Astrocartography Map: Planetary Lines

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how astrocartography is calculated

How astrocartography is calculated, step by step

Everything the map shows comes from three numbers per body and Greenwich sidereal time. This page walks through the formulas in the order the tool uses them, with values you can check.

The formulas, in calculation order

First the position of each body as seen from the center of the Earth is obtained: the astronomy-engine library returns the geocentric vector, which the tool rotates to the equator and equinox of date and converts to right ascension (RA) and declination (Dec). Then the apparent Greenwich sidereal time (GST) is computed. The MC sits at longitude RA minus GST, because that is the meridian where local sidereal time equals the body RA. Example: on 1 January 2000 at 12:00 UTC the Sun has an RA of 281.28 degrees and a GST of 280.46 degrees, and it culminates about 0.8 degrees east of Greenwich, with a declination of 23.03 degrees south.
For the curves, the body is on the horizon when its hour angle H satisfies cos H = minus tan(latitude) times tan(declination). The half-arc H0 is the arccosine of that value, between 0 and 180 degrees. On the ASC curve the body is rising, with H equal to minus H0, and the longitude is the MC longitude minus H0. On the DSC, with H equal to plus H0, the longitude is the MC longitude plus H0. Instead of sweeping latitude, the tool sweeps H0 from 0 to 180 and gets the latitude from tan(latitude) = minus cos H0 divided by tan(Dec), which gives a smooth curve with no jumps. For the Sun at the solstice, at 60 degrees of latitude, H0 is 138.7 degrees.
The arccosine only exists when the value is between minus 1 and 1, which is the same as a latitude of absolute value at most 90 degrees minus the absolute value of the declination. With the Sun at 23.44 degrees at the June 2024 solstice, the limit is 66.56 degrees, the Arctic Circle; farther north the Sun does not set and the curve simply ends. The two curves of a body meet at its MC and IC, at the extremes. The tool uses the geometric horizon, without refraction, and measures distances in kilometers with the haversine formula and a radius of 6,371.0088 km. We checked the result against the altitude calculation built into astronomy-engine: on every line the altitude of the body comes out as zero.

Values to check

Sun MC on 1 Jan 2000, 12:00 UTC

Input: RA 281,28° menos GST 280,46°
Expected output: 0,82° L

Matches the subsolar point from the NOAA formula within 0.2 degrees.

Sun declination at that instant

Input: Sol, 1/1/2000
Expected output: 23,03° S

Close to the yearly maximum of 23.44 degrees, which happens at the solstice.

Sun half-arc H0 at the solstice at 60 degrees N

Input: cos H0 = menos tan 60° x tan 23,44°
Expected output: 138,7°

About 9.2 hours between rising and noon, consistent with the long June day.

Polar limit of the Sun curves on 20 Jun 2024

Input: 90° menos 23,44°
Expected output: 66,56°

This is the latitude of the Arctic Circle.

Full tool FAQ

What is astrocartography?

It is an astrological technique that shows on a world map where each body of your natal chart stood at an angle (rising, setting, overhead or at the lowest point) at the moment you were born. It was developed by astrologers between about 1930 and 1960 and popularized by Jim Lewis in the 1970s and 1980s. Each body gives four lines, so the Sun to Pluto plus the North Node make 44 lines.

Does astrocartography work? Is it science?

Do I need my birth time?

What is the difference between MC, IC, ASC and DSC?

Why do the ASC and DSC lines disappear near the poles?

How are the lines calculated?

Which bodies are left out?

Does a Mars, Saturn or Pluto line mean I should avoid the place?

What are crossings (parans)?

Is my data sent to a server? Can I export the map?

Frequently asked questions

Which library computes the body positions?

astronomy-engine, an open-source astronomy library, running in your browser. For the North Node we use the mean lunar node formula, and the tool does not depend on any server or network call.

Why use declination and not just ecliptic longitude?

Because the Moon and planets do not sit exactly on the ecliptic. Treating the ecliptic longitude as if the celestial latitude were zero shifts a planet line by a few degrees, and the Moon can sit up to about 5 degrees off the plane. Real RA and Dec solve that.

Do the lines include refraction or the size of the body disc?

No. They use the geometric horizon, with the center of the body at zero degrees of altitude, which is the astrocartography convention. An almanac sunrise accounts for the upper limb and refraction and differs by a few minutes, which in astrocartography is lost against the usual birth time errors.

Next steps

The formulas, in calculation order

First the position of each body as seen from the center of the Earth is obtained: the astronomy-engine library returns the geocentric vector, which the tool rotates to the equator and equinox of date and converts to right ascension (RA) and declination (Dec). Then the apparent Greenwich sidereal time (GST) is computed. The MC sits at longitude RA minus GST, because that is the meridian where local sidereal time equals the body RA. Example: on 1 January 2000 at 12:00 UTC the Sun has an RA of 281.28 degrees and a GST of 280.46 degrees, and it culminates about 0.8 degrees east of Greenwich, with a declination of 23.03 degrees south.

For the curves, the body is on the horizon when its hour angle H satisfies cos H = minus tan(latitude) times tan(declination). The half-arc H0 is the arccosine of that value, between 0 and 180 degrees. On the ASC curve the body is rising, with H equal to minus H0, and the longitude is the MC longitude minus H0. On the DSC, with H equal to plus H0, the longitude is the MC longitude plus H0. Instead of sweeping latitude, the tool sweeps H0 from 0 to 180 and gets the latitude from tan(latitude) = minus cos H0 divided by tan(Dec), which gives a smooth curve with no jumps. For the Sun at the solstice, at 60 degrees of latitude, H0 is 138.7 degrees.

The arccosine only exists when the value is between minus 1 and 1, which is the same as a latitude of absolute value at most 90 degrees minus the absolute value of the declination. With the Sun at 23.44 degrees at the June 2024 solstice, the limit is 66.56 degrees, the Arctic Circle; farther north the Sun does not set and the curve simply ends. The two curves of a body meet at its MC and IC, at the extremes. The tool uses the geometric horizon, without refraction, and measures distances in kilometers with the haversine formula and a radius of 6,371.0088 km. We checked the result against the altitude calculation built into astronomy-engine: on every line the altitude of the body comes out as zero.

Values to check

Sun MC on 1 Jan 2000, 12:00 UTC

Input: RA 281,28° menos GST 280,46°
Expected output: 0,82° L

Matches the subsolar point from the NOAA formula within 0.2 degrees.

Sun declination at that instant

Input: Sol, 1/1/2000
Expected output: 23,03° S

Close to the yearly maximum of 23.44 degrees, which happens at the solstice.

Sun half-arc H0 at the solstice at 60 degrees N

Input: cos H0 = menos tan 60° x tan 23,44°
Expected output: 138,7°

About 9.2 hours between rising and noon, consistent with the long June day.

Polar limit of the Sun curves on 20 Jun 2024

Input: 90° menos 23,44°
Expected output: 66,56°

This is the latitude of the Arctic Circle.

Full tool FAQ

What is astrocartography?

Does astrocartography work? Is it science?

Do I need my birth time?

What is the difference between MC, IC, ASC and DSC?

Why do the ASC and DSC lines disappear near the poles?

How are the lines calculated?

Which bodies are left out?

Does a Mars, Saturn or Pluto line mean I should avoid the place?

What are crossings (parans)?

Is my data sent to a server? Can I export the map?

Frequently asked questions

Which library computes the body positions?

astronomy-engine, an open-source astronomy library, running in your browser. For the North Node we use the mean lunar node formula, and the tool does not depend on any server or network call.