Lesson 1 answers

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namaste guruji,

 

Here are my answer attempts for Lesson 1; thank you for reviewing them.

 

namaste,

Beau

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SJVC LESSON 1 -- Astronomical Definitions in Jyotish

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Shishya: Beau Binder

2001-NOV-12

 

Assignment #1 -- Explain the changing of the seasons and its

connection with the astronomical factors mentioned in this lesson.

 

The Earth's center (CE), the Sun's center (CS), and the orbit of

the Earth all reside in a plane called the Ecliptic Plane (EP).

Define an axis (T) passing through CE which is perpendicular to

EP. The Earth's axis of rotation (A) is canted away from T by a

constant angle D; D is approximately 23 rekha 26 kala of arc, at

present. This canting of A away from T occurs about another axis

(Q), which also passes through the point CE and also resides in the

plane EP; thus, Q is perpendicular to the plane (ATP) containing

both A and T.

 

Q's orientation changes very slowly over the course of a year,

minimally rotating about T, so A's orientation is also essentially

constant throughout the year. When Q is aligned with the line (L)

connecting CE and CS, which happens twice a year, the plane ATP is

perpendicular to L. This means that each part of the globe has

equal amounts of night (equi-nox = equal-night) and day since A

resides in plane ATP.

 

This shows Q defines the direction of the vernal and autumnal

equinoxes, the beginning and midpoint of the sayana zodiac.

 

When Q is perpendicular to L, i.e., the Earth is halfway in its

orbit between the two equinoctial points, either the north pole is

facing maximally toward or away from the Sun. This causes the

terminator (the circle defining the border between light and dark

on the Earth) to tilt away from the A by its maximum extent, the

angle D. This results in the terminator either intersecting or

missing a circle of constant akshamsa as far from A as possible;

therefore, circles of constant akshamsa in one hemisphere either

have most or all of their arc in sunlight, while those in the

opposite hemisphere have most or all of their arc in darkness.

 

Take the moment of the year, NS, when the north pole is maximally

toward the Sun. This means the northern akshamsas have their

longest day of the year because the terminator intersects, or

excludes, the northern circles of constant akshamsa as far away from

A as it can get; conversely, the southern latitudes are

experiencing the shortest day of the year since most, or all, of

each arc of constant akshamsa is in shadow.

 

1/2 a year later, the situation is reversed when the south pole

is facing maximally toward the Sun. Call this moment SS.

 

Note that for a region, G, on the Earth's surface, the akshamsa is

defined by the angle between: 1) a ray emanating from CE and

passing through the region in question and, 2) a ray emanating from

CE and passing through the vishvarekha at the same rekhamsa as G.

This implies that the angle of a line normal to G, with respect to

the vishvarekha (and, hence, the co-planar nadivritta) is equal to the

akshamsa. Also, note that the angle of incidence, AI, for an incoming

ray on G is defined by the angle between the ray and the G's

normal. Thus, the AI = 0 when G is directly facing the incoming

ray, and AI = 90 rekha when the ray is parallel (tangent) to G.

 

Therefore, at the moment NS, the average AI of the Sun's light

on the Earth's surface is at its minimum for akshamsas in the

northern hemisphere and at its maximum for akshamsas in the southern

hemisphere, while the converse holds true at the moment SS.

 

Now, let's focus on a small localized area of the Earth's surface.

The amount of the Sun's light intercepted by this area during a day

is a function of: 1) how directly it faces the Sun on average

during that day, and 2) how long it is exposed to the Sun during

that day. The amount of light intercepted determines how much

energy that area receives during that day and, hence, strongly

affects the average local temperature. Therefore, the average

temperature and length of day for the northern hemisphere vary from

their maximum values at NS (northern summer) to their minimum

values at SS (southern summer), the reverse holding true for the

southern hemisphere. As these two quantities, average temperature

and length of day, define a season, the above discussion shows the

reason for the change of seasons.

 

 

Relating the above discussion with the astronomical factors

mentioned in the lesson, the variation of the Sun's angle of

incidence with the surface of the Earth due to:

 

1) the rotation of the Earth about the Sun being constrained to

a plane, EP

2) the tilt of Earth's axis of rotation, A, and its effective

invariance in orientation relative to EP during a year

 

shows the reason for variation in the Sun's kranti. This is

because the nadivritta and vishvarekha are co-planar, so variation

in the average angle of incidence of the Sun with the surface of

the Earth, and hence the vishvarekha, bring about a variation of

the Sun's angular distance (kranti) from the nadivritta.

 

The path of motion of the Sun against the stars viewed from the

Earth, the Ravimarga, also occurs because of the rotation of the Earth

about the Sun being constrained to a plane and the tilt of the

Earth's axis.

 

The Ayanamsha occurs due to the long-term cycle of rotation of

the Earth's axis A about the aforementioned axis T, perpendicular

to EP. As A rotates, the line Q defining the directions of the

equinoxes also shifts in the Ecliptic Plane, causing the shift of

the Ravimarga against the background of nakshatras. This creates

the difference between the constant starting point of the Nirayana

zodiac and the equinoctial starting point of the Sayana zodiac.

 

 

Assignment #2 -- There are some days of the year when the Sun either

doesn't rise or set above certain parts of the globe. Please explain

this phenomenon.

 

Referring to the discussion above, mention was made of the

terminator, the circle defining the border between day and night on

the Earth's surface. During certain parts of the year, such as

those close to northern summer, the south pole is tilted so far

away from the Sun that akshamsas greater than (90 - D) degrees south,

where D is the angle of tilt of the Earth's axis, are always on

the night side of the terminator. At the same time of year, those akshamsas

greater than (90 - D) degrees north are in perpetual daylight,

i.e., the sun does not set, since no point on them crosses the

terminator into night.

 

Another way of looking at it would be that at some times during the

year the difference between the absolute value of the Sun's kranti,

|K|, and the local akshamsa is greater than 90 rekhas, causing the

Sun to always be below the local horizon.

 

For example, when the Sun's kranti is at 15 rekha of arc south,

then akshamsas north of 75 rekha north could not see the Sun. This

is comes from the fact that the lowest angle visible for these

akshamsas, measured from the vertical of the local surface, would

be greater than (75 - 90) rekhas north (i.e., less than (90 -75)

rekhas south).

 

Likewise, at the same time of year, for akshamsas south of 75

rekha south, i.e., those under 15 rekha of arc from the south

pole, the angle between the vertical at the local surface

and the Sun never goes above 90 rekha. This keeps the Sun visible

at all times of the day.

 

 

Assignment #3 -- Parashara mentions two classes of heavenly bodies:

the moving and the non-moving ones. Please explain what will be the

difference between their roles in the astrological interpretation.

 

A moving body has variance associated with it, whereas a

non-moving body has constancy associated with it.

 

I am inclined to feel that, by analogy, the influences

associated with a non-moving body would maintain themselves, be

constant. This would hint that these influences are somehow

fundamental and foundational -- basic 'building blocks' that other

influences would be combinations of. By further implication, the

influences would then be more closely related to underlying

Reality, the absolute Truth. These influences would then give

indications about the core of things.

 

By contrast, moving bodies' influences, and hence indications,

would vary according to speed and position. Being inconstant, they

would be related to Maya and give indications about more subjective

'realities'; the qualities of individuals; the results of

differentiated, restricted awareness.

 

 

Assignment #4 -- If you are able to construct your own chart, please

do it and explain as many astronomical principles from it as you can

(terrestrial latitude/longitude, season, Sun's cycle, Sunrise/Sunset

etc.). Also try to determine which planets are above and under the

horizon in your chart. In which Ayana the Sun is?

 

I used Jagannath Hora Lite 3.0 (thank you, guru narasimhaji) to

obtain the positions of the planets and lagna, and the ayanamsha for

this answer.

 

Birthtime: 23:26:30 (PST / -8 GMT) 1963-DEC-11

Birthplace:

akshamsa = 45 N 31 = 45 rekha 31 kala north of vishvarekha

rekhamsa = 122 W 41 = 122 rekha 41 kala west of prime meridian

 

Ayanamsha = 23 rekha 20 kala 56 vikala from origin of the

Nirayana zodiac, according to Lahiri.

 

Ascdt 20 Le 57

Sun 26 Sc 12

Moon 15 Li 14

Mars 11 Sg 55

Mercury 15 Sg 15

Jupiter 16 Pi 16

Venus 22 Sg 24

Saturn 25 Cp 16

Rahu 19 Ge 03

Ketu 19 Sg 03

 

The season was autumn since the birthtime falls between the autumn

equinox (Sept 21) and the winter solstice (Dec 21). The Sun was

approaching close to winter solstice, the Tropic of Capricorn, and

so was in Dakshinayana.

 

With the Ascdt marking the 1st house and angular position of the

local horizon w.r.t. the bhacakra, planets from 20 Aq 57 to 20 Le

57 (going zodiac-wise, i.e. forward through the zodiac) are on or

above the horizon. As Pisces and Gemini are the only rasis above

the horizon containing planets, Jupiter and Rahu are above the

horizon, while the rest are below. Since the Sun was south of the

nadivritta at that time of year, the larger portion of the ravimarga

'seen' at night is north of the nadivritta.

 

OM NAMO GURAVE