For use with Schaefer's lunar occultation limiting magnitude calculator written in QBasic at url: http://media.skyandtelescope.com/binary/occvis.bas at S&T's Basic program archive at url http://www.skyandtelescope.com/resources/software/3304911.html. For instructions on how to run an old Qbasic calculator under Windows XP, see Sky & Telescope. "Question: Can I run programs from past issues of S&T, written in BASIC, on my Windows XP computer? " (last accessed Aug. 29, 2009).
The output of Schaefer's lunar occulation limiting magnitude program is the faintest star that can be visually seen just before occultation.
The Schaefer lunar occultation program has also been adapted to report the sky brightness at the lunar limb in mpsas. (Schaefer's program already computed brightness at the lunar limb in nanoLamberts. See code adaptation at Lines 811-815.) Another online calculator will determine the contrast index. See Fisher, Kurt A. (amateur). 2008. Conversion Calculator for NELM(V) to MPSAS (B) systems. (Web calculator). url: http://members.csolutions.net/fisherka/astronote/plan/tlmnelm/html/NELM2BCalc.html (last accessed 26 Aug. 2009).
A version of Schaefer's lunar occulation limiting magnitude program with the above modifications has been prepared and is available at url:
http://members.csolutions.net/fisherka/astronote/observed/LCROSS/occvis_slcut.bas
The modified model responds to inputing light pollution parameters. A table of the appropriate light pollution values is provided below. The input units are in nanoLamberts formatted in scientific notation as recited in the light pollution parameter table.
Modeling using light pollution as a factor indicates that light pollution may be a factor in observing the LCROSS impact. It is recommended that observers travel to a dark sky or rural sky site to observe the impact.
Default parameters are suggested for Salt Lake City, Utah for the LCROSS impact specific values for a dark sky in northern Utah at the end of astronomical twilight on Oct. 9, 2009 11:30UT and a 10 inch Newtonian visually observing at 300 power.
The parameter values suggested below can be used to explore several questions using a quantitative model:
To use the model at other observing points, the two main observing point specific parameters that need to be determined from a planetarium program:
Program output demonstrating how the model is used, modified for Salt Lake City UT LCROSS-impact assumptions is:
Moon's sunlit percentage 71 Alt in SLC UT is 74.58 degs (90-74.58=15.4 Zenith Distance) Zenith distance of star (degrees) for SLC Enter 15.4 or enter your o.p.'s Sun altitude. Zenith distance of star 15.4 Height of Sun above horizon in SLC Enter -23.1 or enter your o.p.'s Sun altitude. Height of Sun above horizon -23.1 Cusp angle (<0 for bright side) in deg. Enter -87 for an assumed impact slightly on bright terminator side or enter 87 for an assumed impact slighty on dark side of terminator. Cusp angle (<0 for bright side) in deg -87 Vis. extinction coeff. (mag./airmass) 0 Brightness from light pollution (nL) in SLC Enter 7.96E+08 for a 3.8 ZLM. Or enter 0. Recommend entering 0 first for a dark sky, then rerun with light polluted sky. Brightness from light polution (nL) 0 Seeing disk diameter at zenith (arcsec) 1.5 Moon fraction in field of view (%) 17 Telescope aperture (inches) 10 Magnification 300 Telescope throughput (%) 88 Equivalent LCROSS cloud integrated magnitude .9 Chose program mode -- (1) Minimum aperture (2) Limiting magnitude ? 2 Limiting magnitude is 5.263015 Apparent sky brightness (in atmosphere) (nL) at lunar limb 4.567543E+08 Apparent sky brightness (in atmosphere) MPSAS at lunar limb 14.7617
The program example output suggests that from a dark sky site an integrated magnitude 5.3 star is the faintest star that could be seen next to the polar lunar limb using that 10 inch Newtonian at a 71% lunar illuminated fraction. (Without moonlight, the scope can reach stars of magnitude 14.0.) The sky brightness at the limb, including lunar glare is predicted at 14.8 mpsas.
Since the LCROSS team has predicted a cloud brightness of about 3.0 mpsas at 550nm, it would appear that neither lunar glare nor advancing astronomical twilight will overwhelm the ejecta cloud brightness. There is an ample contrast index of 4.7.
Changing the program example by adding a 3.0 mag light polluted sky (1.56E+11 nanoLamberts from the light pollution parameter table, below), suggests that -0.9 star is the faintest star that could be seen just on the bright side of the terminator at a lunar pole. The apparent sky brightness just above the pole is predicted at 12.0 mpsas. The contrast index is still positive at 3.6.
Users can adapt these parameters for their predicted local observing circumstances.
This is an amateur note. Corrections and criticisms to this note are welcomed.
The Moon's illuminated fraction for your observing point taken from a planetarium program or other ephemeris source.
For the LCROSS impact use 71%.
90 degrees minus the star's altitude. Since the star is at the same altitude as the Moon, this also zenithal distance of the Moon. Use the altitude of the Moon or the lunar south pole, taken from a planetarium program or other ephemeris source.
The projected altitude of the Sun at the time of observation. This is important for events like LCROSS that will occur between astronomical and nautical twilight. Between astronomical and nautical twilight, sky brightness changes by the minute. Obtain from a planetarium program or other ephemeris source.
Range is between 0 (North lunar pole) to 90 (south lunar pole) on the dark limb and 0 (north lunar pole) to -90 (south lunar pole).
Use -87.0 to -85.0 for the LCROSS impact. The impact will most probably be just into the bright limb. If the impact area is Faustini, Faustini will be slightly in the dark limb and use 87.0.
Leave at 0.7. The Moon reflects sunlight. The sun is yellow type G2: CI = 0.63
| Altitude range degs | Adjustment |
|---|---|
| 90-52 | 0.0 |
| 52-36 | 0.1 |
| 36-29 | 0.2 |
| 29-24 | 0.3 |
| 24-20 | 0.4 |
| 20-18 | 0.5 |
In testing the model's sensitivity, the model does respond to light pollution values. This factor can be ignored. Leave it at zero or enter the value from the table below in the exponential format shown.
Sensitivity analysis indicates that the LCROSS ejecta curtain will not be visible from light polluted urban areas.
Average naked-eye-limiting magnitude without the Moon at the the Moon's projected altitude. Read the NELM from the left-hand column. Read-out nano-Lamberts from the right-hand column.
| NELM | MPSAS | nL |
|---|---|---|
| 6.0 | 20.8 | 1.20E+03 |
| 5.8 | 20.5 | 2.52E+03 |
| 5.6 | 20.2 | 4.87E+03 |
| 5.4 | 19.9 | 9.20E+03 |
| 5.2 | 19.6 | 1.67E+04 |
| 5.0 | 19.3 | 3.02E+04 |
| 4.8 | 19.0 | 5.35E+04 |
| 4.6 | 18.8 | 9.09E+04 |
| 4.4 | 18.5 | 1.54E+05 |
| 4.2 | 18.3 | 2.63E+05 |
| 4.0 | 16.0 | 3.24E+07 |
| 3.8 | 14.5 | 7.96E+08 |
| 3.6 | 13.7 | 4.72E+09 |
| 3.4 | 13.0 | 1.88E+10 |
| 3.2 | 12.5 | 5.77E+10 |
| 3.0 | 12.0 | 1.56E+11 |
| 2.8 | 11.6 | 3.98E+11 |
| 2.6 | 11.2 | 8.71E+11 |
| 2.4 | 10.8 | 1.87E+12 |
| 2.2 | 10.5 | 3.76E+12 |
| 2.0 | 10.2 | 7.26E+12 |
Use a 10 inch minimum scope.
Based on experience, 200 power is a reasonable minimum and 500 power a reasonable maximum.
This value is dependent on the magnification applied. Assuming that the Moon has a mean diameter of 1850 arcsecs and that the telescope is pointed at the south polar limb with the limb bissecting the image, then:
| Power | EP_AFVO | TFOV_arcsec | Moon_dia_arcsec | Moon_frac | Moon_frac_bisected | |
|---|---|---|---|---|---|---|
| 150 | 52 | 1248 | 1866 | 67% | 33% | |
| 200 | 52 | 936 | 1866 | 50% | 25% | |
| 250 | 52 | 749 | 1866 | 40% | 20% | |
| 300 | 52 | 624 | 1866 | 33% | 17% | |
| 350 | 52 | 535 | 1866 | 29% | 14% | |
| 400 | 52 | 468 | 1866 | 25% | 13% | |
| 450 | 52 | 416 | 1866 | 22% | 11% | |
| 500 | 52 | 374 | 1866 | 20% | 10% |
| Telescope type | Transmission (%) |
|---|---|
| Refractor | 99% |
| Newtonian | 88% |
| SCT | 87%> |
Calculate from your eyeglass prescription. If you observe without your glasses, use the uncorrected value. If you observe with your glasses on, use your corrected vision.
Mag. 8.61 - the default value in Schaefer's calculator - represents the magnitude for a faint occultation star. For the LCROSS impact use the equivalent integrated magnitude for one of the following scenario values depending on what you expect to occur. The equivocation of the LCROSS team maximum predicted cloud brightness of about 3.0 mpsas at a single frequency of 550nm to an integrated magnitude is false and understates brightness. To convert between mpsas and an integrated magnitude, the mpsas based on the full visual spectrum between about 380 nm and 1100 nm is needed. That value has not been reported. Therefore, the more conservative single frequency mpsas is substituted here.
| Scenario | Conservative cloud dia arcs | Integrated mags | Max cloud dia estimate | MPSAS | Integrated mags |
|---|---|---|---|---|---|
| 3.0 mpsas at 550nm | 3 arcsecs 0.05 arcmins 10km x 5km | 0.9 | 12 arcsecs 0.2 arcmins 20km x 20km | -2.1 | |
| 4.0 mpsas at 550nm | 3 arcsecs 0.05 arcmins 10km x 5km | 1.9 | 12 arcsecs 0.2 arcmins 20km x 20km | -1.1 | |
| 5.0 mpsas at 550nm | 3 arcsecs 0.05 arcmins 10km x 5km | 2.9 | 12 arcsecs 0.2 arcmins 20km x 20km | -0.1 | |
| 6.0 mpsas at 550nm | 3 arcsecs 0.05 arcmins 10km x 5km | 3.9 | 12 arcsecs 0.2 arcmins 20km x 20km | -0.9 |
Prepared K. Fisher fisherka@csolutions.net rev. 8/29/2009