observation - What were the challenges for the ancients to observe the orbit of the Moon (instead of Mars)?

Wasn't it pretty obvious to a careful astrologer a thousand years ago, that the Moon does not have a circular orbit and does not describe epi-cycles?

The ancient Greek model of the motion of planetary bodies remained unchallenged for almost two millennia, so obviously not.

Hipparchus' model did a fairly good job dealing with the elliptical motion of the Moon; it did even better with the planets. The Moon's motion is tough to model because of perturbations by the Sun, Venus, and Jupiter. Ptolemy discovered what would eventually be called evection, the largest of the perturbations caused by the Sun. There was one problem with Ptolemy's model: It had the Moon swinging in and out by a huge amount. If Ptolemy's model was correct, we would see the Moon changing in diameter by a factor of two over the course of a bit over half an orbit. Copernicus much later came up with a scheme that fixed this problem and still relied on those old concepts of deferents, equants, epicycles, etc.

While Newton pointed the way to describing the Moon's orbit, it wouldn't be until 200 years after Newton's death that a decent (one that matches observations) model of the Moon's orbit was developed.

spectra - Definition question: continuum-subtracted spectrum

A spectrum of, say, a star or a galaxy, consists of wavelengths emitted from various physical processes. In the case of the star, there is the blackbody spectrum that reflects the temperature of all of its gas, whether it is hydrogen, helium, or metals. On top of this, there are lines, i.e. emission from certain atomic transitions that are excited and then de-excite emitting photons in a very narrow wavelength interval. The blackbody spectrum is said to comprise the continuum of the total spectrum.

In the case of galaxies, the continuum consists of the combined spectrum of many different stars' different blackbody spectra, infrared light from dust, etc. On top of this, there are lines, e.g. from nebular processes such as my favorite line Lyman $alpha$, which is emitted when hard UV radiation from hot O and B stars ionize their surrounding neutral hydrogen, which subsequently recombines emitting mostly Lyman $alpha$.

If we want to measure the total flux in a given line, we are usually only interested in the flux that comes from a particular physical process, and not the part of the flux that comes from the "underlying" sources which contribute to the continuum. Hence, we need to subtract the continuum. This is usually done by fitting some functional form to the continuum (e.g. a straight line or a second order polynomial), substract this fit from the spectrum, and finally integrate from one side of the line to the other in the resulting "continuum-subtracted spectrum".

In the top figure below, the total spectrum's flux density$^dagger$ is in black, and the fit is the red lines. Underneath is drawn the continuum-subtracted spectrum, and a few dashed green lines show some lines that rise above the continuum. The integrated line flux is indicated by light red.

$^dagger$_{Note that many authors use the term "flux" where it should actually be "flux density". Integrating flux density in $mathrm{erg},mathrm{s}^{-1},mathrm{cm}^{-2},mathrm{Å}^{-1}$ over wavelength in Å$^{-1}$ gives flux in $mathrm{erg},mathrm{s}^{-1},mathrm{cm}^{-2}$.}

solar system - Why did Mercury not appear to transit through the middle of the sun?

As Mercury is inclined by 7 degrees relative to the orbit of the Earth (the ecliptic) at any given time it may be above the ecliptic or below. However there are two times during its orbit when it crosses the ecliptic. These are known as "nodes".

A conjunction occurs when the planet is vertically above or below the sun. A superior conjunction happens when the planet is on the far side of the sun, an inferior conjunction happens when the planet is closer to the Earth than the sun.

When a node occurs at about the same time as an inferior conjunction, then the planet will appear to travel in front of the sun. Whether it travels through the middle of the solar disk, or through the upper or lower part, depends on whether the exact time of the node occurs just before the conjunction or just after.

In May 2016, Mercury crossed the ecliptic at about 08:00 (utc), and had it inferior conjuction at about 15:00. It was a little below the ecliptic by the time of conjunction, but still close enough to cross the solar disk.

The exact position of Mercury also depends on the location you are viewing from on Earth, a fact that Edmond Halley noticed could be exploited to calculate the distance to the planet, and by extension, the distance to the sun.

Are stars really "burning balls of gas"?

While I agree that it boils down to semantics, I actually disagree on the scientific use of the term in the comments. In astronomy, we know there's a difference between gas and plasma, but we almost always use the term "gas" when talking about what's in stars. E.g. "the fraction of gas locked up in stars" (as opposed to in the interstellar medium). We also talk about the metallicity of gas, meaning both gas and plasma. I think we only use the term plasma when specifically discussing properties that are unique to plasma, like being "frozen" in magnetic fields. And googling ["ionized gas" -plasma] (the '-plasma' is to get rid of articles explaining what plasma is) returns 243,000 hits, of which by far the most seem to be scientific papers and websites.

So I think the answer is: "No, stars aren't made of gas, they're made of plasma, but go ahead and call it gas, you won't offend any astronomer."

However, I agree with Rob Jeffries that we don't like when you call it burning gas. It's nuclear power! It's a million$^dagger$ times more powerful than fire!

$^dagger$_{Why "a million"? Because nuclear reactions are measured in MeV, while chemical reactions are measured in eV.}

Do stars have exactly sphere shape?

No, no stars have an exactly spherical shape. The reason for this is that the centrifugal force of the star's rotation is much greater at the equator of the star than it is at the poles, for the simple reason that the rotational velocity is greater. This greater centrifugal force pushes the equator outwards, stretching the star into an oblate shape. This is called gravity darkening.

Because we have only visually resolved the surfaces of a few other stars, it's not something that is commonly directly observed (though the effect can also be observed from stellar spectra). Regulus is one star that has been observed as an oblate spheroid spectrographically. The image below shows the star Altair, directly imaged using the CHANDRA space telescope. Go here for an animation!

Some stars are also non-spherical due to the effects of a nearby star in a close binary orbit. Much like how the Moon causes tides on Earth, two stars can stretch each other's surfaces. If they're very close to one another, as in the picture below, there can even be mass transfer between them (ref common envelope).

solar system - Why do comets appear to have a continuous supply of dust?

The rate of loss of mass from a comet is perhaps surprisingly low. A paper The calculation of $Afrho$ and mass loss rate for comets gives a rate for a "typical" comet at 1.29AU as 153kg/s. A typical comet has a mass of about $10^{13}kg$. Even if the comet is constantly active (and they are not) it would have enough material for over 2000 years.

In fact comets are only active when the are near perihelion, and they are only near perihelion for a small fraction of their orbit. Put it together and you have the potential for an active life of hundreds of thousands of years.

Eventually, however, comets do run out of volatile substances, at which point they become inactive, and appear as small dark asteroids. An example of which is the object 2015 TB145, which passed the Earth on Halloween 2015.

Note: not "oxidising", but "vaporising", the ices in the comet are changing into gas, but there is no burning.

the moon - Illusion of a lunar eclipse

A little over half a year ago, I think it was mid March 2015, I glanced out of my window at about 4 am, to see what appeared to be a very bright total lunar eclipse, as in, the moon was full and bright orange-red. As I watched, it disappeared before my eyes, looking as if someone slid a paper down in front of it. The moon was not full that night (and by extension that means that there couldn't have been an eclipse that night) and the next few nights, the moon was on the other side of the sky at 4 am.

The room I was in was dark, so it couldn't have been a reflection on the window of something inside the house. It might have been a reflection on the window of something outside the house, but that's not very likely, because it was very bright and opaque (something would have to be really bright to look so bright and opaque when reflected off a window, and I can't think of anything that would have been so bright. Plus, I probably would have noticed something something so bright), it didn't move when I moved my head around, and it looked exactly like the moon – it had the same dark and light spots. I would have taken a picture of it, it would be a lot easier to understand what I mean if you would see it, but it disappeared really fast.

It might have been a reflection on the clouds. I don't recall if there were clouds in the sky, I wasn't paying that much attention to the sky around it, because while it was happening I just thought it was an eclipse. But if it was a reflection on the clouds, there's still the question of what was being reflected.

I asked someone who knows a lot about a bunch of topics, but is not good at explaining what he means, what it could have been, and he said something about solar flares, I didn't really get what he was saying. I would ask him again, but I don't know him personally and I don't know how to contact him, and in any case, I don't think he would explain it any better the second time.

I searched everywhere I could possibly think of (on the web, on Q&A sites, on SE) for a cause for this, but couldn't find anything like it.

What I'm asking is this: Could it have been a reflection on the clouds, and if so, what could it have been of? Could it have been caused by a solar flare or something like it, and if so, how? Is there an astronomical event that occurred around that time that could have caused something like that, and if so, what and how?

This question was put on hold as unclear what you're asking, so if anyone has any suggestions that can make the question more clear, I would love to hear it. I wish I could be more precise about when it happened, or what exactly it looked like, but I didn't write it down or note it in any way at the time, so this is pretty much all I remember.

solar system - Is Pluto still a dwarf planet?

A lot of the push to have Pluto reinstated as the 9th planet is coming from Harvard, from their press release Is Pluto a Planet? The Votes Are In (Released September, 2014), they state the following outcomes from a debate:

Science historian Dr. Owen Gingerich, who chaired the IAU planet definition committee, presented the historical viewpoint. Dr. Gareth Williams, associate director of the Minor Planet Center, presented the IAU's viewpoint. And Dr. Dimitar Sasselov, director of the Harvard Origins of Life Initiative, presented the exoplanet scientist's viewpoint.

Gingerich argued that "a planet is a culturally defined word that
changes over time," and that Pluto is a planet. Williams defended the
IAU definition, which declares that Pluto is not a planet. And
Sasselov defined a planet as "the smallest spherical lump of matter
that formed around stars or stellar remnants," which means Pluto is a
planet.

We will have a better understanding of Pluto, hence its classification when NASA's Horizons mission reaches it. But, at this stage, Pluto is still classified as a dwarf planet.

galaxy - Help w/ Hubble's Law + Doppler Effect.

I had a question about the following chart. What mathematical observation or equation could be made about the data given in respect to the doppler effect? I'm confused if this means that planets are moving at an exponential rate away from us? Would these galaxies appear blue shifted? Thank you in advance for any sort of help.

jupiter - Need help with the math in Python program to flag Jovian radio emissions

A few days ago I decided to take on the little project of converting a Qbasic program into Python (as a side project to my Radio Jove project), and I've managed to get it to run, but the math is definitely off. I was hoping for a fellow astronomer or astrophysicist to assist in the mathematical side of my Python code. Obviously something is wrong with the math aspect of the code since most of the values in the python program are very skewed. My apologies in advance for the single character variables. I would make them better if I knew everything going on.

Qbasic code:

'Program to flag Jovian Decametric windows
 m$ = "JANFEBMARAPRMAYJUNJULAUGSEPOCTNOVDEC"
     wi = 42.46 / 360
     pi = 3.141593
     kr = pi / 180
     f$ = "###    ##   ##.#     ###      ###    ##.##       "
 OPEN "jovrad.txt" FOR OUTPUT AS #1
 INPUT "Year for which predictions are required"; yy
 e = INT((yy - 1) / 100)
 f = 2 - e + INT(e / 4)
 jd = INT(365.25 * (yy - 1)) + 1721423 + f + .5
 d0 = jd - 2435108
 incr = 0
 IF yy / 400 - INT(yy / 400) = 0 THEN incr = 1
 yyly = yy / 4 - INT(yy / 4)
 yylc = yy / 100 - INT(yy / 100)
 IF yyly = 0 AND yylc <> 0 THEN incr = 1
 ty = 59 + incr
 dmax = 365 + incr
 tx = ty + .5
 PRINT #1, "******************************************************"
 PRINT #1, "  JOVIAN IO-DECAMETRIC EMISSION PREDICTIONS FOR"; yy
 PRINT #1, "******************************************************"
 PRINT #1,
 PRINT #1, "Day   Date   Hr(UT)  Io_Phase   CML   Dist(AU)  Source"
 PRINT #1,
 th = 0
 DO
   GOSUB Compute
   s$ = ""
       IF L3 < 255 AND L3 > 200 AND U1 < 250 AND U1 > 220 THEN s$ = "Io-A"
   IF L3 < 180 AND L3 > 105 AND U1 < 100 AND U1 > 80 THEN s$ = "Io-B"
       IF L3 < 350 AND L3 > 300 AND U1 < 250 AND U1 > 230 THEN s$ = "Io-C"
   IF s$ <> "" THEN GOSUB Outdat
   th = th + .5
 LOOP UNTIL INT(th / 24) + 1 > dmax
 PRINT "Program completed - results in file JOVRAD.TXT"
 END

Compute:
 d = d0 + th / 24
 v = (157.0456 + .0011159# * d) MOD 360
 m = (357.2148 + .9856003# * d) MOD 360
 n = (94.3455 + .0830853# * d + .33 * SIN(kr * v)) MOD 360
 j = (351.4266 + .9025179# * d - .33 * SIN(kr * v)) MOD 360
 a = 1.916 * SIN(kr * m) + .02 * SIN(kr * 2 * m)
 b = 5.552 * SIN(kr * n) + .167 * SIN(kr * 2 * n)
 k = j + a - b
 r = 1.00014 - .01672 * COS(kr * m) - .00014 * COS(kr * 2 * m)
 re = 5.20867 - .25192 * COS(kr * n) - .0061 * COS(kr * 2 * n)
 dt = SQR(re * re + r * r - 2 * re * r * COS(kr * k))
 sp = r * SIN(kr * k) / dt
 ps = sp / .017452
 dl = d - dt / 173
 pb = ps - b
 xi = 150.4529 * INT(dl) + 870.4529 * (dl - INT(dl))
 L3 = (274.319 + pb + xi + .01016 * 51) MOD 360
 U1 = 101.5265 + 203.405863# * dl + pb
 U2 = 67.81114 + 101.291632# * dl + pb
 z = (2 * (U1 - U2)) MOD 360
 U1 = U1 + .472 * SIN(kr * z)
 U1 = (U1 + 180) MOD 360
RETURN

Outdat:
 dy = INT(th / 24) + 1
 h = th - (dy - 1) * 24
 IF dy > ty THEN
   m = INT((dy - tx) / 30.6) + 3
   da = dy - ty - INT((m - 3) * 30.6 + .5)
 ELSE
   m = INT((dy - 1) / 31) + 1
   da = dy - (m - 1) * 31
 END IF
 mn$ = MID$(m$, (m - 1) * 3 + 1, 3)
     PRINT #1, USING f$; dy; mn$; da; h; U1; L3; dt; s$
RETURN

Sample output:

******************************************************
  JOVIAN IO-DECAMETRIC EMISSION PREDICTIONS FOR 1994 
******************************************************

Day   Date   Hr(UT)  Io_Phase   CML   Dist(AU)  Source

  4  JAN  4   11.0     228      205     5.81     Io-A
  4  JAN  4   11.5     233      224     5.81     Io-A
  4  JAN  4   12.0     237      242     5.81     Io-A
  6  JAN  6    6.0     233      325     5.78     Io-C
  6  JAN  6    6.5     237      343     5.78     Io-C
  7  JAN  7    6.5      81      133     5.76     Io-B
  7  JAN  7    7.0      86      152     5.76     Io-B
  7  JAN  7    7.5      90      170     5.76     Io-B
  9  JAN  9   20.0     241      203     5.73     Io-A
  9  JAN  9   20.5     246      222     5.73     Io-A
 11  JAN 11   12.5     225      232     5.70     Io-A
 11  JAN 11   13.0     229      251     5.70     Io-A
 11  JAN 11   14.5     242      305     5.70     Io-C
 11  JAN 11   15.0     246      323     5.70     Io-C
 12  JAN 12   15.0      90      113     5.68     Io-B
 12  JAN 12   15.5      94      131     5.68     Io-B
 12  JAN 12   16.0      98      150     5.68     Io-B
 14  JAN 14    8.5      82      179     5.66     Io-B
 16  JAN 16   21.0     234      214     5.61     Io-A
 16  JAN 16   21.5     238      232     5.61     Io-A
 16  JAN 16   22.0     242      250     5.61     Io-A
 18  JAN 18   15.5     234      315     5.59     Io-C
 18  JAN 18   16.0     238      333     5.59     Io-C
 19  JAN 19   16.0      82      124     5.57     Io-B
 19  JAN 19   16.5      86      142     5.57     Io-B
 19  JAN 19   17.0      91      160     5.57     Io-B
 19  JAN 19   17.5      95      178     5.57     Io-B

Python code:

#!/usr/bin/env python
from __future__ import print_function, division
import math
print('Program to flag Jovian Decametric windows')
month = ['JAN','FEB','MAR','APR','MAY','JUN','JUL','AUG','SEP','OCT','NOV','DEC']
week = 42.46/360
pi = 3.141593
kr = pi / 180
form = "###    ##   ##.#     ###      ###    ##.##       \"
num1 = open('jovrad.txt', 'w')
yy = int(raw_input(("Year for which predictions are required ")))
e = math.trunc(((yy-1) / 100))
f = 2 - e + math.trunc(e/4)
jd = math.trunc(365.25 * (yy - 1)) + 1721423 + f + .5
d0 = jd - 2435108
incr = 0
dmax = 0
tx = 0
ty = 0
yyly = 0
yylc = 0
if yy / 400 - math.trunc((yy / 400)) == 0:
    incr = 1
    yyly = yy / 4 - math.trunc((yy / 4))
    yylc = yy / 100 - math.trunc((yy / 100))
if yyly == 0 and yylc != 0:
    incr = 1
    ty = 59 + incr
    dmax = 365 + incr
    tx = ty + .5
print("******************************************************", file=num1)
print("  JOVIAN IO-DECAMETRIC EMISSION PREDICTIONS FOR ",yy, file=num1)
print("******************************************************", file=num1)
print("n", file=num1)
print("Day   Date   Hr(UT)  Io_Phase   CML   Dist(AU)  Source", file=num1)
print("n", file=num1)
th = 0
def compute(d0, th, dmax):
    global U1, L3, dt, s
    d = d0 + math.trunc(th / 24)
    v = (157.0456 + .0011159 * d) % 360
    m = (357.2148 + .9856003 * d) % 360
    n = (94.3455 + .0830853 * d + .33 * math.sin(kr * v)) % 360
    j = (351.4266 + .9025179 * d - .33 * math.sin(kr * v)) % 360
    a = 1.916 * math.sin(kr * m) + .02 * math.sin(kr * 2 * m)
    b = 5.552 * math.sin(kr * n) + .167 * math.sin(kr * 2 * n)
    k = j + a - b
    r = 1.00014 - .01672 * math.cos(kr * m) - .00014 * math.cos(kr * 2 * m)
    re = 5.20867 - .25192 * math.cos(kr * n) - .0061 * math.cos(kr * 2 * n)
    dt = math.sqrt(re * re + r * r - 2 * re * r * math.cos(kr * k))
    sp = r * math.sin(kr * k) / dt
    ps = sp / .017452
    dl = d - dt / 173
    pb = ps - b
    xi = 150.4529 * math.trunc((dl)) + 870.4529 * (dl - math.trunc((dl)))
    L3 = (274.319 + pb + xi + .01016 * 51) % 360
    U1 = 101.5265 + 203.405863 * dl + pb
    U2 = 67.81114 + 101.291632 * dl + pb
    z = (2 * (U1 - U2)) % 360
    U1 = U1 + .472 * math.sin(kr * z)
    U1 = (U1 + 180) % 360
    s = ""
    while math.trunc(th / 24) + 1 < dmax and math.trunc(th / 24) + 1 == dmax:
        if L3 < 255 and L3 > 200 and U1 < 250 and U1 > 220:
            s = "Io-A"
        if L3 < 180 and L3 > 105 and U1 < 100 and U1 > 80:
            s = "Io-B"
        if L3 < 350 and L3 > 300 and U1 < 250 and U1 > 230:
            s = "Io-C"
        if s != "":
            outdat()
        th = th + .5
    print("Program completed - results in file JOVRAD.TXT", file=num1)
compute(d0, th, dmax)

def outdat(th,tx,ty):
    dy = math.trunc((th / 24)) + 1
    h = th - (dy - 1) * 24
    if(dy > th):
        m = math.trunc((dy - tx) / 30.6) + 3
        da = dy - ty - math.trunc((m - 3) * 30.6 + .5)
    else:
        m = math.trunc((dy - 1) / 31) + 1
        da = dy - (m - 1) * 31
    mn = month[(m-1)*3+1:(m-1)*3-1+3]
    print(dy, mn, da, h, U1, L3, dt, s, file=num1)
outdat(th,tx,ty)

My current output:

******************************************************
  JOVIAN IO-DECAMETRIC EMISSION PREDICTIONS FOR  1998
******************************************************


Day   Date   Hr(UT)  Io_Phase   CML   Dist(AU)  Source


-12.9775 1.0 ['AUG'] -0.5 0.0 135.325782651 10.6054462674 5.7071322535