The eclipses
There are two kinds of eclipses :

1. Solar eclipses.
2. Lunar eclipses.

A solar eclipse occurs when the shadow of the moon falls on the earth. This means that at the time of the eclipse the moon lies between sun and earth.This happens on a new moon day,  when the sun and the moon are conjunct and lie on the same side of the earth. SInce the orbit of the moon is tilted at an angle of 5 degrees approximately to the ecliptic , the sun-moon-earth trio does not fall on same line on every new moon day. Hence there is no eclipse on every new moon day.

Solar eclipse
A lunar eclipse occurs when the moon lies opposite to the sun with the intervening between the two. The shadow of the earth falls on the moon. This happens on the full moon day when the sun-moon-earth trio falls on the same line.Again, because of the obliquity of the moon's path to the ecliptic,this situaution does not arise every full moon day.

Lunar Eclipse
It has been pointed out that the moon's path crosses the sun's path at the ascending and the descending nodes (i.e. Rahu and ketu). The moon must,therefore, be fairly close to rahu and ketu and the sun too must be close enough to ensure that the earth ,the sun and the moon fall on the same line. ""Swallowed by rahu"  is an expression applied to the eclipsed luminary.
A solar eclipse is likely to occur if a new moon occurs within 18.5 degrees of the node (rahu or ketu) and certainly if the distance is less than 15 degrees.A lunar eclipse occurs on a full moon day, likely when the distance between the moon and the sun nodes is less than 12 degrees, and certainly when the distance is less than 9.5 degrees. A maximum of seven eclipses (4 or 5 solar;2 or 3 lunar) are possible in any given year
Tithis or lunar dates
There are thirty lunar dates or  tithis, of 12 degrees each  (12*30 = 360 degrees). A tithi is indicative of the moon's separation from the sun. It is obtained by subtracting the longitude of the sun from the longitude of the moon,and dividing the above value by twelve.The quatient plus one gives the number of the tithi operating on any particular day. Thus,

(Moon - Sun) /12
Tithi = Q+1

Phases of the moon
The tithis are counted from the 1st of the bright half or shukla paksha. The sun's conjunction with the moon coincides with the 30th tithi or the amavasya. When the moon overtakes the sun,but lies within it's 12 degrees, it is the 1st lunar date of the shukla paksha. At 180 degree separation,with the moon opposed to the sun  ,it is the 15th of the shukla paksha, called as poornima. From here onwards starts the krishna-paksha, or the darker half. The tithis here again start from 1st and goes upto the 15th or the amavasys, when the moon and the sun conjoin.A tithi that is operating at the time of sunrise, on a particular day is the tithi operating on that whole day. Tithi is extremely important in performing day to day rituals and in electional astrology.
Vriddhi or additional tithi: A tithi that extends from before sunrise on one day to after sunrise on next day is called as vriddhi tithi. such a tithi operates on successive two days.
Kshaya or omitted tithi: A tithi that begins after sunrise and ends before sunrise on next day is called as kshaya or omitted tithi. This tithi is supposed to miss operation during that lunar cycle.
There are twenty seven yogas. Each yoga measures 13.20 degrees of arc (360/27=13.20).A yoga indicates a sum of the longitudes of the moon and the sun in multiples of 13.20 deg.  Although this measure of a yoga is the same as that of a nakshatra , there is no link between the two. Add the niryana longitudes of the sun and the moon and divide by the first one (vishkumbha) onwards. The 27 yogas are listed below :
1.Vishkumbha 2. Preeti
3. Ayushman 4. Saubhagya
5. Shobhana 6.  Atiganda
7. Sukarma 8. Dhriti
9. Shool 10. Ganda
11. Vriddhi 12. Dhruva
13. Vyaghata 14. Harshana
15. Vajra 16. Siddhi
17. Vyatipata 18. Variyana
19. Parigha 20. Shiva
21.Siddha 22. Sadhya
23. Shubha 24. Shukla
25. Brahma 26. Indra
27. Vaidhriti

Yogas like tithis find extensive use in electional astrology and day to day rituals.

A karna is half the tithi ,or 360 minutes (6 degrees) of arc. In thirty tithis comprising a lunar month,there are sixty half-tithis or karnas.There are four karnas that occur only once in a lunar month. They are the fixed karnas and called as :

1. Shakuni : assigned to the latter half of the 14th day of the krishna paksha.

2. Chatuspada : assigned to the first half of the amavasya (15th day of the krisna paksha).

3. Naga : assigned to the latter half of the amavasya.

4. Kimstughna : assigned to the first half of the first day of the shukla paksha.

The remaining 7 karna recur eight times during rest of the lunar month.Their names are :

1. Bava
2. Balava
3. Kanlava
4. Taitila
5. Gara
6. Vanija
7. Vishti

These karnas recur in regular order starting from the second half of the first day of the shukla paksha until the first half of the 14th day of the krishna paksha. Karnas too find their use in rituals and electional astrology.

Some astronomical facts about planets
The following is a very brief discription of the planets which are of relevance in vedic astrology.
This is the most important of the nine grahas. In fact the sun is our nearest star in the space with planets revolving around it. It is the source of all the natural light and the heat of the earth. It provides the centripetal force to balance the centrifugal force generated by the planets going around it. It's diameter is 1.392 million kilometers, which is almost 109 times the diameter of the earth.The mass of the sun is some 323,000 times the mass of the earth.It has extremely high surface and core temperatures, and goes on producing immense amount of energy. At one time the sun was considered as the center of the universe (this was never the view of vedic astrology), but now we know it lies near the edge of the spiral arm of the milky way galaxy, lying some 30,000 light years from the galactic center, and sharing the rotation of the galaxy.
It is a satellite of the earth. In vedic astrology it is of great importance.It is the fastest moving grah and has the usual west to east mvement along the zodiac. It has relatively small size, it's diameter being only about 3476 kilometers. It's average distance from the earth is about 384,400 kilometers. It always presents the same face towards earth because it takes the same time to rotate once on it's axis as it does to revolve once around the earth i.e.27.32 days.Since the rotation is a uniform motion,while the motion in orbit is not,we may sometimes see an extra strip of the moon's surface on one or the other side.Some 59% of the total surface of the moon may thus be visible to us on the earth at one time or the other.This phenomenon is called as liberation.

The luminosity of the moon is caused by the light from the sun.It is the varying relative positions of the sun and the moon that produce the phases of the moon.These lunar phases,earlier discussed as tithis,are extremely important in vedic astrology.
Mars is the first of the outer planets and fourth in order of distance from the sun. It's orbit is highly eliptical as compared to that of earth, due to ehich it's closest position may be only 56 million kms. whereas at it's farthest it may reach upto 100 kms. The brilliance of the mars depends upon it's location. Mars is only twice as large than earth's moon.It's diameter being 6786 kms. It is at a mean distance of 227.8 million kms from the sun.

The synodic period of the mars is 780 days, which is the interval between martian oppositions to the sun, with the earth lying in between. Mars rotates on it's own axis in 1.026 days and has an orbital period of 687 days. Mars has two small satellites called phobo and deimos.
Mercury is the planet nearest to the sun and hence is extremely hot. It has a very eccentric orbit so it's minimum distance (periphelion) from the sun is much less than it's maximum distance (aphelion). It's mean distance from the sun is about 58 kms. and it's diameter is 4870 kms, and it's maximum inclination of about 7 degrees on either side of the ecliptic. Mercury rotates once round it's axis in 58.65 days which is 2/3rd of it's orbital period of about 88 earth days. (planet has maximum speed at periphelion and minimum at aphelion).
Jupiter is the largest planet of the solar system, it's mass exceeding that of all the other planets combined together. It's rapid spin (once in 9 hours 50 minutes) has caused it to bulge at equator (diameter at equator 143,000 kms.) and to flatten at the poles (diameter 133,000 kms.). It is 318 times as massive as the earth and less than the 1000th part of the sun. It's mean distance from the earth is 778 million kms. and has an orbital period of 11.86 earth years.

Being far away from the sun,it is a cold planet with it's gaseous cloud having a temperature of 140 deg.below freezing point.There are perhaps 16 satellites which circle around jupiter
Venus is the second nearest planet to the sun. It's dense cloudy atmosphere reflects light extremely efficiently and accounts for the brilliance of this planet in the sky. The maximum inclination of this orbit is about 3.24 deg. on either side of the ecliptic. It is located at a mean distance of 108 million kms. and has a diameter of about 12,000 kms.

The rotation period of venus is 242.6 days.An important fact about the rotation of venus is that it is retrograde, that is opposite to the general direction of rotations in the solar system. The orbital period of venus is about 224.7 days.
It is the last of the naked eye planets. It's mean distance from the sun is 1426 million kms. It's rotation period is approximately 10 hours 14 minutes, and it's orbital period is 29.46 years. Saturn has a diameter of over 142 thousand miles at the equator. Being further away from the sun, saturn is a cold planet . It is larger than the rest of the planets (expect jupiter) and is about 95 times as massive as the earth. It's characteristic feature is the presence of rings around it.  At least twenty satellites are known to revolve around the planet.

The extra -saturnine planets (uranus,neptune and pluto) need the help of a telescope for their identification They do not form a part of predictive vedic astrology and are, therefore, not treated of here.