Quote of the Day
Successful ... politicians are insecure and intimidated men. They advance politically only as they placate, appease, bribe, seduce, bamboozle or otherwise manage to manipulate the demanding and threatening elements in their constituencies.
— Walter Lippmann (1955). Hmm … no change in politicians over the last 61 years.
Introduction
Figure 1: Artist's Conception of the View From a Base on Metis. (Source)
The arrival of the Juno spacecraft at Jupiter has motivated me to take a look a closer look at the Jovian system. I was surprised to see that we have cataloged 67 moons, sixteen of which have been discovered since 2003 and are not yet named. One moon that was new to me is called Metis (Figure 2), which is Jupiter's innermost moon. It is very tiny and resides within Jupiter's main ring, where it acts as a shepherd.
Figure 2: Metis Photograph from Galileo Spacecraft. (Source)
The Wikipedia's article on this moon had an interesting statement that I thought I would try to verify.
Because Metis orbits very close to Jupiter, Jupiter appears as a gigantic sphere about 67.9° in diameter from Metis , the largest angular diameter as viewed from any of Jupiter's moons. For the same reason only 31% of Jupiter's surface is visible from Metis at any one time, the most limited view of Jupiter from any of its moons.
I was able to confirm the 67.9° angular diameter, but I believe the 31% value is in error and should be 22%. I have posted a comment to the Wikipedia requesting that those folks double-check that number.
P.S. The Wikipedia has removed this statement from the Metis article because it could not be corroborated with a peer-reviewed reference.
Analysis
Geometry
Figure 3 shows the basic Jupiter viewing geometry from Metis. For information on how to compute the viewing area on a sphere in terms of the viewing angle θ, see the Wikipedia article on spherical caps.
Figure 3: Visual Geometry of Metis to Jupiter. All dimensions to scale except that of Metis, which would be invisible at this scale.
Calculations
Figure 4 shows my calculations that verify the Wikipedia's statement on Jupiter's viewing angle from Metis. I could not confirm their statement on percent viewable area, but I believe that I understand where our calculations differ – I obtain their value if I fail to divide the viewing angle by half for the spherical cap area calculation.
I present an alternative form of the percent viewable area formula in Appendix A. You can find further discussion on this form on this web page.
Figure 4: Viewing Angle and Jupiter Viewing Area Calculations.
Conclusion
I like to imagine looking up at night and seeing a sky full of a planet. It would be an incredible sight. Unfortunately, Metis is a tiny, cold world that is exposed to an enormous amount of radiation. I cannot imagine humans ever visiting there.
Figure 5 shows a beautiful rendering of the view of Jupiter from Metis.
Figure 5: View of Jupiter from Metis Using Space Engine. (Source)
Appendix A: Alternative Percent Viewable Area Formula
A Wikipedia editor commented that I could express the viewable area of a satellite using a simpler formula if I chose a different parameter than the angular diameter. Figure 6 shows percent viewing area formula using the satellite and planet radii as parameters.
Figure 6: Alternative Form of the Percentage Viewable Area Formula.