October 2008 Sky from the Keeble Observatory
Some quick updates, then on to more triangles! NASA has extended the Mars Phoenix
mission for another 30 days. Once full winter sets in, it will likely be the end,
since the batteries are not likely to survive the low temperatures and almost complete
lack of sunlight for the solar arrays. The return of summer in the southern hemisphere
has improved the power situation for both rovers, Spirit and Opportunity.
Opportunity is undertaking an ambitious 12 km overland trek to a crater about
twenty times the size of “Victoria Crater” where it spent most of the last two years.
Getting to its next major target could take two years – truly ambitious for a robot
5 years past its 90 day design “warranty.” “We may not get there, but it is scientifically
the right direction to go anyway," said Steve Squyres of Cornell University, principal
investigator for the science instruments on Opportunity and its twin.
We described in the July column how astronomers use basic geometry and trigonometry
to measure the distance to the Moon. Basically, we imagine simultaneously looking
at the Moon from two locations separated by a baseline of known (and ideally great)
length. It will appear in slightly different positions relative to the background
stars, and we can measure the angles defining these different directions. We can
then imagine drawing a triangle with the known baseline and the two known angles
to find the actual distance. This works for the Moon, since it is relatively close
by – on average a bit less than a quarter million miles!
Geometry and trigonometry were invented by the Greeks to accurately survey the land
and mark boundaries between properties. This was especially useful for the Alexandrian
Greeks in Egypt, since the annual Nile floods washed away any markers they may have
put up. (Geometry literally means “measure the Earth” while trigonometry means “measure
We’d like to apply the same trick for the Sun … but you can’t see the background
stars when the Sun is out! Also, terrestrial baselines would be limited to about
8000 miles, which is too short for an accurate distance determination. But, we can
still use triangles.
As the inner planets follow their orbits around the Sun, we see them sometimes to
the east and sometimes to the west of the Sun on the sky. This is why they can both
be referred to as “morning star” or “evening star.” Because Mercury is the innermost
planet, it has the smaller orbit and can never be more than about 23 degrees from
the Sun, its greatest elongation. Similarly, Venus has its greatest elongation
at roughly 47 degrees from the Sun. When this happens, the Sun, Earth, and either
Venus or Mercury form a right triangle, with the planet at the 90 degree vertex,
and the elongation angle at Earth. On average, the Sun-Earth distance is 150 million
kilometers (about 93 million miles), a distance known as the Astronomical Unit.
Knowing the elongation and this distance means we can calculate (or draw to scale
and measure) the distance from the Sun to the planet. But … how can we know the
Earth-Sun distance? Historically we would combine the elongation measurements with
another geometric challenge, that of tracking either Mercury or Venus on one if
their rare times of passing directly between Sun and Earth, an event called a transit.
Today, we have it far easier. We can bounce powerful radars off the planet at elongation,
thus directly measuring the hypotenuse of our right triangle. Knowing this
and the elongation angle, we can directly calculate the Earth-Sun distance. Similarly,
we can also use this information to accurately determine the orbits of Mercury and
Unfortunately, this technique wouldn’t work for the outer planets. So, next month,
we’ll see how to measure the distances to planets farther from the Sun. In a subsequent
column, we’ll push the triangles even farther out to measure distances to the stars.
Lunar phases for October: First Quarter on the 7th, at 5:04 am;
Full Moon on the 14th, at 4:02 pm; Last Quarter on the 21st,
at 7:55 am; New Moon on the 28th, at 7:14 pm.
Predawn planet watchers will find Saturn rising to the east about 90 minutes before
sunrise early in the month. Look for it about 25 degrees above the horizon as the
Sun first appears. It will be joined around mid-October by Mercury, which rapidly
climbs into the fading twilight, reaching its greatest western elongation on the
22nd. Look for it low to the east-southeast. By month’s end it will already
be slipping back into the solar glare.
Jupiter begins the evenings nearly due south all month, about 30 degrees off the
horizon, setting to the southwest about 5½ hours after sunset. Venus and Mars start
the month low to the southwest at sunset. Both should be very bright, with reddish
Mars lower and closer to the horizon. Mars moves closer to the Sun as the month
advances, while Venus moves away from the Sun on the sky because it’s catching up
with us in our orbit, but hasn’t yet reached its greatest eastern elongation. By
month’s end, Venus will be a bit above Antares (the name means “against Mars”) –
but, don’t confuse this red star with Mars.