Transits
of Venus have long been useful to scientific research. In the 1700s,
they helped us determine our distance to the Sun and gave us the first
clue that Venus might have an atmosphere.
How do we know how far away the Sun is? Now we use radar to establish
our distance from celestial objects, but before there was radar, we
had to resort to trigonometry to figure out the astronomical unit (AU)—the
distance between Earth and the Sun. In 1677, English astronomer Edmond
Halley (of comet fame) proposed that a transit of Venus—and some
geometry—could be used to determine the astronomical unit. Though
Halley died in 1742, which was 19 years before the 1761 transit of Venus,
other scientists followed his suggestion and journeyed to the ends of
the Earth to make the necessary observations. The astronomical unit
obtained from these observations, roughly 95 million miles, is respectably
close to our current measure of 92,955,807.267 miles (149,597,870.691
kilometers).
It was also during the 1761 transit of Venus that observers noticed
something strange: a fuzzy halo of light surrounding the dark spot of
Venus. The fuzzy halo was only visible when Venus was at the Sun’s
edge. Scientists of the time concluded that Venus must have an atmosphere,
and we’ve since confirmed that it does: a dense atmosphere of
mainly carbon dioxide, with clouds of sulfuric acid.
Transits are still of interest to scientists today, because they can
be used to find planets outside our solar system, also known as extrasolar
planets, or exoplanets. Extrasolar planets are too distant and too dim
to be viewed directly, but when one passes in front of (that is, transits)
its parent star, it blocks a little bit of the star’s light. (The
dimming is detectable but extremely slight; just 1 percent for a giant
planet like Jupiter and .01 percent for a planet the size of Earth.)
Scientists analyzing the changing light from stars can not only identify
the presence of a planet, but can also determine the planet’s
size, temperature, and atmospheric composition. The transit of Venus
provides great practice for these scientists, allowing them to track
the optical changes that take place during a transit.
In 2007, NASA will launch the Kepler Mission, which will use a space
telescope to search for Earth-sized exoplanets. Kepler will watch 100,000
stars that are similar to our Sun, looking for variations in brightness
caused by planets transiting their parent stars. (For more information,
go to http://www.kepler.arc.nasa.gov.)
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Finding the AU:
How the Transit of Venus Tells Us Our Distance from the Sun
By 1619, German astronomer Johannes Kepler had figured out the relative
distances of all the planets from the Sun. For example, if the Earth’s
distance from the Sun is one astronomical unit (AU), then Venus’s
distance from the Sun is .72 AU, Mars’s is 1.5 AU, and so on.
However, no one knew the value of AU, so the absolute distances between
the celestial spheres was not known.
In 1716, English astronomer Edmond Halley proposed a method for calculating
our distance from the Sun—the astronomical unit—using the
transit of Venus.
The underlying principle behind Halley’s method is something called
parallax, the shift in position that comes from viewing an object from
two different points.
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What
Is Parallax?
Try this:
Point your index finger towards an object on the opposite
side of the room. Look at it first with just your left
eye, then switch to looking at it with just your right
eye.
Can you see that the place across the room that your
finger points to seems to jump, depending on which eye
you use to look at it? That’s parallax. The farther
away the object you point at, the more it seems to jump
when you switch eyes.
Halley’s method uses parallax to find our distance
from the Sun. Observers stationed far apart on Earth
are the two eyes, Venus is the pointing finger, and
the Sun is the object across the room.
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Imagine two different people, one on each pole of the Earth, viewing
the transit of Venus. The person on the North pole sees Venus following
one path across the Sun. The person on the South pole sees Venus follow
a slightly higher path, one that’s shifted a little to the north.
Because we see the Sun as a circle, these two different paths will have
different lengths. Halley proposed that an easy way to measure the difference
between the lengths of these two paths would be to time the transits,
using the four phases of the transit—the first, second, third,
and fourth contacts—as indicators.
With the two different paths known, the distance between the Earth and
the Sun can be pretty easily calculated using trigonometry and Kepler’s
third law of planetary motion.
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Finding the AU: Calculation of the Sun-Earth Distance
During the transit of Venus, two observers on Earth view Venus at two
different points on the Sun.
We’ll
call the angle between the two paths measured from Earth E.
Thanks to Kepler’s third law, we know the relative distances of
all the planets from the Sun. Case in point: We know that Venus’s
distance from the Sun is .72 times the Earth’s distance from the
Sun.
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Kepler’s
Third Law
Johannes Kepler’s third law of planetary motion
established relative distances of all the planets from
the Sun, but not absolute distances. Published in 1619,
the law goes like this: The cube of a planet’s
distance from the Sun is proportional to the square
of its orbital period (one year for Earth, 5/8 of a
year for Venus).
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This distance relationship also tells us angle V, the angle
between the two paths as seen from Venus: angle V is angle
E divided by .72. (This is true only for small angles, which
these are.)
During the transit of Venus, two observers on Earth view Venus at two
different points on the Sun.We’ll call the angle between the two
paths measured from Earth E.
Thanks to Kepler’s third law, we know the relative distances of
all the planets from the Sun. Case in point: We know that Venus’s
distance from the Sun is .72 times the Earth’s distance from the
Sun.
This distance relationship also tells us angle V, the angle between
the two paths as seen from Venus: angle V is angle E divided by .72.
(This is true only for small angles, which these are.)
Besides the angle V, the only other thing we need to know is
the distance between the two observers on Earth, at points A
and B.
Call this distance  .
Then, to get the distance from Venus to Earth, all we need is basic
trigonometry. There is a right triangle formed between the Earth and
Venus.
Or, rearranging the equation:
For small angles, tan (1/2 A) = 1/2 tan A, so:
Once we have the distance between Earth and Venus
, it’s easy to find the distance from the Earth to the Sun, again
using Kepler’s third law. This law tells us that the distance
between the Earth and Venus is .28 times the distance between the Earth
and the Sun.
So:
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