Re: I'm curious as to the light levels around the 4 gas giants.

7/11/00

Dear Douglas,

Better than I could ever describe in words--scientists at the Space Telescope Science Institute have made "true color" images of Jupiter and Saturn from HST WF/PC2 shots.

For the one of Saturn, see http://heritage.stsci.edu/public/oct22/saturn/saturntable.html

For the one of Jupiter(bonus--with comet S/L9 impact), see http://oposite.stsci.edu/pubinfo/Comet/Comet_2.html

Caveat about these "true color" images. There are 3 components to answering your question about how the outer planets would look to your eye:resolution, color, and sensitivity. Take the example of Jupiter.

1. resolution- How much detail could you see?

The HST can see details 200 miles across from 420 *million* miles away (from the photo caption). If you're vision were that good at such long distances, your eye doctor would call it about 61000/20. The practical resolution of the human eye, on the fovia centralis (the central region of the retina, densely packed with cones), after aberrations and averaged over individual variation, is between 5 and 10 minutes of arc for point sources. Linear structures can often be resolved down to 1 min. (from C.R. Kitchin's Astrophysical Techniques, 2nd ed.) In order to see detail like the HST did from Earth orbit in that photo with 5 min resolution, you have to be in orbit at a distance of about 221,000 km, or about ten times further out than the farthest moons of the planet. From there, Jupiter (with a radius of 71680 km) would be about 36 degrees across on the sky. Not too bad a view!

2. color- What color(s) would it appear to be?

This is a primary reason I refer you to the HST WF/PC2 composites. They are constructed from properly combined red, green, and blue filter images to show the colors of the planets as your eye would perceive them. What you would see is the scattered sunlight from the clouds of different chemical compositions, altitudes, temperatures, and pressures. It would be very difficult for me to calculate how the colors would look a priori, so the composites are the answer to the color component. The details behind making images like this are an application of the field of "colorimetry", which is the study of the spectral sensitivity of human vision and the quantification of colors (ever wonder about the gorey details of color standards and mappings, like RGB and CMYK?).

3. sensitivity- How bright would it appear to you?

Let's do a little optical photometry. Although astronomers tend to use the term "photometry" much more loosely, a professional in the field of optics would define it as something like "the study of the propagation of light power through free-space and passive elements (a.k.a. radiometry) relating to the sensitivity of the human eye".

The photometric unit of power is the "lumen". Think of it as the physical power output of a source corrected for the spectral response function of the eye. The next time you shop for light bulbs, look for the amount of lumens it provides on the label. This is what tells you how well it lights up a room for you, as opposed to the watts which just tell you how big your electric bill will be. To get the most brightness for your energy buck, maximize lumens/watt when you shop. Flourescents will be efficient compared to incandescents.

Brightness, as we see it, is proportional to "illuminance" at the retina (lumens/m^2). Some examples: The sun at zenith = 1.2*10^5, 60 W incandescent lamp at 1m = 100, full moon at zenith = 0.27.

It's not too hard to estimate the illuminance due to Jupiter, given some basic facts and an assumption. We know the "luminance" (a.k.a. surface brightness) of the sun, the solid angle the sun subtends from Jupiter(2.5*10^-6), and the albedo of Jupiter (0.51). We also know the basic optical properties of the eye; the index of refraction of the vitreous humor (1.336), and the opening angle of the pupil (3 deg). We assume that Jupiter is a Lambertian scatterer (scatters power equally into all directions). From these, the luminance of Jupiter is about 810 lumens/m^2/sr. Then, the illuminance at your retina is about 9 lumens/m^2, about 33 times brighter than the full moon, but less than 1/10,000th the brightness of the overhead sun.

In case you (or I) don't immediately believe me, we can use this result to predict Jupiter's apparent visual magnitude. According to the UKIRT calibration web site, a magnitude 0.00 star corresponds to a flux density of 3.44*10^-8 W/m^2/micron. If the method of the above calculation for the scattered luminance of Jupiter is basically correct (by conservation of radiance and dilution by lambertian scattering), then I can estimate a physical flux density at earth during opposition of about 10^-6 Watt/m^2/micron in the visible, which with calibration data from the UKIRT website gives an apparent visual magnitude of -3.7. When I looked it up, it was about -2.7. Ok--the estimate was a magnitude bright-- but I didn't take absorption in earth's atmosphere into account (which would adjust my number a bit toward -2.7), and considering that I was also assuming that Jupiter is a perfect scatterer, dividing by the visible band as a block, and generally rounding here and there, that's not too bad a correspondence (within a factor 2.5 in flux units).

So, the visceral experience you should be imagining is something noticibly brighter than the moon, but taking up a round area of about 72 moon diameters in your sky (each moon is 0.5 degrees), and looking a lot in color and detail like the Hubble images I referred you to.

Finally, I'm going to refer you to a couple of things so you can investigate more deeply into photometry and colorimetry matters if you're interested. Then you can explore the outer planets yourself! Please pick up Robert Boyd's Radiometry and the Detection of Optical Radiation. It's an excellent, clear and concise book for introducing yourself to the basics of light propagation, meausurement, detectors, and noise, and it has a good chapter on photometry and the eye. For a pretty neat introduction to the whole topic of vision and color, see the Web Book Joy of Visual Perception by Peter Kaiser of York University, under the Technical Division of Vision and Color of the Optical Society of America (OSA) (http://www.osa.org/homes/vision/). Be prepared for some funny physical units when learning about photometry. Finally--though their website is not too illustrative for the lay-person, the most widely recognized organization for establishing standards in human perception of light and color is the CIE (Commission Internationale de l'Eclairage --http://www.cie.co.at/cie/).

Thanks for being patient ;},

Kristin Nelson-Patel