이상한 행성계 Zing (2부)

이상한 행성계 Zing (2부)

Zing's solar system
Some more information about Zing's orbit around its sun (Zun).

The orbit has a semi-major axis of 0.05 astronomical units, and a perihelion of 0.02 astronomical units (an astronomical unit is ). The Zun has a mass of 0.1 solar masses (a solar mass is , as you can deduce from the orbital period and semi-major axis).

The Zun has a luminosity of  solar luminosities (a solar luminosity is ).

The rotation axis of Zing is 9.4 degrees away from the pole of its orbit around the Zun.

Note that we are using units such as Earth days, solar luminosities and astronomical units that would be unfamiliar to the astronomers of Zing, as they are all based on the properties of Earth's solar system. The astronomers of Zing use quite different units, but I've converted them for the benefit of students in this class.

Historical records
You carried out a search of the historical archives to see if there were any records suggesting that the brightness or position of Zeor and the bloodstain had changed. Using records going back around 4000 years, you found no record of any observable changes in the brightness or position of either object. Neither Zeor nor the bloodstain move by a detectable amount as Zing orbits its Zun.

More sensitive images
Telescopes have been constructed to get more sensitive, higher resolution images of various parts of the sky.

The first target was Zeor. At first, it appeared to just be a white dot even when observed through telescopes. But as the telescopes became more refined and the image quality improved, you were able to make out details for the first time. Here is what the current best image looks like:

Close-up image of Zeor, showing two white rings surrounding a very faint red fuzz

This image is four arcseconds across. The fuzzyness is due to atmospheric seeing.

Next, your telescopes were pointed at the Bloodstain. Here is an image of a small central part of the bloodstain:

Close-up image of part of the bloodstain, showing close-packed red and yellow dots

Thirdly, you turned your telescopes on the rest of the sky, where nothing is visible to your unaided eyesight. Initially nothing was seen, but as more powerful telescopes were constructed and more of the sky was surveyed, a number of small faint red fuzzy shapes were seen:

Small red fuzzy object seen against black background

These objects are much too faint to be seen without the aid of telescopes. As more of the sky was surveyed, more of these red fuzzy things were found. Extrapolating, there seem to be thousands of them across the sky. Mostly they are so far apart that you never see two in the field of view of your telescope at once. But if you use a very wide-field telescope, there are a few places in the sky where a number of these objects seem to cluster, such as the region shown below:

Cluster of red fussy objects against a black background

Needless to say, these observations caused a sensation. For all of history, people on Zing had believed that there were only two objects in the sky. Now there seem to be thousands! Philosophers and religious leaders are mobbing the astronomers, TV shows about astronomy are topping the ratings, and online astronomy courses are being taken by tens of thousands of students, keen to learn more about these amazing results.

spectra
You obtained spectra of the bloodstain, the Zun and of Zeor. Here is a spectrum of the inner ring of Zeor:

Spectrum of the inner ring of Zeor. A flat, featureless spectrum

The spectrum of the outer ring looks similar:

Featrueless spectrum of the outer ring of Zeor

Here is a spectrum of the Zun:

Spectrum of the Zun. Very red with many broad features

Digital data here.

This spectrum has been studied for over a hundred years and is well understood. Most of the features are due to Titanium Dioxide, which forms clouds in the Zun's atmosphere. There are three well-studied absorption lines in the red - the Calcium Triplet, with laboratory wavelengths of 850.036 nm, 854.44nm and 866.452 nm. They show the doppler shifts you would expect due to the orbital motion of Zing around the Zun.

Finally, you obtained a spectrum of the bloodstain:

Spectrum of the bloodstain - red, and with similar but weaker features than the spectrum of the Zun.

Digital data here.

This too showed the Calcium triplet spectra lines. You took a higher spectral resolution spectrum of the wavelength region around these lines:

Bloodstain calcium triplet lines, at around 852.5nm, 857 nm and 869nm

Digital data here.

location of Zeor and the bloodstain in the sky
With all these new data coming in, you have decided to set up a coordinate system for objects in the sky. You have chosen to define Zeor as your north celestial pole. The centre of the bloodstain lies 170 degrees from Zeor, and you have chosen the great circle through Zeor and the centre of the bloodstain to be your prime meridian. This chart may help explain the coordinates you are using:

Chart showing coordinate system

You use Declination to indicate the north/south angle, and RA (Right Ascension) to indicate the East/West angle. Zeor is at Dec=+90 degrees. The centre of the bloodstain is at Dec=-80 degrees, RA = 0 degrees.

The pole of Zing's orbit around the Zun is at Dec=+27 degrees, RA=193 degrees. As seen from Zing, the location of the Zun when it is most distant from  Zing is in the direction Dec=-29 degrees, RA=265 degrees.