Sky & Telescope - December 2024 - 66

Imaging Science
would be if we could observe it at a distance of 1 astronomical
unit (au) and a perfect elongation of 180°.
The equations to calculate the geometric albedo differ for
each planet and each color, and they are complex. However,
you don't need to be an accomplished mathematician to use
them. Simply input the formulae in Microsoft Excel, and the
program will do all the necessary work for you. To give one
example, I measured the apparent magnitude of Jupiter in the
V band to be −2.75 using two stars in Aquarius on the night
of November 9, 2022; the result is extremely close to the
expected value of −2.74. The equation is:
M = m − (−0.37 × α/100) + 0.616 × (α/100) + 5 × log (r × d)
where M is the absolute magnitude, m is the apparent magnitude
(−2.75), α is the phase angle in degrees (which was 8.6
that night), r is the distance between Jupiter and Earth in au
(4.238), and d is the Jupiter-Sun distance in au (4.952). The
coefficients of −0.37 and 0.616 characterize the behavior of
Jupiter in the V band. The result is a magnitude of −9.38.
Then, I find the ratio between the flux of Jupiter to that of
the Sun, which is called the L ratio. The equation is:
L ratio = 10^((MSun − MJup)/2.5)
MSun being simply the absolute magnitude of the Sun in V
(−26.75), and MJup the previously found, normalized magnitude.
The result is 1.13 × 10−7.
Finally, the geometric albedo is:
Albedo V = L ratio / sin2 (r/au)
where r is the radius of Jupiter (69,911 km) and au is the distance
of 1 au in kilometers (1.49 × 108). This produces a value
of 0.52, meaning that in the V band, Jupiter was reflecting
52% of the light it receives from the Sun.
Once the geometric albedo of a planet is established, you
can then measure its colors in two ways. I've determined the
global photometric profile of Jupiter's zones and belts using
the free software RSpec (rspec-astro.com). This program
allows me to analyze a light profile across a strip of an image
of my choosing. Positioning the aperture slit over the central
meridian of an image spanning north to south produces a
graph of the reflectivity of the belts and zones of the planet's
atmosphere. I focus on longitudes that I find representative
of the global state of the planet near opposition, at the
hemisphere opposite that of the GRS. This profile is measured
on a projected map of the calibrated image created in
the program WinJUPOS (https://is.gd/winJUPOS) in order
to accurately map the latitude of the features I am examining,
as seen on the top of the facing page. Another method
would be to aggregate a wider range of longitudes in each
measurement. This method requires very good seeing conditions,
so I rarely perform this action.
Finally, it's necessary to scale the albedo profile. In IRIS, I
APERTURE IS KEY Measuring the signal of a planet in IRIS
using its Aperture photometry tool is similar to measuring a
star, except the first circle needs to be large in order to encompass
the entire planet.
66 DECEMBER 2024 * SKY & TELESCOPE
measure the intensity of the entire globe with the Aperture
photometry tool described earlier, and in a second measurement
I use a circle that only covers the center of the Equatorial
Zone (EZ). Then I determine the ratio between the intensity
value of the EZ as if it had the same surface as the whole
planet and divide the former by the latter. The result is then
http://www.rspec-astro.com https://www.is.gd/winJUPOS
Sky & Telescope - December 2024

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