35

This can get a bit confusing, because "arcminute" and "minute" are both sometimes used in celestial coordinate systems but mean two different things. An arcminute is 1/60th of a degree, and an arcsecond is 1/60th of an arcminute. That's simple enough, and when talking about small angular distances, it's often much handier to refer to ...


15

Your trigonometry book isn't wrong: both "minute" and "arcminute" can refer to $\frac1{60}$ of a degree. It's certainly a very good idea to use the term "arcminute" when referring to $\frac1{60}$ of a degree, but it's not essential if there's no ambiguity, eg, in a static geometry problem where there's no mention of time. The ...


12

Your best bet is probably a distance-limited catalog designed to include everything within a specific distance. The most recent such compilation I'm aware of is Reylé et al. (2021), which has a limit of 10 pc and includes slightly more than 300 (hydrogen-burning) stars, along with about 20 white dwarfs and several dozen brown dwarfs. They note that they are ...


10

When I look at my clock (which is 3 metres from my chair) I see how it was about 10 nanoseconds ago. I don't see the clock "now", but always a little time in the past. When you look at the sun, you see how it looked 8½ minutes ago. When you look at GN-z11 you see how it looked 13.4 billion years ago. That is a fundamental fact about our universe. ...


8

I did some rough calculations, and 100 light-years doesn't seem to be a bad guess. If we assume that the average mass of a halo star is $\sim0.3M_{\odot}$, as would be expected for a typical IMF, and that the total stellar halo mass is $\sim10^9M_{\odot}$ (Deason et al. 2019), then we should expect there to be $\sim3.3\times10^9$ halo stars.$^{\dagger}$ The ...


8

Trigonometric parallaxes are measured, not calculated. Simbad reports the source of its parallax measurements if you look carefully. For example, Simbad reports Rigel's parallax as $3.78\pm 0.34$ milli-arcsecs, which comes from the revised Hipparcos catalogue of van Leeuwen et al. (2007) (which will be the case for many bright stars that do not feature in ...


7

The distance is that reported by Bihain et al. (2013), which is based on a mean relationship between absolute magnitude and spectral type that has a lot of scatter. i.e. in contrast to most (all?) the other objects in that list, there is no reported trigonometric parallax measurement for this very faint T7.5 brown dwarf. In fact, if it turned out to be a ...


7

To find the distance from one star to another, we need three things for both of the stars: their right ascensions, declinations, and the distance from Earth to those stars. So, let's get those things: From the Wikipedia page on Alpha Centauri: $RA = 14^h\:39^m\:36.49400^s$ $DEC = -60^{\circ}\:50'\:0.23737''$ $R = 4.37\:\rm{ly}$ (you gave 4.366, some other ...


7

Shameless self-plug: I made a catalog of the BSC5P that has 3D positions, colour, and other goodies ready for use: https://github.com/feynmansbongos/BSC5P-JSON-XYZ It is released to public domain under CC0. In case it's useful, I detail below how I created it. Obtaining the raw data I started with the BSC5P data from HEASARC, but 95% of the stars in that ...


6

There seems to be a misconception. You can use type 1a supernovae as standard candles for nearby and distant galaxies. But nearby galaxies have individual stars visible and resolvable, and these include Cepheid variables which can also be used as standard candles. Moreover, supernovae only occur rarely, so if no supernova occurs, you have to wait, whereas ...


5

I can show you an ESA Series exercise I did a few months ago for an astronomy class. Given the light curve of 12 cepheid variable stars in the galaxy M100 (which are very nice standard candles to measure large distances): We can find the distance between us and the M100, a spiral galaxy in the Virgo cluster, using the apparent magnitude m and the absolute ...


5

This is a really interesting question to many and it deserves an answer post even if folks close it. In Wikipedia's List of the most distant astronomical objects we can see that the distances that the light travelled to get to us are all around 13 giga light years, and it's no coincidence that the age of the universe is also about 13 billion years. We can't ...


5

That depends on how accurate you want your answer. The reason is that the angle $\theta$ spanned by a length $L = 1\,\mathrm{Mpc}$ depends on the distance $d$ of that length — in comoving coordinates, $\theta$ keeps decreasing with $d$, just like a normal item, say a bicycle, looks smaller the farther away it is (curiously, in physical coordinates, this is ...


4

In about 26,000 years, Proxima Centauri will no longer be the closest star. Instead, Alpha Centauri AB will be the closest, but only for about ~7000 years, soon replaced by Ross 248 for 10000 years, and Gliese 445 for 6000 years. Then, Alpha Centauri will continue to be the nearest star for another ~28000 years, then briefly becoming Ross 128. Refer to the ...


4

You can calculate the absolute magnitude of a star: $$M=m-5\log_{10}(\frac{d}{10\,\text{pc}})$$ where $M$ is absolute magnitude, $m$ is apparent magnitude and $d$ is the distance. Then you take a look at the HR diagram. One can easily see, that you need two data to obtain the third one, but we have only one data (absolute magnitude). That means, that you ...


4

Our eyes are not good enough to see the difference; Jupiter has an angular diameter of 29.8" to 50.1", while Saturn's is 14.5" to 20.1"; with rings, which are about 2.25 times as wide as the planet, this becomes 32.6" to 45.2". All well within the 60" (1 arcminute) angular resolution of the human eye. Now, when you use a ...


4

As far as I know direct parallax measurements are the only way to directly measure the distances to stars. Once parallaxs of hundreds of stars were known and diagrams of the relationship between stellar luminosity and spectral types, such as the Hertzsrpung-Russel diagram, were made, it became possible to estimate a star's absolute magnitude more or less ...


4

First, to measure the angle accurately, you need a point of reference at approximately infinite distance. In astronomy, this is in the form of very distant stars; for your earthly example, perhaps it can be an even more distant building almost on the horizon. Next, we look at the angular separation between the object with significant parallax, and the object ...


4

In actual fact its a bit more complicated, because the Earth's orbit is not perfectly circular, The star does not lie exactly on the Earth's orbital plane, so the observation is not a line of movement but an ellipse both the Sun and the Star are moving relative to everything, so the ellipse is not an ellipse but a helix Observational errors from various ...


4

Ned Wright's cosmology calculator will calculate all of the distances, and the age of the universe at the time the light was emitted, given a redshift $z$ and some cosmological parameters. Your best bet is to look up the redshift of the objects you're interested in, rather than trying to start from a comoving distance (which was originally calculated from ...


3

From Wikipedia In his 1698 book, Cosmotheoros, Christiaan Huygens estimated the distance to Sirius at 27664 times the distance from the Earth to the Sun (about 0.437 light years, translating to a parallax of roughly 7.5 arcseconds). and It was also in this book that Huygens published his method for estimating stellar distances. He made a series of smaller ...


3

Supplementary to @uhoh's answer: According to the wikipedia page he links, the most distant imaged object is a galaxy classed GN-z11. GN-z11 is a high-redshift galaxy found in the constellation Ursa Major. The discovery was published in a paper headed by P.A. Oesch and Gabriel Brammer (Cosmic Dawn Center). GN-z11 is currently the oldest and most distant ...


3

I'm not looking stuff up to write this so any inaccuracies are secondary to my feeble 63 year old memory yet again betraying me. In A Treatise on the System of The World. (His own Principia for Dummies which was published posthumously because he didn’t want to give his critics and those that wanted to dispute the new science ammunition against him) Newton ...


3

Parsec or Parallax-arcsecond is defined as the 'distance' of something that has a parallax angle of one arc second. The International Astronomical Union (IAU) define 1 parsec(pc) as: $$1 \text{pc} = 1/\tan(1'') \ \text{au}$$ $$\Rightarrow 1 \text{pc} = 1/\tan({1\over60}') \ \text{au}$$ $$\Rightarrow 1 \text{pc} = 1/\tan({1\over60\times60}^{\circ}) \ \text{au}...


3

You can just use these upper and lower bounds to create an upper/lower bound for the distance modulus. The lower bound is $168-14.9 = 153.1$, and the upper bound is $168+27.5 = 195.5.$ You can calculate the distance moduli for these values to get upper and lower bounds: $$5\log(153.1) - 5 = 5.924876 \\ 5\log(195.5) - 5 = 6.455734$$ Then we calculate the ...


3

You measure it on the photographs. If you take multiple images of the same star over the year you will find that it moves in a loop (compared to the very distant background stars) You measure the size of the loop. A larger loop is a larger angle. Because the angles are small, the size of the loop is in direct proportion to the angle. If you know the scale ...


3

Most distance methods are luminosity-based: you measure an object's flux, assume it has a particular luminosity, and then determine the distance from that using the inverse-square law. So the question becomes: how do you determine the luminosity? The eclipsing-binary method uses the idea that a star's luminosity can be defined as $L = 4 \pi f_{s} R^{2}$, ...


3

The answer is Yes. Everything you see in deep space is old. We see the sun 8 minutes in the past, the Proxima Centauri we see is 4.2 years old, The Andromeda galaxy we see is 2.5 million years old, The black-hole scientists took a picture of is 50 million years old. The deeper we look, the older it is, because the light we see has to travel a longer distance ...


2

Angular diameter distance is the reduced circumference of the circle, centered at our location, on which the object was located when it emitted the light (or the reduced area of the sphere if you prefer). If the universe is spatially flat then this is the same as the metric radius of the circle. In general it's related to the radius by the function $S_k$ ...


2

The Gaia EDR3 catalogue gives a parallax of $10.965 \pm 0.028$ milli-arcseconds. This differs from the DR2 parallax by 0.115 milli-arcseconds. This is not unexpected because there are systematic errors of order 0.1 milli-arcsec in the DR2 parallaxes. The new EDR3 parallax is expected to have systematic errors that are no bigger than the statistical error bar ...


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