Posts Made By: Curt Renz

Below are my algorithms for computing the graze path in Oregon, Washington and Scotland. Input and output are all decimal. The only input is the western longitude as a positive number. The zenith angle is the position of Mars along the lunar limb measured counterclockwise from the zenith.


This first set for Oregon and Washington is only accurate between western longitudes 118° and 125°.

W = Western Longitude (as a positive number)
M = W - 122 (M may be positive or negative, but M² is always positive)

Northern Latitude = 46.110909 - 0.561886 M - 0.001628 M²
Hour PST = 17.82509 - 0.00928 M + 0.00027 M²
Zenith Angle = 222.418 + 0.178 M - 0.005 M²
Altitude of Mars = 15.319 - 0.942 M - 0.003 M²


This second set for Scotland is only accurate between western longitudes 1° and 8°.

W = Western Longitude (as a positive number)
M = W - 4 (M may be positive or negative, but M² is always positive)

Northern Latitude = 57.138948 + 0.407761 M - 0.006249 M²
Hour UT = 3.68868 - 0.02086 M + 0.00006 M²
Zenith Angle = 154.843 + 0.721 M + 0.004 M²
Altitude of Mars = 43.393 + 0.544 M - 0.011 M²

Below is my algorithm for computing the graze path across the Netherlands, Germany and Austria. It is only accurate between eastern longitudes 4.9° and 16.1°. Input and output are all decimal. The only input is the eastern longitude as a positive number. The zenith angle is the position of Mars along the lunar limb measured counterclockwise from the zenith.

E = Eastern Longitude (as a positive number)
M = 10 - E (M may be positive or negative, but M² is always positive)

Northern Latitude = 50.215533 + 0.572911 M - 0.004654 M²
Hour UT = 3.98432 - 0.02031 M - 0.00014 M²
Zenith Angle = 145.799 + 0.553 M + 0.008 M²
Altitude of Mars = 33.518 + 0.861 M - 0.010 M²

Immediately below is a wider view of the photo in true colors that may put things in better perspective. It includes a part of the rover’s solar panel. NASA says the hill that is dotted with rocks and is seen just above the center is about 30 meters away. Across the bottom third or quarter of the photo is the edge of the plateau on which the rover is sitting. Near the left end of the photo on the plateau edge is the object of interest. It appears to be a couple of meters away and a couple of centimeters in height. Nothing that moves should be in the picture since it takes at least several minutes for the camera to cycle through three different colored filters to produce a colored photograph.

The bottom image gives a closeup view. NASA should instruct the rover to give the poor little man a few drops of water. He’s probably dehydrated from wandering the planet for millions of years in search of a mate.

From the New York Times:

WASHINGTON — The Pentagon plans to shoot down a disabled 5,000-pound spy satellite within the next two weeks, before it tumbles from orbit, because the rocket fuel it carries could be a danger to people, Pentagon officials said Thursday.

http://www.nytimes.com/2008/02/14/science/14cnd-satellite.html?_r=1&8au&emc=au&oref=login

Here’s a photo I captured of the lunar eclipse two minutes after maximum totality. It was taken from Arlington Heights, Illinois on 2008 FEB 20 at 21:28 CST. Saturn is toward the lower left and Regulus near the top. A reddish hue is apparent on the Moon. Even though the eclipse was in totality, the lower right limb of the Moon appears brightened because as viewed from that region the Sun would have been barely hidden by the Earth. The coloration and brightening were enhanced by the 0.4 second exposure and F/2.4 aperture.

And here's a special challenge for those who live near Los Angeles and would like to witness a grazing occultation of Venus. The northern graze path will sweep in a northeasterly direction from Topanga State Park through Palmdale to Lockhart.

Below is my algorithm for the northern graze path which passes slightly to the north of Los Angeles. It is only good between western longitudes 117.3° and 118.7°. Input and output are all decimal. A Western Longitude is the only input. The hour is in Pacific Standard Time. The Zenith Angle is the position of Venus on the lunar limb measured counterclockwise from the zenith.

Feel free to ask questions.

W = Western Longitude as a positive decimal value
M = W - 118

Northern Latitude = 34.552472 - 0.784811 M - 0.011230 M²
Hour PST = 12.54922 - 0.02488 M - 0.00089 M²
Zenith Angle = 290.295 + 0.245 M + 0.026 M²
Venus Altitude = 32.528 + 1.292 M + 0.014 M²

The occultation graze path will also pass a little north of Las Vegas, Nevada.

Below is my algorithm for the northern graze path over that portion of Nevada. It is only good between western longitudes 114.5° and 115.9°. Input and output are all decimal. A Western Longitude is the only input. The hour is in Pacific Standard Time. The Zenith Angle is the position of Venus on the lunar limb measured counterclockwise from the zenith.

Feel free to ask questions.

W = Western Longitude as a positive decimal value
M = W - 115

Northern Latitude = 36.806255 - 0.719914 M - 0.010443 M²
Hour PST = 12.61647 - 0.02012M - 0.00059 M²
Zenith Angle = 289.767 + 0.113 M + 0.018 M²
Venus Altitude = 28.779 + 1.208 M + 0.014 M²

There were clouds in the wrong area of the sky here near Chicago on Saturday evening. Apparently many North Americans had even worse weather.

The Dark Moon will next conjunct the Sun on 2008 APR 06 at 03:56 UT. That will present an opportunity for Europeans to sight a really young Moon later that evening. Even North Americans may spot a New Moon aged less than 24 hours. I might see it at less than 21 hours, which would break my personal record of 21:45.

The celestial geometry in April will be so ideal that the Moon’s crescent will appear to be hanging straight down in a U-shape like the Cheshire Cat’s smile for those of us near the latitude of Chicago. For those further south in the U.S. it will appear tilted the “wrong” way. Don’t be surprised if we hear from folks asking about the strange orientation of the Moon. A preview graphic is already on my website at: http://www.curtrenz.com/astronomical.html

Ed “katodog” posted his pictures of last night’s Moon at the Chicago Astronomer message board. He lives not far from me but had better luck seeing through the clouds. Here’s a link to the thread in which he posted his pictures: http://astronomer.proboards23.com/index.cgi?board=Lunar&action=display&thread=1204481222&page=1#1205026327

Apparently we were all shut out by clouds. As a heads up, the circumstances surrounding the May New Moon will present North Americans with a rare opportunity to spot the Moon aged only half a day or a little more. That might be tough, but the unusual celestial geometry could allow some observers to set what will remain their lifetime record. I’ll post details when the event nears, although preview graphics are already on my website.

With the decreasing apparent tilt of the orbital plane of the Galilean satellites, #4 Callisto can once again be involved in transits, occultations, eclipses and shadow transits. The other three participate in all of these events each time they orbit Jupiter. But Callisto only does so during periods that last about three years in alternation with approximately three-year periods in which it appears to pass north or south of Jupiter at each conjunction.

This means more of these events will be occurring during this year’s apparition of Jupiter compared to recent years. Quadruple shadow transits are impossible due to a commensurability among the orbital periods of the inner three Galilean satellites. Triple shadow transits are only possible when Callisto participates. However, this will never happen during the current series of Callisto shadow transits. The next triple shadow transit will occur in 2013. But numerous dual shadow transits will be happening during the current apparition. The next such event will occur on 2008 JUN 01, but will only be visible from the eastern hemisphere. Data and graphics regarding that dual shadow transit can be seen by clicking: http://www.curtrenz.com/astronomical.html