Astronomy Trivia Challenge: Can You Answer These Questions About the Night Sky?

[marcus]

Originally posted by schwarzchildradius
OK, how do you measure the distance to the moon using lunar eclipse? What other observation of the moon must be made to find the distance to the sun?

Hipparchus measure the distance to the moon using eclipse data and got the result that the moon is 30 Earth diameters away which is quite close to the right answer.

However Hipparchus method is more complicated than I want to try to explain.

Earlier, Aristarchus (around 250 BC?) estimated the size of the moon compared with the Earth by observing an eclipse of the moon.

He judged that the Earth's shadow (roughly comparable in size to earth) was twice as big as the moon just by looking at the curve the shadow's edge made on the moon-----actually he should have guessed THREE times but he guessed twice the size.
Aristarchus was very back-of-envelope.

Knowing (in a rough sense) the size of the moon and the angle it made in the sky, Aristarchus could estimate the distance to the moon in Earth diameters.

He then observed the lunar dichotomy, which gave him at least a rough lower bound on the distance to the sun as a multiple of the distance to the moon.

Noting that the sun was an order of magnitude farther than the moon and therefore huge compared with the earth, he surmised a heliocentric model.

This guy was from Samos, same birthplace as Pythagoras.
Well Schwarzschild there is at least part of an answer
god save all Samians and the empire of the mind

 

[schwarzchildradius]

There you have it folks, righty-o.

The other observation was of the half moon - the moon is at 90 deg. from the sun when it is half full. You can use geometry to then (since you know the length of one side) find the distance and size of the sun. Your go.

 

[marcus]

Originally posted by schwarzchildradius
There you have it folks, righty-o.

The other observation was of the half moon - the moon is at 90 deg. from the sun when it is half full. You can use geometry to then (since you know the length of one side) find the distance and size of the sun. Your go.

Schwarzschildradius is a man of cultivation and discernment and has explained to us the method of lunar dichotomy.

In fact the sun is roughly 400 times the distance to the moon and therefore the angle (at halfmoon) is not 90 degrees but
90 degrees MINUS 1/400 RADIANS. Something like 89.8 or 89.9 degrees.

Aristarchus around 250BC measured it and got IIRC something like 89.5 degrees (he was clumsy at measuring angles, this Greek)
and so he judged that the sun was quite far away perhaps IIRC ten times as far as the moon! All the other greeks were quite astonished by this and could scarcely believe it. He should be awarded the Nobel prize postumously. Lunar dichotomy is a great phrase.

I like responding to questions a great deal better than I like asking them. Am tempted to appoint Schwarzschild my proxy and in invite him to pose a question for me. But perhaps it is better to keep it simple and stick by the rules.

QUESTION:
Describe "co-moving distance"
This is the astronomer's def of distance which works in the Hubble law v=H₀ D

So if you ever use that law you need to understand what the comoving distance to an object is.

What is the comoving distance to an object (at this moment in time) which is currently receding from us at 30 thousand kilometers a second?

 

[schwarzchildradius]

The answer to your particular question, is r=c/H, or something like 2e26 meters away. The answer to your general question, is that its the ratio of dx/dt (transverse velocity) to dθ/dt (proper motion), in other words, the distance measured by a "ruler" at specific time t.

 

[marcus]

Originally posted by schwarzchildradius
The answer to your particular question, is r=c/H, or something like 2e26 meters away. The answer to your general question, is that its the ratio of dx/dt (transverse velocity) to dθ/dt (proper motion), in other words, the distance measured by a "ruler" at specific time t.

Hello, your answer 2E26 meters is off by more than a factor of two so I'm afraid it will not do. But if you recalculate you will almost certainly get it.

Suggest using Hubble parameter of 71 km/s per Megaparsec
since that figure is not considered fairly reliable---the uncertainty has narrowed substantially about H₀.

I should have been more explicit about the Hubble Law distance.

There is a particular definition of distance that works in the law
and other types of distance (angular size distance, luminosity distance, light traveltime distance) do not work.
In his javascript distance calculator
http://www.astro.ucla.edu/~wright/CosmoCalc.html
Wright refers to this definition of distance as the
"comoving radial distance, which goes into Hubble's law".

That expression contains a link to where the distance is
defined and described, using diagrams and some detailed
explanation. That "comoving distance which goes into Hubble's law" is what I am looking for.

But I won't insist on the general question---just get the
specific one right and you win the prize.

 

[schwarzchildradius]

Fine
71 km/s/Mpc = 2.3e-18 s^-1
R = 1.3e26 m
off by 2^1/2, much less than the uncertainty in H
or if you like,
3R = 3.9e26 m

Do you (or anyone) know the metric for Homogeneous Isotropic Cosmological Models?

 

[marcus]

Originally posted by schwarzschildradius
Fine
71 km/s/Mpc = 2.3e-18 s^-1
R = 1.3e26 m...


Do you (or anyone) know the metric for Homogeneous Isotropic Cosmological Models?

Still not right. You have to solve the equation v = HD

for D, where H is exactly what you say it is and
v = 30,000 km per second.

You do realize, do you not, that I said 30 thousand km per second----a speed which is not equal to the speed of light?
When I said your answer is off by more than a factor of 2, I meant *more* than a factor of two, also more than a factor of 3.
Your answer is off by more than a factor of 4, hint hint.

Your answer, namely 1.3E26 meters. Is 13.7 billion light years!
Way too big!

 

[schwarzchildradius]

Someone else will have to play with you.

 

[marcus]

an algebra problem

Schwarzschildradius gives up.

Perhaps the problem is too simple for him.

The problem is, solve v = H₀ D, for D

where v is 30 thousand km/sec, i.e. one tenth the speed of light,

and H₀, the Hubble parameter, is (1/13.8 billion years).

 

[schwarzchildradius]

Whatever. Its against the rules for me to keep guessing, and the value is in fact irrelevant because of uncertainty in H.

 

[marcus]

Originally posted by schwarzchildradius
Whatever. Its against the rules for me to keep guessing, and the value is in fact irrelevant because of uncertainty in H.

Both of us are nice people and we just experienced a power-of-ten problem. That's all and it happens quite regularly.

You kept saying 13.7 billion light years when you should have
been saying 1.37 billion light years. And you were off because
you thought that when I said "30 thousand km/sec" I was saying the speed of light.

When actually I was saying c/10.

I blame this on the metric system. If I had simply said "c/10"
then you would have gotten the right result immediately.
c is the natural unit to use in astronomy.

Let's have it be your turn, since you got the right answer except for the dratted order magnitude

 

[Labguy]

General Comment:

Isn't this thread meant to be a "general" astronomy Q&A session instead of math excercises based on someone's assumptions (criteria) regarding some specific set of circumstances, sometimes theoretical and beyond "generally accepted"??

I don't mind the "Here is my theory" stuff, but there is another PF forum named "Theoretical Physics" where that is discussed with attempts to prove / disprove.

Carry on.

 

[Phobos]

Originally posted by Labguy
General Comment:

Isn't this thread meant to be a "general" astronomy Q&A session instead of math excercises based on someone's assumptions (criteria) regarding some specific set of circumstances, sometimes theoretical and beyond "generally accepted"??

I don't mind the "Here is my theory" stuff, but there is another PF forum named "Theoretical Physics" where that is discussed with attempts to prove / disprove.

Carry on.

Mentor hat on...

Overall, this forum is intended for "generally accepted" (dare I say, "mainstream") astronomy. "Here's my theory" goes into the Theory Development forum. Just keep that in mind...no major problems here so far.

As far as the general Q&A vs. math-heavy Q&A. I suppose it's either (1) up to Nicool002 (who started this thread) or (2) free market...if y'all want math, then knock yourselves out...if not, then this topic will evolve or die accordingly. Whatever. As long as it's good clean astronomy, then I'm happy. Certainly, many PF members have mastered general astronomy Q&A and are ready for more. But many PF members are new to astronomy.

Might I recommend 2 topics...one for beginners and one for advanced folks?

 

[marcus]

Originally posted by Phobos
Mentor hat on...


Might I recommend 2 topics...one for beginners and one for advanced folks?

Hello Phobos, why don't you ask a question at kick off another round?


The last question was about the v=H₀ D (Hubble law).

I asked, if v is a tenth of the speed of light (v = 30 thousand km/s)
then solve for D, the distance.

It did not get answered so maybe I can just invite someone to pose a question.

My thought is that the last question was about as basic, mainstream, and beginner-level as you can get in cosmology.
The Hubble parameter has been the main thing to measure and to use in estimating distance for several generations, the law
is fundamental to the field. So I wonder how the issue of "mainstream" arose. Is it too much math to involve a basic
equation like v=H₀ D?

 

[marcus]

Afterthought. I guess the other most basic thing
in cosmology is the density of the universe (rho)
as it compares to the critical density (rho_crit) required for flatness.

For some decades cosmologists have been
talking about how "the fate of the universe" depends
on the ratio

rho/rho_crit-------whether it is less than one
or equal to one (flatness) or greater than one.

Would it by any chance be considered not mainstream to
ask a question about the critical density on this thread?
I don't recall that I have, as yet, but was just now wondering,
since it seems so central to the field that I can't really
picture what conventional cosmology would be like without it.

 

[schwarzchildradius]

Just let's get this thing moving please ;)

 

[marcus]

Originally posted by schwarzchildradius
Just let's get this thing moving please ;)

OK, since no one else volunteers a question, I will ask:

What famous astronomer's mother was almost burnt as a witch?


(it didnt actually come to lighting the fire but she was tried
and came close to being burned)

god save the Hapsburgs and the holy roman empire!

 

[J-Man]

marcus asked:
What famous astronomer's mother was almost burnt as a witch?

Johannes Kepler

 

[marcus]

Originally posted by J-Man
Johannes Kepler

Attaboy! Your question

 

[J-Man]

What is a "reflection nebula"?
-Give a definition.
-Give an example.
-Extra points for brown-nosing.

 

[Labguy]

Originally posted by J-Man
What is a "reflection nebula"?
-Give a definition.
-Give an example.
-Extra points for brown-nosing.

A reflection nebula is an accumulation of dust and gas where the light, usually blue in color, is reflected off the dust and gas from one or more embedded stars. M20, the Trifid Nebula, is an example where it is seen as blue. It also happens to be an emmission nebula as well, with light being emmitted from ionized Hydrogen, usually seen as red.

I don't know any brown-nose points.

 

[J-Man]

Labguy answered:
A reflection nebula is an accumulation of dust and gas where the light, usually blue in color, is reflected off the dust and gas from one or more embedded stars. M20, the Trifid Nebula, is an example where it is seen as blue. It also happens to be an emmission nebula as well, with light being emmitted from ionized Hydrogen, usually seen as red.

Very good.

I don't know any brown-nose points.

That's okay, it's still your turn.

 

[Labguy]

Originally posted by J-Man
Very good.


That's okay, it's still your turn.

Ok, here is an EASY one. Two-parter.

(1) What event, important to observational astronomy, will happen on August 27, 2003? (**Later edit**: If we need very specific, you can use universal time OR EDT, since we are not always on the same day worldwide)

(2) When was this event last seen, to the same or greater degree, by any astronomer using any telescope or optical device to enhance the unaided eye??

Note: I expect this one to be answered instantly by the first PF member to read it...(?)

 

[Ivan Seeking]

Originally posted by Labguy
Ok, here is an EASY one. Two-parter.

(1) What event, important to observational astronomy, will happen on August 27, 2003? (**Later edit**: If we need very specific, you can use universal time OR EDT, since we are not always on the same day worldwide)

(2) When was this event last seen, to the same or greater degree, by any astronomer using any telescope or optical device to enhance the unaided eye??

Note: I expect this one to be answered instantly by the first PF member to read it...(?)

The closest approach of Mars in 73,000 years.
Never.

 

[Labguy]

Originally posted by Ivan Seeking
The closest approach of Mars in 73,000 years.
Never.

CORRECT.
Your question.

 

[Ivan Seeking]

Originally posted by Labguy
CORRECT.
Your question.

You tricky devil you.

Ok. Now if you read my other posts don't worry. I'm not going pseudo or philosophical on you.

What are the hypothetical circumstances, if we can show [mathematically] that one can control his position in time but not in space?

Edit:The language used may be a little optimistic:

What are the hypothetical circumstances, if we can show [mathematically] that one can affect his position in time but not in space?

 

[Ivan Seeking]

I quoted since I wasn't sure if edits alert readers of a change.

Originally posted by Ivan Seeking
Edit:The language used may be a little optimistic:
What are the hypothetical circumstances, if we can show [mathematically] that one can affect his position in time but not in space?

 

[schwarzchildradius]

So, are you asking the circumstances under which a particle can move in space but not in time? If v=c, this is the case I think. (T=infinity)

 

[Ivan Seeking]

Originally posted by schwarzchildradius
So, are you asking the circumstances under which a particle can move in space but not in time? If v=c, this is the case I think. (T=infinity)

But that would violate Relativity. [?]
I don't think that qualifies unless you mean some really abstract circumstance that "actually" occurs, or could occur. schwarzchildradius

 

[schwarzchildradius]

only if you consider light abstract, which I guess it kind of is. if you could "ride" light, of course, you wouldn't be moving through time.

 

[Ivan Seeking]

Originally posted by schwarzchildradius
only if you consider light abstract, which I guess it kind of is. if you could "ride" light, of course, you wouldn't be moving through time.

"...one can affect his position in time but not in space"

No voodoo needed. But it wouldn't be pretty! schwarzchildradius

 

[J-Man]

Originally posted by Ivan Seeking
The language used may be a little optimistic:
What are the hypothetical circumstances, if we can show [mathematically] that one can affect his position in time but not in space?

I'm not sure I understand the question but...

f(x) = 0 * x = 0 for all x
f(y) = 0 * y = 0 for all y
f(z) = 0 * z = 0 for all z
f(t) = h(t)

Where h(t) is some function of time independent of the 3 spatial "variables".
Basically, position is invariant, or the coordinate system used moves with the hypothetical person.

 

[Ivan Seeking]

Originally posted by J-Man
I'm not sure I understand the question but...

f(x) = 0 * x = 0 for all x
f(y) = 0 * y = 0 for all y
f(z) = 0 * z = 0 for all z
f(t) = h(t)

Where h(t) is some function of time independent of the 3 spatial "variables".
Basically, position is invariant, or the coordinate system used moves with the hypothetical person.

Clever, but I don't mean to be that tricky. I am trying to ask a hard question not a tricky one; but the thing that makes it hard is tricky.

Hint: Where is our schwarzchildradius?

 

[marcus]

as soon as one gets inside the event horizon of a black hole

"one can no more avoid the singularity than one can avoid
next Tuesday"

the direction towards the center becomes the time direction.

perhaps this responds appropriately to the question?

 

[chroot]

Originally posted by marcus
the direction towards the center becomes the time direction.

I can't say I agree with the either this message or the language itself.

It is true that all worldlines inside a black hole at some point intersect the singularity, but it is not true that all worldlines are geodesics. You can still have fuel in your rocket when you cross the horizon, and you can still zoom about inside the horizon in non-inertial motion.

The bottom line is that since two observers can cross the horizon at the same place and follow two different trajectories once inside, there's no way you could even qualitatively think of "the direction towards the center" as being the "time direction."

I think this question is bordering on the philosophical, since it eventually comes down to semantics.

- Warren

 

[schwarzchildradius]

Ah, could it be that Ivan is seeking the conditions on the inside of a black hole event horizon?

 

[Ivan Seeking]

Originally posted by marcus
as soon as one gets inside the event horizon of a black hole

"one can no more avoid the singularity than one can avoid
next Tuesday"

the direction towards the center becomes the time direction.

perhaps this responds appropriately to the question?

I was wondering how many times I could say schwarzchildradius and get away with it. CORRECT!
You're up marcus.

 

[Ivan Seeking]

Originally posted by chroot
You can still have fuel in your rocket when you cross the horizon, and you can still zoom about inside the horizon in non-inertial motion.

The space coordinates exchange roles with time and become imaginary. According to my notes from a senior level GR class - taught by a very good professor - this is the proper interpretation. If this is incorrect or outdated, I am not in a position to argue this point with much proficiency.

 

[marcus]

Originally posted by Ivan Seeking
You're up marcus.

The first star to which the distance was measured is_______

(I don't mean the sun I mean a "real" star.)

Who measured the distance? In what year?
How far away is this star?

For extra points, what is the parallax angle by which
the first stellar distance was determined?


Footnote---not part of question---Christian Huygens estimated the distance to the star Sirius in a clever way long before parallax measurement was possible. How he did it is almost funny. But I am not considering that as the first real measurement, so it would
just be distracting to describe his method.

 

[Labguy]

Originally posted by marcus
The first star to which the distance was measured is_______

(I don't mean the sun I mean a "real" star.)

Who measured the distance? In what year?
How far away is this star?

For extra points, what is the parallax angle by which
the first stellar distance was determined?


Footnote---not part of question---Christian Huygens estimated the distance to the star Sirius in a clever way long before parallax measurement was possible. How he did it is almost funny. But I am not considering that as the first real measurement, so it would
just be distracting to describe his method.

(A) 61 Cygni, a double of red dwarfs.
(B) F.W. Bessel in 1838.
(C) 10.3 LY.
(D) 0.29 arc seconds.
(E) Measured by parallax.

 

[marcus]

Originally posted by Labguy
(A) 61 Cygni, a double of red dwarfs.
(B) F.W. Bessel in 1838.
(C) 10.3 LY.
(D) 0.29 arc seconds.
(E) Measured by parallax.

Right on! Labguy it is your go.
This is the kind of conversation!
When people know about Bessel, I mean. 1838 a time of giants.
Darwin was just getting Evolution theory written down that year. Faraday visualizing lines of force.
God bless Bessel, put the first yardstick to the stars.
BTW Britannica say he measured 0.31 arc seconds but
so close and don't know who is right you or Britannica,
so call it 0.29.
Bravo. your turn.

 

[schwarzchildradius]

sun was discovered before 1838. Aristarchus, wasn't it? 300 BC?

 

[marcus]

Originally posted by schwarzchildradius
sun was discovered before 1838. Aristarchus, wasn't it? 300 BC?

the sun was ruled out in the question---we just had a question on the thread relating to Aristarchus----so when I asked the question I said the sun was not the answer I was looking for.
better luck next time

Labguy's turn

 

[Labguy]

Ok, another easy one: An easy internet look-up.

Re-list, in order of size (Stellar Masses), from biggest to smallest, the following stellar classes with approximate masses and lifetimes. This is based on a total lifetime of our Sun as 10 billion years. Not restricted to just main sequence.

Stellar Class:
A:
F:
B:
MO:
BO:
K0:
G2 (Our Sun)
O3:
M7-8

Just type a list (in order) with class, ~Mass and ~Lifetime in years (Use millions, billions or trillions).

EDIT: I removed "size" typed in by mistake. The first criteria is mass.

 

[chroot]

I'm not sure this question is well posed.

The order of surface temperatures is OBAFGKM in order of highest to lowest.

However, the spectral type alone is not enough to determine mass. You would also need luminosity. There's no such thing as an "average mass" for a given spectral type.

Lifetime is, of course, tied to mass.

- Warren

 

[Labguy]

Originally posted by chroot
I'm not sure this question is well posed.

The order of surface temperatures is OBAFGKM in order of highest to lowest.

However, the spectral type alone is not enough to determine mass. You would also need luminosity. There's no such thing as an "average mass" for a given spectral type.

Lifetime is, of course, tied to mass.

- Warren

The surface temperatures can only be seen from the spectra of the photosphere. While on the main sequence, the larger mass leads to higher temperatures, so there is a direct correlation between temperature and mass until the main sequence is left behind. There is a definite "average" mass for an M type star vs. a star formed as a B type. Also there is a huge difference in "average lifetimes", as you say dependent on mass. Part of a giveaway is that there is no way that an M type star (depending on whether M0 to M9) will have a mass below 0.08 Sm or much above 0.1 Sm. This type of star cannot create a high surface temperature simply because there is not enough mass to generate the fusion processes that would lead to high temperatures.

The original question stands, but nobody has to be very exacting, just good estimates in correct order.

 

[marcus]

Originally posted by Labguy
Ok, another easy one: An easy internet look-up.

Re-list, in order of size (Stellar Masses), from biggest to smallest, the following stellar classes with approximate masses and lifetimes. This is based on a total lifetime of our Sun as 10 billion years. Not restricted to just main sequence.

Stellar Class:
A:
F:
B:
MO:
BO:
K0:
G2 (Our Sun)
O3:
M7-8

Just type a list (in order) with class, ~Mass and ~Lifetime in years (Use millions, billions or trillions).

EDIT: I removed "size" typed in by mistake. The first criteria is mass.

http://nrumiano.free.fr/Estars/classes.html

You originally wanted the radius, mass, and lifetime of the different spectral classes listed. I found a table on the web that gives figures for these and other characteristics:
spectral type, luminosity, mass, radius, lifetime, surface temperature, and the relative abundance in our galaxy.

No table can be perfect. There is variation which a simple table cannot adequately cover. But we can try to do the best we can by way of giving representative benchmarks of each range.

I don't see any harm in including the radius (that you edited out).
My problem is that I don't know how to copy a table into PF.
It will take time

 

[marcus]

From the site I gave the link to:

Spectral class
Mass (solar mass)
Radius (solar radius)
Luminosity
Surface temperature (degrees K)
Life time (million of years)

W ---- >40---- 20 ---1.000.000 --- 50.000 ----- <1
O5 ----- 32---- 18 -----600.000 ---- 40.000 ----- 1
B0 ----- 16 -----7.4 ----- 16.000 ---- 28.000 ----- 10
B5 -----6.5---- 3.8 -----600 ------- 15.500 -----100
A0 ----- 3.2----- 2.5----- 60 -------- 9.900 ------500
A5 ----- 2.1 -----1.7 ----20 --------- 8.500 ----- 1.000
F0 ----- 1.75 ---- 1.4 ----- 6 ---------7.400------ 2.000
F5 -----1.25 ------1.2 -----3 -----------6.600 ----- 4.000
G0 -----1.06 ----- 1.1 ----- 1.3 --------6.000 ----- 10.000
G2 Sun -- 1 ----- 1------- 1---------- 5.800 -------- 12.000
G5 ----- 0.92 ---- 0.9 -----0.8 ------- 5.500 --------15.000
K0 ----- 0.80 ---- 0.8 ------ 0.4 ------ 4.900 ------- 20.000
K5 ----- 0.69 ---- 0.7 ------ 0.1 ------ 4.100 ------- 30.000
M0 ----- 0.48 ----0.6 ------ 0.02 ---- 3.500 ------75.000
M5 ----- 0.20 ---- 0.3 ----- 0.001 ---- 2.800 ----- 200.000

 

[Labguy]

Very good summary table. It is not exactly the one I had which showed a few more specific examples, but is close enough to be called correct.

I will "cut and paste" part of where I was looking, but don't want to give the URL now because it has lots of neat stuff I might want to hit you with later...

Here is part of my question source:

Type O3: 120 Sm 63 thousand years.
Type O: 25 Sm 3.2 million years.
Type B: 10 Sm 32 million years.
Type A: 2.5 Sm 1.0 billion years.
Type F: 1.3 Sm 5.2 billion years.
Type G2:(Sun) 1.0 Sm 10 billion years.
Type K0: 0.7 Sm 24 billion years.
Type M0: 0.5 Sm 57 billion years.
Type M7-8 <0.1 Sm 3.2 trillion years.

Note the mere 63 thousand years for an O3! Also, other readers should note from your site that class and mass are related. The exceptions come when a star leaves the main sequence. For example, a large, massive red giant swells to where the temperature is very low (red spectrum), while a tiny white dwarf has little mass but is hotter than hell; high temperature.

Your question next.

 

[marcus]

Originally posted by Labguy
Your question next.

In cosmology there is the idea of being at rest with respect to the CMB or the "Hubble flow"----which is the expansion of space.
So there is an absolute rest frame (unlike in special relativity) which corresponds to being at rest with respect to the expansion of space.

The solar system has an absolute velocity with respect to the CMB.
In what direction is it?
What is the solar system's speed in kilometers per second?