MadSci Network: Astronomy Query:

### Re: Estimating distances based on the speed of light

Date: Fri Feb 19 12:53:08 1999
Posted By: Malcolm Tobias, Post-Doc, Physics, Washington University
Area of science: Astronomy
ID: 916619236.As
Message:

Measuring accurate distances is one of the most important, and most difficult, problems in modern astronomy. One common method for measuring distances in astronomy is through the use of parallax. Simply put, parallax is the apparent shift of an object's position when measured from two different angles. [One simple demonstration of parallax is to hold a pen at arm's length. Look in a direction where you can see lots of things, for instance, out a window. (Do not look at a blank wall.) Close one eye, then the other. The position of the pen, relative to the position of background objects, will appear to shift back and forth as you close one eye then the other.] By measuring this apparent shift, and knowing the distance between the positions of the measurements, one can deduce the distance to the object through simple geometry. This method works well on nearby stars, where distant stars can be used as a background to measure the shift due to parallax. Unfortunately, there are relatively few stars this close whose distance can be measured by parallax. [Typically only stars within a few hundred light years or so can be measured this way.]

[The most recent effort to measure parallaxes was the Hipparcos satellite. (Although Hipparcos was a satellite, it is not necessary to use a satellite to measure parallaxes. The measurement of the parallax of stars has been done for hundreds of years from ground-based telescopes.)]

Another method used to measure a star's distance relies on something often called a "standard candle." [That is, objects for which we are fairly sure we know how much light they emit.] The idea relies on the fact that the intensity of light from an object falls off as 1/(distance*distance). Therefore, if we know the amount of light an object emits, and measure its brightness as measured on the earth, we can determine its distance. There are many different objects that are used as "standard candles" [including particular kinds of stars, supernovae, planetary nebulae, even entire galaxies have been used]. Often, they are identified by the characteristic radiation that they emit. [Indeed, the determination and verification of standard candles is an important part of astronomy.]

So you can see, there are several different methods for measuring distances. Some work better on close objects, some work better on more distant objects, and all of which have some experimental errors associated with them. Typically, one uses the measurements of close objects to estimate the distance to more distant objects. In this way, one builds up the so-called "cosmic distance ladder." Obviously, there are many technical difficulties that I have left out in describing these techniques. I only hope to give the basic idea behind how one carries out these measurements.

One possible source of confusion comes from the fact that we live in an expanding universe. A consequence of this is that more distant objects are moving away from us faster than closer objects. This is expressed by the "Hubble Law" `V = H * D`, or velocity (`V`) is equal to the distance (`D`) multiplied by a quantity called the Hubble constant (`H`). By measuring `V` and `D` for many objects we can determine the Hubble constant `H`. [Conversely, if we measure the velocity of an object, and think we know the Hubble constant, we can estimate its distance.] This often leads to people discussing the distance of an object, by the amount its velocity causes light to be Doppler shifted.

[Another possible source of confusion is that the distance to objects is often quoted in "light years." A light year is the distance that light travels, assuming that it is travelling in a vacuum, in one year. Thus, after determining the distance to a star via parallax, its distance may be quoted as 10 light years, even though the speed of light did not enter in to the determination of its distance. As it turns out, the space between stars is almost a vacuum so there is little difference between the speed of light in a (ideal) vacuum and outer space.]

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