ASC is a shortened term for the word ascendant, or rising degree of the zodiac circle. MC stands for Мedium Сoeli, the midheaven - the culminating degree of the zodiac circle. These two points form the horoscope’s so-called angles . In this article, we will derive formulas for calculating the rising and culminating degrees of the zodiac.

We will start from the assumption that all we know is the local geographic coordinates (more specifically, latitude) and the local sidereal time.

In the previous article, we introduced the concept of sidereal time. The sidereal day begins at 00:00, when 0° Aries culminates, and 0° Cancer rises. Therefore, by knowing the current sidereal hour, one can predict the exact degree of the ecliptic that rises and culminates.

ASC Equation

Let’s look at the figure below:

background Meridian Half-meridian Equator Zodiac RA E S equator outer circle line OA 90° - φ ε 1 2

ASC

We have two right spherical triangles:

  • First with the sides , and angle between them
  • Second with the sides , and angle

Here we use the following notation:

Let’s use our handy equations for spherical triangles.

From (3) we have

From (6) we have

Let’s divide by and expand the sine of two angles by ()

We will rewrite in (1.c) in form:

By substituting in the last equation, we have the formula for the ASC:

As we discussed earlier, the . It means that:

MC Equation

Let’s look at the figure below:

background Meridian Half-meridian Equator Zodiac meridian outer circle line

MC

We have the right triangle with sides , , and angle between them.

From the () it follows that:

It gives us the equation for the MC:

Bottom Line

We have derived equations for ASC and MC for a given sidereal time and a given geographical latitude