Venus is at its brightest -- why? And how to calculate it (Shallow Thoughts)

Venus is at its brightest -- why? And how to calculate it

Venus has been a beautiful sight in the evening sky for months, but at the end of April it's reaching a brightness peak, magnitude -4.7.

By then, if you look at it in a telescope or even good binoculars, you'll see it has waned to a crescent. That's a bit non-obvious: when the moon is a crescent, it's a lot fainter than a full moon. So why is Venus brightest in its crescent phase?

It has to do with their orbits. The moon is always about the same distance away, about 385,000 km or 239,000 miles (I've owned cars with more miles than that!), though it varies a little, from 362,600 km at perigee to 405,400 km at apogee.

When we look at the full moon, not only are we seeing the whole Earth-facing surface illuminated, but the central part of that light is reflecting straight up off the moon's surface. When we look at a crescent moon, we're seeing light that's near the moon's sunrise or sunset point -- dimmer and more spread out than the concentrated light of noon -- and in addition we're seeing less of it.

Venus, in contrast, varies its distance from us immensely. We can't see Venus when it's "full", because it's on the other side of the sun from us and lost in the sun's glow. It'll next be there a year from now, in April of 2013. But if we could see it when it's full, Venus would be a distant 1.7 AU from us. An AU is an Astronomical Unit, the average distance of the earth from the sun or about 89 million miles, so Venus when it's full is about 170 million miles away. Its disk is a tiny 9.9 arcseconds (an arcsecond is 1/3600 of a degree) -- about the size of Mars this month.

In contrast, when we look at the crescent Venus around the end of this month, although we're only seeing about 28% of its surface illuminated, and that only with glancing twilight rays, it's much closer to us -- less than half an AU, or about 45 million miles -- and its disk extends a huge 37 arcseconds, bigger than Jupiter this month.

Of course, eventually, as Venus pulls between us and the sun, its crescent gets so slim that even its huge size can't compensate. So its peak brightness happens when those two curves cross, when the disk is somewhere around 27% illuminated, as happens at the end of this month and the beginning of May.

Exactly when? Good question. The RASC Handbook says Venus' "greatest illuminated extent" is on April 30, but PyEphem and XEphem say Venus is actually brighter from May 3-8 ... and when it emerges from the sun's glare and moves into the morning sky in June, it'll be slightly brighter still, peaking at magnitude -4.8 in the first week of July.)

Tracking Venus with PyEphem

When I started my Shallow Sky column this month, I saw the notice of Venus's maximum brightness and greatest illuminated extent in the RASC Handbook. But I wanted more details -- how much did its distance and size really change, when would the brightness peak again as it emerged from the sun's glare, when would it next be "full"?

PyEphem made it easy to calculate all this. Just create an ephem.Venus() object, calculate its values for any date of interest, then print out parameters like phase, mag, earth_distance and size. In just a few minutes of programming, I had a nice table of Venus data.

import ephem

venus = ephem.Venus()

print '%10s   %6s %6s %6s %6s' % ('date', '%', 'mag', 'dist', 'size')
def print_venus(when) :
    venus.compute(when)
    fmt = '%02d-%02d-%02d   %6.2f %6.2f %6.2f %6.2f'
    trip = when.triple()
    print fmt % (trip[0], trip[1], trip[2],
                 venus.phase, venus.mag, venus.earth_distance, venus.size)

# Loop from the beginning of 2012 through the middle of 2013:
d = ephem.date('2012')
end_date = ephem.date('2013/6/1')
while d < end_date :
    print_venus(d)
    # Add a week:
    d = ephem.date(d + ephem.hour * 24)

I've found PyEphem very handy for calculations like this -- and it's great to be able to double-check listings in other publications.