Author Topic: Venus/Jupiter conjunction 30 June  (Read 1125 times)

charles

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Venus/Jupiter conjunction 30 June
« on: July 01, 2015, 03:12:28 PM »
I had hoped to find both planets during the afternoon, but the weather became partly cloudy, and remained so, and this was not practical. I did manage to track the two planets between about 9 and 11pm, and a striking sight they were.
The most striking thing was the different surface brightnesses of the two planets, which was very apparent when Venus came into easy naked eye visibility at about 9pm. Jupiter was visible nearby, but only just overcoming the brightness of the sky. As the evening went on, and the sky became darker, this contrast was less apparent, but that is clearly a matter of perception by the eye.
This difference was not of itself a surprise. Venus was about 2 1/2 magnitudes brighter than Jupiter, which translates to a ratio of about 11.  Venus was a 1/3 illuminated crescent, whereas Jupiter was fully illuminated, and both had an apparent diameter of about 30", so the apparent surface area of Venus was 1/3 that of Jupiter. It follows that the apparent surface brightness of Venus was 3x11 = 33 times that of Jupiter.
I have tried to explain this brightness difference from the known characteristics of the 2 planets. Venus' albedo is almost twice that of Jupiter, which leaves a factor of 20 to be explained. Jupiter is about 7 times further than Venus from the sun, so by the inverse square law a given actual surface area (well, cloud area!) of Jupiter receives 1/49th of the illumination of the same area on Venus. But it is not as simple as that, because the comparisons I made earlier were of the amounts of light received from bodies of equivalent angular diameter.
I am missing something here on this hot afternoon (30 deg plus outside) . Any ideas? :-\

Chuck McPartlin

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Re: Venus/Jupiter conjunction 30 June
« Reply #1 on: July 02, 2015, 04:23:50 AM »
Charles -

After reading your post, I thought I'd try calculating the brightness difference, ignoring atmospheric absorption (figuring both would suffer equally), and possible albedo differences by wavelength, or Lambert reflection - just using flux in Watts per square meter. My equations were: Flux at Earth := (Flux at planet * Albedo * phase * area) / (distance from Earth) **2.

Values used (from aa.usno.navy.mil and nssdc.gsfc.nasa.gov) were (at 2200 UTC on June 30): Flux at Venus 2613.9 W/m**2, Albedo 0.90, Phase 0.34, Radius 6051800 meters, Distance 0.5167 AU; Flux at Jupiter 50.50 W/m**2, Albedo 0.343, Phase 0.996, Radius 69911000 meters (spherical volumetric equivalent for elliptical Jupiter), Distance 6.0755 AU.

Magnitude difference: Mv - Mj = -2.5 Log10(FEv / FEj), where FE is Flux at Earth above.

I got Mv - Mj of -4.2, or Venus appearing about 10.5 times brighter than Jupiter.

At the time, actual Mv was -4.41 and Mj was -1.64, with Venus appearing 6.96 times brighter than Jupiter.

Still not agreement, and I undoubtedly have something misunderstood, but still a fun exercise. Thanks for the excuse to play. We only saw the conjunction briefly through some clouds just after sunset here.

Hasta nebula - Chuck

charles

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Re: Venus/Jupiter conjunction 30 June
« Reply #2 on: July 11, 2015, 05:00:29 PM »
Chuck
Your method seems pretty good to me, and at least gets close to the observed effect! I am still pondering the surface brightness approach; partly because its implications for  daytime visibility.
But I am puzzled as to how you translate magnitude difference to brightness ratios. I would expect a magnitude difference of 4.2 to correspond to a brightness difference of about 48, and a magnitude difference of (4.4 -1.6 = 2.8 leaving out the negatives for simplicity) to imply a brightness difference of about 13.
Charles

Chuck McPartlin

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Re: Venus/Jupiter conjunction 30 June
« Reply #3 on: July 30, 2015, 08:27:45 PM »
Charles -

You're absolutely right - I goofed up the brightness difference. Not very bright on my part!

Hasta nebula - Chuck