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The 2012 International Transit of Venus

Re-observation

 

Undergraduate Thesis 2009 by Matthew Cooper

Supervised by Dr Craig Roberts

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Venus in transit *

 

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The transit and the distance from Earth to Sun

 

The transit of Venus and why it occurs

The Earth orbits around the Sun in an ellipse, with the Sun at one of its foci. The orbit of the Earth forms a plane, with the Sun lying in the middle, known as the Earth’s orbital plane.

The ecliptic is the apparent path the Sun takes around the Earth in a year, relative to an observer on Earth. The ecliptic is not parallel to the direction of Earth’s rotation (equator), but it is inclined by 23.5°, giving us seasons. Figure 1 shows the ecliptic.

http://hyperphysics.phy-astr.gsu.edu/hbase/solar/imgsol/eclip.gif

Figure 1 – The Ecliptic (Hyperphysics 2006)

The ecliptic plane is the same as the Earth’s orbital plane, and is used as a reference plane to compare the orbits of other planets.

Venus’ orbit is inclined (by 3.39 degrees) relative to the ecliptic, resulting in it crossing Earth’s ecliptic twice in each complete orbit around the Sun. The two points it crosses are known as the ascending node (Venus moves up) and the descending node (Venus moves back down). These are insignificant events, except when Earth just happens to be at a point in its orbit where it aligns with one of the nodes and the Sun, at the same moment as Venus is at the same node. When this happens Venus passes between Earth and the Sun, resulting in a planetary eclipse of the Sun. This event is known as the transit of Venus, and it is an extremely rare event, occurring at the intervals explained in the following section.

Figure 2 – Ascending and descending nodes of Venus’ orbit relative to Earth’s orbit

When transits of Venus occur

Transits occur in a regular pattern (122.5 yrs – 8 yrs – 105.5 yrs – 8 yrs – 122.5 yrs……), with transits occurring in 8 year pairs. The transits in each pair occur upon either an ascending or descending node in Venus’ orbit. In particular, the largest gap occurs after a pair of ascending node transits before a pair of descending node transits.

The distance from Earth to Sun

The astronomical unit (AU) was originally the unknown distance from Earth to Sun, from which all distances in the solar system could be derived from Kepler’s equations, which provided proportions but lacked a scale. Since the Earth’s orbit is not circular but elliptical, this distance had to be defined as the average distance from the centre of the Earth to the centre of the Sun. Thus the Astronomical Unit was originally (until 1976) defined as half the length of the semi-major axis of the Earth’s elliptical orbit.

The AU is now defined as “the distance from the centre of the Sun at which a particle of negligible mass, in an unperturbed circular orbit, would have an orbital period of 365.2568983 days”, and has a value of 149,597,870.691km (International Astronomical Union). This definition is quite abstract, so for the purposes of this investigation the Astronomical Unit is simply the average distance from Earth to Sun, which should be quite close to the theoretical definition of the unit.

From observations to a value for the AU

Deriving the AU from Observations of the transit of Venus requires recording times when Venus contacts the Sun. There are 4 contacts: numbered 1 to 4, the first called external ingress (Venus touches the outside of the Sun’s disk), the second internal ingress (Venus now fully within the Sun’s disk), the third internal egress (Venus touches inside of Sun’s disk on the way out), and the fourth external egress (Venus touches outside of Sun’s disk on way out). Figure 3 below shows how these points of contact appear in the sky.

Figure 3 – Venus transitting across the face of the Sun

The second and third contacts are used to determine the duration of the transit, because they are easier to distinguish visually. This makes it easier to mark an exact time that each contact occurs, making the timing more accurate. The first and fourth contacts are much harder to distinguish as Venus is not visible outside of the Sun during a transit.

The aim is to observe the transit at two locations on Earth as far apart as possible in latitude. This is to create a parallax effect of Venus and the Sun in the sky. Because each location sees Venus and the Sun from a slightly different perspective, Venus will appear to take a slightly different path across the Sun at each location, because Venus is considerably closer to the Earth than the Sun. The separation between the two paths (see figure 3 above) is small, too small to be directly measured, so separation is measured by the timed length of the transit instead. At each observing location, the recorded length of the transit varies (by up to several minutes), so the difference between these two values is used to derive the parallax shift of Venus between the two locations, because it is proportional to this parallax shift.

The mathematical formulae of Halley’s method connect the difference in transit length to the parallax shift of Venus and the Sun at the two locations, and from this derive the distance from Earth to Sun (AU) through geometry.

 

 

Quick Facts about the 2012 Transit of Venus

 

Transit will commence at approximately 22:00 (Universal Time)

 

Transit duration will be about 6 hours 40 minutes

 

(Times above are approximate and will vary according to observer’s location)

 

For Sydney:

First contact: 8:16 AM

Last contact: 2:44 PM

The transit and the distance from Earth to Sun

History of transit observations

Observation methods

Observing conditions

Collaborating data

References

Contacts

 

 

 

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Matthew Cooper 2009

Last modified 30 October 2009