Befriending Venus :-)
During the months of February-April 2004, it will be difficult to miss Venus in the western skies, after sunset, as it easily outshines every other celestial object than the Sun or the Moon.
The 23rd-24th Of February, 24th-25th of March and the 23rd of April, are dates when Venus will be in close conjunction with the crescent Moon - one of the most inspiring visions in the Sky. On the last date mentioned, the pair will also have company from the Planet Mars, now shorn of the glory it had, during its close approach to Earth in August 2003. On the 21st of May and the 10th of November 2004, Venus will be occulted by the Moon as seen from any location in India.
The two inner planets Mercury and Venus would never be at Opposition - exactly 180 degrees away from the Sun, as seen from Earth.
From the time of inferior conjunction, when they are hidden in the glare of the Sun, they move away to greater and greater elongations (angular distance from the Sun, as seen from earth) - Mercury achieving a maximum elongation of about 28 degrees while Venus moves a little further away from the Sun than that - with a maximum elongation of about 48 degrees.
This maximum elongation - has a significance for the determination of the Earth-Sun distance, from Transit measurements
In the year 2004, the dates of maximum elongation of Venus are - the 29th of March (evening sky) and the 17th of August (morning sky). For the year 2012 the corresponding dates are 27th of March and the 15th of August.
There is a small jitter in the maximum elongation of Mercury and Venus year to year, arising from their elliptical orbits.
The orbit of Venus, is almost circular, compared to that of Mercury and the jitter seen in the figure above, has contributions mainly from the changing Earth-Sun distance, at each maximum elongation.
In the year 2004, for instance, Venus starts as a bright evening object in the south western sky, in the constellation of Capricornus – easy to identify as it rules the skies – the brightest object other than the Moon (when visible), following Sunset. In the months following that, it goes through increasing elongation and appears higher in the sky following sunset, going through the constellations of Aquarius, Pisces, Aries and reaching Taurus, by April. It will have company from Mars, in this month. Before that, on the 29th of March, it will have its maximum eastern elongation and start falling back towards the Sun, again. After going through inferior conjunction and transit on the 8th of June, its elongation will increase to go through another maximum elongation in the month of August. Its phases also change accordingly, decreasing from a maximum Full Phase, through the months of January-June, passing through the New phase on the day of the transit and increasing again. These changes are shown in the figure below.
It will be an exciting activity in the last week of March and the first week of April 2004, or, at other suitable times – August 2004, and again, March and August 2012, for students to directly map the changing elongation of Venus. Some methods for this are here.
Now, for a little about orbits, inclinations and nodes :-)
In the figure above - S is the Sun, E - Earth and V - Venus. For Solar system orbital elements the reference plane is the orbit of the Earth around the Sun - seen projected on the sky - this becomes the ecliptic.
For any other Solar System body than the Earth - Venus, for instance, we can define orbital elements that will fix the orbit of Venus with respect to that of Earth.
The inclination for a Planet will be the angle made by its orbit around the Sun with Earth's orbit. The angle marked at N2 in the figure above, which is 3.39 degrees for Venus. Once this angle is fixed, there is still a number of possible orbits that can intersect Earth's orbit with this angle - one can visualise moving N1 and N2 the intersection points around Earth's orbit to obtain all these possibilities. Once the location of N1 and N2 is fixed we have fixed the orbit - N1 and N2 are the two nodes of intersection - ascending node when the Planet crosses it going South-North and descending when the Planet goes North-South.
These crossings happen for Venus in the months of June (descending) and December (ascending) and in the months of May (descending) and November (ascending) for Mercury - these are the times that Transits can take place - just as eclipses get related to the New and Full phases of the Moon. And the same reasoning also tells us that Transits do not occur with every node crossing - just as, eclipses do not occur at every Full Moon night or a New Moon day. Transits can happen if the Inferior conjunction of the Planet (when the Planet is between the Earth and the Sun) happens within a day or two of the time when the Planet crosses the ecliptic at these nodes.
The node crossing points can be defined in terms of a longitude co-ordinate - with the Sun having a longitude of zero at the time of Equinox. Ascending Node of Venus is at longitude of about 77 degrees and descending one at a longitude of about 257 degrees.