November 2008 Sky from the Keeble Observatory
Some quick updates: The Hubble Space Telescope had a failure in the on-board computer “Side A router” which communicates between the science instruments and the telemetry, preventing the telescope from taking any data or relaying results to the ground. All instruments have now been switched to “Side B” and the telescope has resumed science activity. There was some trepidation about the switch-over, since those backup circuits had not been tested since before its initial deployment in April 1990. 18 years is a long time for electronics to sit unused! The next and final servicing mission has been delayed from its initial October launch target, likely until May to allow for the installation of a new router.
Mars Phoenix is running low on power as Martian northern winter drops overnight temperatures into the -150 degree range. The probe has gone into “safe mode” because of low power at least once, though it has recovered. The good news is that all the major science tasks have been completed. Observing the onset of winter is “gravy” to the mission team.
One could hope to apply the same idea of triangles to planets in the outer solar system that we used for the inner solar system, but it doesn’t quite work. If we observe a planet when it is 90 degrees away from the Sun in the sky, it is said to be at quadrature. This duplicates the right triangle we drew last month for the inner solar system, but … there are infinite possibilities for the distance to an outer planet from this triangle, because we don’t know in what direction it lies as seen from the Sun. So, instead of drawing triangles, we’ll measure these distances with our clocks!
There are two relevant periods that we need to measure. One is the time it takes for an outer planet to complete one orbit around the Sun. This is called its sidereal period – sidereal means “relative to the stars,” so this is the period for the planet to return to a given position relative to the background stars as seen from the Sun. The other period is the time for the planet to return to the same position relative to the Sun as seen from Earth. This is called its synodic period. Let’s consider measuring from opposition to opposition (i.e. when the planet is 180 degrees from the Sun in the sky and use this as our synodic period. It turns out that there is a simple relationship between the synodic period and the sidereal period. Let the synodic period be S, the sidereal period P, and let’s measure time in years. (Earth’s sidereal period is defined as one year.) Then we have the following relation: 1/S = 1 – 1/P. This gives us the sidereal period from observing the time from opposition to opposition, i.e. the synodic period.
The next step is to look at the work of Kepler in the early 17th century. He used observational data to determine that planetary orbits were not circles, but ellipses. However, they’re close enough to circular for this discussion. Let the radius of the orbit be A (technically we want the semi-major axis of the ellipse). Kepler was able to show that there was a simple relationship between A and the sidereal period, namely that the ratio between the square of the period and the cube of the semimajor axis was the same for all the planets. We write this as A3/P2 = constant. The easiest constant is to use the Earth-Sun distance (1 astronomical unit, or 1 AU) and Earth’s sidereal period (1 year). Then we can solve for the size of the external planet’s orbit, A, in multiples of the distance from Earth to Sun. The last step is to adjust all these distances, which are in AU in terms of more conventional units, like kilometers. We do this by bouncing radar off those planets which reflect radar (Venus, Mercury, and Mars) and timing the round trip for that signal. Knowing the speed of light, we now have the various orbits calibrated into kilometers. So, how big is the solar system? We orbit an average 150 million kilometers (93 million miles) from the Sun, taking one year for a complete trip. Mercury lies only 58 million kilometers from the Sun, and orbits in just 88 days. Jupiter, at 5.2 AU takes nearly 12 years for one orbit. Saturn lies 9.6 AU from the Sun … a staggering 1.44 billion kilometers, or just under 900 million miles, and takes just under 29.5 years to go completely around. The most distant “official” planet is Neptune, at 30 AU. We have identified a number of “dwarf” planets, known also as plutoids, at larger distances. For example, Pluto itself has an orbital period of 248 years, with a semi-major axis equal to 39.5 AU. Another is Eris’s 559 year orbit at nearly 68 AU (that’s 6.3 billion miles!).
Next month – on to the stars!
Lunar phases for November (all times are Eastern Standard): First Quarter on the 5th, at 11:03 pm; Full Moon on the 13th, at 1:17 am; Last Quarter on the 19th, at 4:31 pm; New Moon on the 27th, at 11:55 am.
Pre-dawn planet watchers will have to settle for Saturn, high to the southeast, about 47 degrees above the horizon at sunrise. It’s below Regulus in Leo. Mercury rises about an hour before sunrise, but it will disappear into the Sun’s glare at midmonth. By the end of the month, look for Saturn high to the south at sunrise.
At sunset, Jupiter and Venus are bright to the southwest. They’ll get closer together as the month passes (see below). Mars is low on the west-southwest horizon at sunset, but it’s unlikely you’ll pick it out of the horizon clutter and haze.
The almost full moon in the early morning hours on the 17th will make the Leonid meteor shower a modest viewing experience, at best. Only the brightest of these comet fragments will be bright enough to be visible. Nonetheless, if you’re inclined to try, you’ll need to find a dark spot away from city lights. While the “radiant” of this shower lies in the constellation Leo (which will be below the Moon at 5 am on the 17th), you may be able to see some meteor activity in any direction on the sky. The radiant is the direction from which the meteors appear to originate.
Our overhead look at midmonth, about 2 hours after sunset, finds the Milky Way dividing the sky roughly from northeast to southwest. The rather unimpressive constellation Lacerta (the Lizard) is at zenith. Your eye is more likely to draw your attention a bit to the west-northwest of zenith, where you’ll encounter Deneb, the brightest star in Cygnus. About 45 degrees below zenith is Vega, which will be the brightest star in this general direction, and likely among the first to emerge from twilight. Below Vega, in a region of sky generally devoid of bright stars (you’re looking out of the plane of the Galaxy), you’ll notice a modest diamond shape with four stars marking the corners. This is Hercules. Binoculars pointed at the right-most star will also pick out the globular cluster M13, just below and to the left.
To the northeast we find the familiar shape of Cassiopeia – here looking like a back ward Greek sigma (S). Follow the lowest two stars up and to the right – on a clear night you should see the faint patch marking the Andromeda Galaxy. It won’t look as spectacular as the deep exposures printed in textbooks, but be reminded that this is the most distant object you can see with your own eyes without a telescope. It’s a system of several hundred billion stars, about 2 million light years distant.
To the southwest, those two brilliant “stars” are the planets Venus and Jupiter. By month’s end, they’ll pass within about 3 degrees, with Venus the brighter of the two.
Copyright 2008George Spagna