by construction — the precession of the equinoxes is built into the mean-longitude rates. No additional correction is needed.

Mercury through Pluto — JPL Standish + precession

For the outer planets we use NASA JPL's Standish Keplerian element tables (the 1800–2050 set), implemented as a heliocentric Kepler-equation solver with the Earth-orbit subtraction that produces geocentric ecliptic coordinates. These elements are the standard "approximate positions of the planets" reference distributed by JPL.

The Standish elements are referenced to the J2000 mean ecliptic and equinox. Western astrology and astro.com use the tropical zodiac referenced to the equinox of date — the equinox of date precesses about 50.29 arcseconds per year due to the slow wobble of Earth's rotational axis. To bring J2000-frame positions into the equinox-of-date frame we apply the standard precession-in-longitude correction from Lieske 1977:

This correction is required for any astrocartography tool that uses J2000-frame ephemerides — without it, every outer planet's lines drift by roughly 0.014° per year from J2000, which is about one mile per year. Cosmos Daily applies the correction. The tropical longitudes you see in your chart and the line positions on your map are both in the equinox-of-date frame, matching astro.com.

Sidereal time — Meeus IAU formula

Greenwich Mean Sidereal Time is computed via the elapsed-time-corrected IAU formula in Meeus Chapter 12. This is the same formula used by the Swiss Ephemeris. Accuracy is sub-millisecond across the supported date range, which corresponds to sub-arcsecond positional error on the sky.

Cross-validation against the Swiss Ephemeris

The Swiss Ephemeris is the reference ephemeris that powers astro.com and the majority of professional astrology software. It draws from NASA JPL's high-precision DE431 ephemeris and is the gold standard for planetary positions in this domain. We test every release of our line code against it.

The table below shows the worst-case line offset on Cosmos Daily relative to the Swiss Ephemeris for each planet, across five birth charts spanning 1879 to 2024 — totaling 150 individual line measurements (10 planets × 3 line types × 5 charts). Errors are expressed in degrees of longitude and in equivalent miles on the ground at the equator.

Planet	Worst-case Δ (°)	Worst-case (miles)	Source of residual
Sun	0.007	0.5	Meeus Ch.25 truncation
Moon	0.016	1.1	Meeus Ch.47 truncation
Mercury	0.013	0.9	Standish element drift
Venus	0.013	0.9	Standish element drift
Mars	0.021	1.4	Standish element drift
Jupiter	0.091	6.3	Standish element drift
Saturn	0.127	8.8	Standish element drift
Uranus	0.020	1.4	Standish element drift
Neptune	0.015	1.0	Standish element drift
Pluto	0.017	1.2	Standish element drift
Median across all 150 measurements	0.010	0.7	—

The headline number: median error of 0.01° (about 0.7 miles), worst case 0.13° (about 8.8 miles). The largest residuals are on Jupiter and Saturn, where the Standish element approximation contributes a few miles of drift on charts furthest from J2000. Every other planet, including Sun and Moon, sits inside a 1.5-mile envelope.

For context, Jim Lewis's original astrocartography orb of influence was 700 miles; modern practitioners use an orb of 300–500 miles for primary effect and treat anything inside 70 miles of a line as a direct hit. Our residuals are two orders of magnitude inside that 70-mile direct-hit zone — which means the line positions on your map are visually identical to the Swiss Ephemeris at any normal map zoom.

Why your lines might look different from another tool

If you overlay your Cosmos Daily map against another astrocartography tool and the lines look meaningfully different, three things are almost always the cause — in order of frequency.

1. Birth time precision

Astrocartography is more sensitive to birth time than any other astrological technique. MC and IC lines shift by approximately one degree of longitude every four minutes of birth-time difference, which is about 70 miles of east-west movement on the ground. If one tool defaults to "12:00 noon" when the time field is left blank and another defaults to "00:00", the lines will look like completely different maps. Always verify both tools have identical birth time and timezone entered before drawing any conclusions about the math.

2. Extra lines versus core lines

Some astrocartography tools draw additional features that resemble Lewis lines but were not part of the original system:

• Parans: latitude bands where two planets are simultaneously on different angles. Drawn as horizontal lines.
• Arabic Lots / Parts: derived points (Lot of Fortune, Lot of Spirit, etc.) sometimes plotted as additional lines.
• Asteroid lines: Chiron, Ceres, Juno, and other minor bodies. Some tools include them by default.
• Outer-planet aspects: lines marking conjunctions or oppositions to specific natal points.

Cosmos Daily draws the canonical ten planets across the four chart angles — Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto, on MC / IC / AC / DC — and nothing else. This is the original Lewis system. If another tool is drawing parans or asteroid lines and you're comparing them to our Lewis lines, you're comparing different sets of objects, not different math.

3. Tropical versus sidereal zodiac

Cosmos Daily and astro.com both default to the tropical zodiac — longitudes referenced to the equinox of date. Some tools allow the user to switch to the sidereal zodiac, which references longitudes to the fixed stars. The two systems differ by approximately 24 degrees at present (the precession-accumulated drift since the systems coincided, around AD 285). If another tool is in sidereal mode while ours is in tropical, every line will appear shifted by about 24 degrees of longitude.

If after checking these three the lines still disagree by more than a few miles, our methodology is to side with the Swiss Ephemeris. That is the reference ephemeris we cross-validate against, and it is what powers astro.com.

References

• Meeus, Jean. Astronomical Algorithms, 2nd ed. Willmann-Bell, 1998. (Chapters 12, 25, 47.)
• Standish, E.M. "Keplerian Elements for Approximate Positions of the Major Planets." NASA JPL Solar System Dynamics group, 2000–2050 element set.
• Lieske, J.H., et al. "Expressions for the Precession Quantities Based upon the IAU (1976) System of Astronomical Constants." Astronomy & Astrophysics, 58 (1977): 1–16.
• Lewis, Jim. The Psychology of Astro*Carto*Graphy. Penguin, 1989.
• Swiss Ephemeris, Astrodienst AG. astro.com/swisseph — the reference ephemeris this page cross-validates against.