Shadow of Phobos on Mars
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The satellite Phobos orbits very close to Mars and casts a penumbral shadow on the Martian surface. This shadow has been observed by space probes on numerous occasions. Locations on the Martian surface that the shadow passes over experience a transit of Phobos across the Sun, which could also be called a partial eclipse of the Sun by Phobos.
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Early observations of the shadow
In the 1970s, the Viking 1 Lander detected the penumbral shadow of Phobos passing across it.[1] (http://history.nasa.gov/SP-425/ch38.htm) This was detected as a slight dimming of the ambient light; the Viking camera did not image the Sun. The shadow took about 20 s to pass over the Lander, moving at 2 km/s. The shadow was simultaneously imaged from the Viking Orbiter 1, which permitted locating the position of the lander in the orbiter pictures.
Far more detailed images of the shadow were taken with the arrival in 1997 of the Mars Global Surveyor and its high-resolution Mars Orbital Camera.
August 26 1999 image of Phobos shadow
Phobos_shadow.jpg
One such image was taken by the Mars Global Surveyor on August 26 1999 and shows the shadow at high resolution. This image was featured in a November 1 1999 NASA press release (http://mars.jpl.nasa.gov/mgs/msss/camera/images/11_1_99_phobos/index.html).
By examining maps of Mars (Map of area (http://pdsmaps.wr.usgs.gov/explorer-bin/mapmars3.cgi?WHEREFROM=PZ&VERSION=ADVANCED&DATA_SET_NAME=v2mars_viking_bw&PIXEL_TYPE=BIT8&SCALE=pixels/degree&PROJECTION=SIMPLE_CYLINDRICAL&RESOLUTION=64&RESAMP_METHOD=NEAREST_NEIGHBOR&BANDS_SELECTED=1&FORMAT=JPEG&LONBOX=6&LATBOX=10&GRIDLINE_FREQUENCY=1&STRETCH=AUTO&LAT=11&LON=50&LINE=512&SAMP=512) Map zoom (http://pdsmaps.wr.usgs.gov/explorer-bin/mapmars3.cgi?WHEREFROM=PZ&VERSION=ADVANCED&DATA_SET_NAME=v2mars_viking_bw&PIXEL_TYPE=BIT8&SCALE=pixels/degree&PROJECTION=SIMPLE_CYLINDRICAL&RESOLUTION=256&RESAMP_METHOD=NEAREST_NEIGHBOR&BANDS_SELECTED=1&FORMAT=JPEG&LONBOX=2&LATBOX=2&GRIDLINE_FREQUENCY=0.1&STRETCH=AUTO&LAT=10.9&LON=49.2&LINE=512&SAMP=512)) we see the shadow is centered at around 10.9°N 49.2°W.
We can also look up the original image files at M04-03241 (http://www.msss.com/moc_gallery/ab1_m04/images/M0403241.html) (red) and M04-03242 (http://www.msss.com/moc_gallery/ab1_m04/images/M0403242.html) (blue), part of the gallery of MOC Wide-Angle Images, Region Lunae Palus, Subphase M04 (http://www.msss.com/moc_gallery/ab1_m04/watables/mc10-M04-wa.html). The "image start time" was 03:26:13.01 UTC, the "line integration time" is 80.4800 milliseconds, and the "downtrack summing" factor is 4. Since the shadow is centered at 6400 pixels from the bottom of the original 10800-pixel-high image (Mars Global Surveyor had a south-to-north sun-synchronous orbit), we add (6400 * 0.08048 * 4) = 2060.3 seconds = 34 minutes 20.3 seconds to get a time of 04:00:33.3 UTC for the center of the shadow.
Putting in the longitude/latitude/altitude coordinate values -310.8,10.9,0 into
JPL Horizons (http://ssd.jpl.nasa.gov/horizons.html) we see that the predicted time of mid-transit was 04:00:36 UTC, in perfect agreement within the error of determining the exact longitude and latitude of the center of the shadow. This was about 14:41 Martian local solar time, and the Sun's altitude was 46.5° above the horizon. JPL Horizons also shows that on August 26 1999 the distance between the Earth and Mars was 9.6 light-minutes.
Other shadow images
Phobos_shadow_1999-09-01.gif
Many dozens of other images of the shadow exist, but these are much lower resolution (by a factor of 27/4). Three such images are shown in the November 1 1999 NASA press release (http://mars.jpl.nasa.gov/mgs/msss/camera/images/11_1_99_phobos/index.html).
Note the timestamps printed on the photos in the NASA press release do not correspond to the actual time that the shadow was imaged, rather they represent the "image start time" of a vertically much larger original image. Mars Global Surveyor orbits Mars in a sun-synchronous polar orbit with orbital period 117.65 minutes, moving from south pole to north pole, and continuously points its camera straight down. The result is an image in the form of a very long thin vertical strip, where the pixels in the top part of the image are imaged nearly one hour after those in the bottom part of the image. In principle the image could be as much as 43200 pixels high, but "downtrack summing" is used to merge adjacent lines. For instance, a downtrack summing factor of 27 causes every 27 lines to be merged into one, resulting in an image 1600 pixels high. Thus to determine the actual time that the Phobos shadow was imaged, it is necessary to locate the original image and measure how many pixels from the bottom of the image the shadow is found and add the corresponding offset to the image start time.
For example, we examine the image labeled with the timestamp 9/1/1999 20:13:05 (UTC). We have the original images M07-00166 (http://www.msss.com/moc_gallery/m07_m12/images/M07/M0700166.html) (red) and M07-00167 (http://www.msss.com/moc_gallery/m07_m12/images/M07/M0700167.html) (blue), part of the gallery of MOC Global-Map Images, Subphase M07 (http://www.msss.com/moc_gallery/m07_m12/gmtables/M07-gm.1999-09-01.html). The shadow is situated at roughly 14°N 236°W (map (http://pdsmaps.wr.usgs.gov/explorer-bin/mapmars3.cgi?WHEREFROM=PZ&VERSION=ADVANCED&DATA_SET_NAME=v2mars_viking_bw&PIXEL_TYPE=BIT8&SCALE=pixels/degree&PROJECTION=SINUSOIDAL&RESOLUTION=64&RESAMP_METHOD=NEAREST_NEIGHBOR&BANDS_SELECTED=1&FORMAT=JPEG&LONBOX=20&LATBOX=10&GRIDLINE_FREQUENCY=1&STRETCH=AUTO&LAT=13&LON=235&LINE=960&SAMP=960)).
In this case the image start time is 20:13:04.69 UTC, the line integration time is 80.48 milliseconds, and the downtrack summing factor is 27. The shadow is about 8 pixels high, centered at 993 pixels from the bottom of the original 1600-pixel-high image. We add (993 * 0.08048 * 27) = 2157.75 seconds = 35 minutes 57.75 seconds to get a time of 20:49:02.4 UTC for the center of the shadow.
Putting in the longitude/latitude/altitude coordinate values -124,14,0 into JPL Horizons gives an expected time of 20:49 for the transit, which is in good agreement once again. On September 1 1999 the distance between the Earth and Mars was 9.9 light-minutes.
Seasonal variation in latitude
Phobos orbits near the equatorial plane of Mars, with an orbital inclination of only 1.08° and orbits fairly close to the surface of Mars. Thus, the latitude of its shadow projected onto the Martian surface shows a seasonal variation, moving from 70.4°S to 70.4°N and back again over the course of a Martian year. Phobos is so close to Mars that it is not visible south of 70.4°S or north of 70.4°N; for some days in the year, its shadow misses the surface entirely and falls north or south of Mars.
Thus for any given fixed geographical location on Mars, there are two intervals in each Martian year when the shadow of Phobos is passing through its latitude. During each such interval, that geographical location can experience about half a dozen transits of Phobos.
It is easy to see that the shadow always falls on the "winter hemisphere", except when it crosses the equator during the vernal equinox and the autumnal equinox. Thus transits of Phobos happen during Martian autumn and winter in the northern hemisphere and the southern hemisphere, roughly symmetrically around the winter solstice. Close to the equator they happen around the autumnal equinox and the vernal equinox; farther from the equator they happen closer to the winter solstice.
See also
External links
- NASA press release (http://mars.jpl.nasa.gov/mgs/msss/camera/images/11_1_99_phobos/index.html)
- Refinement of Phobos ephemeris using Mars Orbiter laser altimeter radiometry (http://www.lpi.usra.edu/meetings/lpsc2004/pdf/1820.pdf)
- JPL Horizons (http://ssd.jpl.nasa.gov/horizons.html) (use telnet interface for ephemeris of Phobos from points on Martian surface)
- Mars Global Surveyor Mars Orbiter Camera Image Gallery (http://www.msss.com/moc_gallery/)