Ascendant

The ascendant or rising sign is the astrological sign on the eastern horizon when the person was born. It signifies a person's physical appearance, and awakening consciousness.
Because the ascendant is specific to a particular time and place, to astrologers it signifies the individual environment and conditioning that a person receives during their upbringing, and also the circumstances of their childhood. For this reason, astrologers consider that the ascendant is also concerned with how a person has learned to present themself to the world, especially in public and in impersonal situations.

History

Although Babylonian astronomers observed the actual rising times of the signs, there is no specific mention of the ascendant in the texts that have survived on clay tablets. By the 3rd century BCE, Egyptians looked at the rising of specific asterisms to identify the ascending sign and get an approximate time of night, and that is reflected in the name subsequently given by the Greeks to the ascendant: horoskopos, or "hour marker." ὡρόσκοπος in the sense of "ascendant," and ὡροσκοπία, "observation of the ascendant," was used in the Greek manuscript of Ptolemy's Tetrabiblos. First documented mention of an ascendent contained in the works by Balbilus.

Vedic astrology

In Vedic astrology, the ascendant is referred to as the Lagna. It is the sign rising on the eastern horizon at the time of birth and serves as the starting point of the horoscope. The entire chart, including house placements and planetary influences, is built around the Lagna. It reflects the native's physical body, general health, and how they interact with the outer world.
The ruling planet of the Lagna sign is called the Lagnesha or ascendant lord. It plays a central role in interpreting a person's nature, life direction, and important events. A strong Lagna and Lagnesha are said to contribute to vitality, stability, and personal strength. In predictive astrology, the placement of the Lagna lord, its aspects, and dignity are closely analyzed.

Calculation

The ascendant, from an astrological point of view, is the value of the ecliptical geocentric longitude which is easterly on the horizon. This intersection of the horizon with the ecliptic can be calculated from:
where is the local sidereal time in degrees, is the inclination of Earth's equatorial plane to the ecliptic. For values referred to the standard equinox J2000.0 use = 23.4392911°; for J1950.0 use = 23.4457889°. is the observer's terrestrial latitude. The ascendant is then found in the correct quadrant by using the two rules.
If 'then
Ascendant = Ascendant + 180
else
Ascendant = Ascendant + 360
By definition of ascendant, we have to take the point easterly by using a final rule:
if then
Ascendant = Ascendant + 180
else'
Ascendant = Ascendant - 180
Otherwise a direct result in the correct quadrant can be determined if calculator or programming software has the atan2 math function and then using the last rule.
For latitudes north of the Arctic Circle, the ascendant function has two discontinuity points, occurring at instants where the horizon and the ecliptic planes do not intersect. Between those instants, the ascendant's longitude actually decreases.

Long and short ascension

Because the Earth's axis is tilted relative to the ecliptic, the twelve signs do not take the same amount of time to cross the eastern horizon. At the equator, there is very little difference, but as one moves from the equator, larger and larger differences emerge.
In the northern hemisphere, the signs of Capricorn, Aquarius, Pisces, Aries, Taurus and Gemini take much less time than the theoretical two hours to cross the eastern horizon, whilst the signs of Cancer, Leo, Virgo, Libra, Scorpio and Sagittarius take much longer than two hours to do so. For example, at the latitude of Paris, France:

Pisces and Aries take only one hour to cross the eastern horizon.
Aquarius and Taurus have an ascension of one hour and fifteen minutes.
Capricorn and Gemini have an ascension of one hour and fifty minutes.
Cancer and Sagittarius have an ascension of two hours and thirty minutes.
Leo and Scorpio have an ascension of two hours and forty minutes.
Virgo and Libra have an ascension of two hours and forty-five minutes.

At higher latitudes, these differences become even more marked. At the latitude of St. Petersburg, Russia:

Pisces and Aries have an ascension of thirty-five minutes.
Aquarius and Taurus have an ascension of forty-five minutes.
Capricorn and Gemini have an ascension of one hour and twenty-five minutes.
Cancer and Sagittarius have an ascension of two hours and forty minutes.
Leo and Scorpio have an ascension of three hours and fifteen minutes.
Virgo and Libra have an ascension of three hours and twenty minutes.

Astrologers consider the differences between the rate at which the signs ascend to be of importance. In many house systems, houses can become very large when they cover Aquarius, Pisces, Aries and Taurus because these signs are seen to be much smaller from the perspective of a northern hemisphere observer.
Some astrologers, such as Richard Nolle, consider the preponderance of ascendants in signs from Cancer through Sagittarius to be symbolic of the relationship-oriented character inherent in the northern hemisphere and ascendants in the signs from Capricorn through Gemini to be symbolic of the more individual-oriented character in the southern hemisphere.
In the southern hemisphere, long and short ascension are reversed. For instance, at the latitude of Concepción, Chile:

Pisces and Aries ascend in two hours and thirty minutes.
Aquarius and Taurus ascend in two hours and twenty-five minutes.
Capricorn and Gemini ascend in two hours and fifteen minutes.
Sagittarius and Cancer ascend in two hours.
Scorpio and Leo ascend in one hour and thirty-five minutes.
Libra and Virgo ascend in one hour and fifteen minutes.
Effects of polar astrology

At the Arctic and Antarctic circles, at roughly 66.5° north and south latitude respectively, a degree of the ecliptic becomes circumpolar. If the sun, for example, occupies that degree, it will neither rise nor set, but will lie upon the horizon for twenty-four hours. As we move into higher latitudes, more and more degrees of the ecliptic will neither rise nor set until, at the north pole, none of them will rise or set, and therefore none of them can become the ascendant, although no human being could be born exactly at the north pole, since it is a dimensionless point. Therefore, the omission of extreme latitudes from most house tables due to the added complexity of calculating the ascendant implies that there is no ascendant at these latitudes. This is of course untrue, yet there is a limitation on the degrees that can ascend at extreme latitudes and a further restriction on degrees that can form house cusps in time-based house systems. The simpler and earlier ecliptic-based house systems can form house cusps at extreme latitudes based on the available ascendant and midheaven degrees.

Effects of the ascendant

There are a couple of factors that influence how strong or weak a force the ascendant may be in the chart.

It is generally believed that the closer to the beginning of the sign the ascendant falls, the stronger it will be. This is because most of the first house will fall into that sign. If the ascendant falls late in a sign, most of the first house will fall into the following sign and thus weaken the effect of the ascendant's power.
The ascendant is thought to be stronger in influence when the sun is in a weak position in the chart. For example, it is traditionally believed that the sun is in a weaker position when it is placed at the bottom of the chart, near the imum coeli or IC. This is because the sun was literally on the other side of the earth when the subject was born, hidden from view.
According to some, the sun may also be weaker in influence if it is unaspected; in other words, if it forms no major aspects to the other planets. According to other astrological observations, unaspected suns and planets show greater than usual effect and are more free.
The sun in a sign that is intercepted, meaning it does not have a house cusp, may also be weaker and put more emphasis on the ascendant and house cusp of the solar house in such a chart.

Another factor concerning the effect of the ascendant is the theory that people become more like their sun sign after around 29 years old, as they grow older and more confident, as the sun embodies essential ego energy and self-esteem, and thus perhaps have less of a need to present a public face to others. It is also theorised that when the progressed ascendant moves into the following sign, it weakens the influence of the natal ascendant.

Planets and the ascendant

Planets have added importance in the birth chart due to their relationship to the ascendant. The planet that rules the astrological sign of the ascendant is called the chart ruler and is said to be of particular importance. So for example, if the ascendant sign is Gemini, Mercury will be the chart ruler, and so "set the tone" for the chart in many ways. In addition, the planet nearest the ascendant, especially located in the first house, is usually called the rising planet and has a particular significance in the chart. However, if a planet in the twelfth house is very close to the ascendant, then it can be interpreted as the rising planet instead. If a planet is actually in conjunction with the ascendant, it then becomes vitally important in its effect on the personality, to the extent of being as important as the sun. Finally, any planets in the first house will always have an added emphasis.