# Measuring distances in space

1. Jan 11, 2015

### Starlover

When we measure distances in space -- for example, when we say a star is 20 lightyears away --
are we measuring in a straight line ("as the crow flies"), or are we including the dips and curves in spacetime (that light travels along)?

Thank you in advance?

2. Jan 11, 2015

### Matterwave

In space, the extra lengths induced by gravitation are negligible, so it's basically the straight line distance.

3. Jan 11, 2015

### SteamKing

Staff Emeritus
You should also understand that measuring distances in space, like from one star to another, is somewhat approximate, with objects further away from us having the most uncertainty in their estimated distances from earth.

http://en.wikipedia.org/wiki/Stellar_parallax

4. Jan 11, 2015

### DaveC426913

Have a look at "gravitational lensing" and "Newton's Rings".You'll get an idea that, while space time curvature does affect light paths from distant objects, it has very little overall effect.

1] Space is so empty that it is uncommon for a light path to be unobstructed by intervening gravity wells (otherwise you'd see Newton's rings everywhere)
2] When a light path is affected by an intervening object, it's because the object is hugely massive, like an entire galaxy cluster.
3] The magnitude of deflection - even from a galaxy's huge gravity well - is still very, very small - on the order of arc seconds.

The upshot is that, barring exceptional, notable cases, one can consider space to be very, very flat.

Last edited: Jan 11, 2015
5. Jan 11, 2015

### Starlover

Thank you, Matterwave, SteamKing, and Dave! Your answers are all helpful to me!

6. Jan 11, 2015

### Drakkith

Staff Emeritus
7. Jan 11, 2015

### marcus

Lots of stars are farther than that, though. If you were saying that a star IS 20,000 lightyears away, would you mean at this very moment?

Or would you instead be meaning that it WAS 20,000 lightyears away from the Earth at the very moment it emitted the light that we are now receiving from it?

And how do we make sense of a phrase like "at this very moment?"

It is true as others have said here that space is approximately flat and distances are approximately "as the crow flies" in most practical situations. And there is a very handy "distance ladder" of different methods for estimating distances of various sizes, and they are approximately consistent etc etc.

But the very meaning of spatial flatness, and the meaning of "distances in space" depend on (usually unspoken) assumptions about simultaneity and what clock you and the distant star are using, and so on.

It begins to matter when you get into cosmology and are talking about cosmological distances---to far-off galaxies and other clusters of galaxies, or to what was once the hot gas whose glow is now the cosmic microwave background. So cosmologists do something simple that makes all the discussions much easier: they have adopted a "universe standard time".

So it's possible to be clear about what distance you mean. The matter whose glow we are now receiving as CMB was 42 million LY from here when it emitted the light and it is now 46 billion LY from here, today, as our antennas detect the (redshifted) light. the distance now is approximately 1090 times the distance then. "Now" and "then" being defined in terms of universe standard time.

Awareness of time matters when you talk about distance in space (but we often gloss over that especially when talking about small distances of a few lightyears like to a neighboring star)

It's something that probably needs to be said once in a while, although it may not matter in many cases. Not necessarily to worry about, but just to be aware of as a possible factor

Last edited: Jan 11, 2015
8. Jan 11, 2015

### D H

Staff Emeritus
The answer depends on distance. For a star within our galaxy, or even within our galactic group, there is no reason to account for "the dips and curves in spacetime". The difference between accounting for versus not accounting for those dips and curves is tiny compared to the errors inherent in estimating the distance to that star.

The concept of distance becomes rather fuzzy and somewhat less meaningful for more remote objects. What is observable is the amount by which light from that distance source is redshifted. With some assumptions about the expansion of the universe, that redshift can be translated to the time taken between light leaving the source and observed by us. What about distance? Multiplying that time by the speed of light yields a distance, and this is what you will see in the pop-sci media. That figure is pretty much meaningless.

Last edited: Jan 12, 2015
9. Jan 11, 2015

### marcus

Starlover, I want to reinforce the point DH is making. Taking the light TRAVEL TIME in years and converting it to light years is not a very meaningful or useful measure of distance. As DH says:
You can read the redshift directly from the galaxy's light and then there are calculators based on standard cosmic model that will tell you proper distances given the redshift.
Ordinarily you don't gauge distance by the light travel time because that bears no simple relation to the actual (technically the so-called "proper") distances at a specified time.
Here's a sample calculator output. z is the redshift (of the wavelengths of the incoming light), and T is the year the light was emitted. 13.78 billion is the present year. And the two distance columns give the galaxy's distance now, and at the moment back then when it emitted the light.
$${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&T (Gy)&D_{now} (Gly)&D_{then}(Gly) \\ \hline 10.000&0.4726&31.447&2.859\\ \hline 7.655&0.6776&29.456&3.403\\ \hline 5.809&0.9710&27.214&3.997\\ \hline 4.358&1.3905&24.693&4.609\\ \hline 3.215&1.9883&21.865&5.187\\ \hline 2.317&2.8355&18.711&5.642\\ \hline 1.609&4.0230&15.233&5.837\\ \hline 1.053&5.6541&11.471&5.587\\ \hline 0.615&7.8185&7.540&4.668\\ \hline 0.271&10.5488&3.635&2.860\\ \hline 0.000&13.7872&0.000&0.000\\ \hline \end{array}}$$

Technically, the redshift (if someone is not familiar) is defined as the factor by which the light's wavelengths have been stretched minus 1. So a redshift of 10 means that the wavelengths have been enlarged by a factor of eleven. A redshift z=4 means that the wavelengths we receive are five times as long when they were emitted by the glowing hot atoms of the star. It is just a convention people got into, to subtract one from the enlargement factor.

You can tell the calculator to include the actual stretch factor (here denoted S) if you want
$${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&z&T (Gy)&D_{now} (Gly)&D_{then}(Gly) \\ \hline 11.000&10.000&0.4726&31.447&2.859\\ \hline 8.655&7.655&0.6776&29.456&3.403\\ \hline 6.809&5.809&0.9710&27.214&3.997\\ \hline 5.358&4.358&1.3905&24.693&4.609\\ \hline 4.215&3.215&1.9883&21.865&5.187\\ \hline 3.317&2.317&2.8355&18.711&5.642\\ \hline 2.609&1.609&4.0230&15.233&5.837\\ \hline 2.053&1.053&5.6541&11.471&5.587\\ \hline 1.615&0.615&7.8185&7.540&4.668\\ \hline 1.271&0.271&10.5488&3.635&2.860\\ \hline 1.000&0.000&13.7872&0.000&0.000\\ \hline \end{array}}$$

You can also tell it what range of stretch factor you want (I just chose 11 down to 1 as an example) and you can indicate how many rows the table should be. I just chose it to have 11 rows as an example.
The calculator is online for anybody to use. It is the "Lightcone" link in my signature. A PF member named Jorrie created this particular one, but there are several others online at various cosmology websites.
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

Last edited: Jan 11, 2015
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