Can someone explain the way in which calculate the distance of celestial objects?

Question

Something about triangulation, I think???

* in which we calculate

Answer 1

There are three methods that are used most frequently:

1. Parallax - For nearby stars, they can measure the angle that the star appears to move through as the earth swings from one side of the sun to the other - this is the most direct and probably the most accurate method, but it only works for stars in the local region.

2. Cepheid variables. - For more distant stars and nearby galaxies, there is a certain type of variable star known as a Cepheid variable that has a predictable range of intensity. Since we know that distance and intensity are related, then wherever we see these stars we can obtain a reasonable measure of the distance to them by measuring the intensity. When this is done with a large number of these stars, the distances to nearby galaxies can be found with reasonable accuracy.

3. Redshift - For the most distant galaxies, we can use the observation that the universe is expanding in order to measure the relative distances to really distant objects. The further away these objects are, the faster thay are receding from us - and the deeper the redshift of the spectrum from that object due to the Doppler effect. This is true in all directions that we look, and for all but a few galaxies. This method is perhaps subject to the most questions, but makes sense for the really distant objects until someone suggests a better idea.

Answer 2

Apparently, you haven't taken geometry in school, yet. It takes a few weeks of geometry class to get to triangulation, so I can't fully expain it here. But the point is, if you know the length of one side of a triangle and the angles at each end of that side, you can calculate the lengths of the other sides.

We can measure the angles to a point on the moon from two sides of the Earth and calculate the distance to the moon. And we can measure the angles to a star from both sides of the Earths orbit around the sun and calculate the distance to the star.

For more distance stars, the angles are so small that the triangle is just a thin straight line, so we need other ways to estimate the distance.

Answer 3

Aero_engr's answer is a very good start, but there are many other techniques that form what's called the "cosmic distance ladder." It would take too long to go into detail here, but there is a great web site on this topic:

http://www.astro.ucla.edu/~wright/distance.htm

It's called "The ABCs of Distances", and the author, Ned Wright, lists a distance method for every letter of the alphabet!
(By the way, this web site is working now, but seemed to be out of service last night. If you have trouble, try again later.)

The term "cosmic distance ladder" is used because the methods generally depend on the lower rungs of the ladder. For instance, Cepheids are a key distance method for external galaxies, but we need to determine their intrinsic brightness to calibrate the method. How do we do this? Until the recent satellite data from Hipparcos, there were no Cepheids close enough to get a reliable distance from stellar parallax; so astronomers had to use a chain of reasoning like the following:

1) Determine the distance to the Hyades, an open cluster of stars. Even though the Hyades are relatively close, they are sufficiently far away for stellar parallax to be unreliable (prior to Hipparcos), so astronomers used a technique called the moving-cluster method.

2) Determine the distance to farther open clusters by assuming that their main sequences of stars should match that of the Hyades, the only difference being the distance.

3) Study the Cepheids in these farther open clusters and determine the relation between their period of variation and their intrinsic brightness.

I've ignored some of the details -- dimming by instellar dust, and the discovery that there are two different types of Cepheids (with a small or large abundance of heavier elements). The whole story of the calibration of the Cepheids could probably fill a book. (Actually, it does; there's a 312-page book called "Cepheids: Theory and Observations.")

Ultimately, the calibrations of all of these methods depend on the distance to a single star cluster, the Hyades! Stellar parallax data from Hipparcos has added to the knowledge we had from the older moving-cluster method, but there is a little controversy about some of the data.

All of the above refers to how we find the distance to objects outside the solar system. Objects inside the solar system are a different matter.

Kepler's laws allowed people to create a scale model of the solar system in terms of astronomical units (AU, the earth-sun distance), but how long is an AU in miles? To answer this, you have to determine the distance to some solar system object (other than our moon) in miles, but that's a tricky business.

For a long time, the best method was to observe a transit of Venus (when Venus moves in front of the sun) from different spots on earth, and compare the timings from these locations. That's why transits of Venus used to be such important astronomical events.

In the twentieth century, astronomers measured the solar-system scale by bouncing a pulse of radar off other objects and measuring the time of the echo reflection; this gave a very accurate distance scale for the solar system.

These two distance scales (inside and outside the solar system) are linked. Stellar parallaxes give us distances to stars in terms of an AU, but our calibration of the AU depends on observations within the solar system.

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I'd like to add one more topic: How do we determine the distances to the more distant galaxies? Red shift correlates with distance, but it doesn't really give us a distance. If we know the red shift of a distant galaxy, we can make a good guess for its distance, but it's not really a fundamental distance determination.

Most fundamental distance determinations for objects outside the solar system are of two types:

1) Geometric methods, of which stellar parallax is the most important.

2) "Standard candles." If we study some type of object and learn that it always has the same intrinsic brightness (or has a brightness that depends clearly on some other observable property, such as the period of variation of Cepheids), we can use this to determine the distance of some other object (such as a galaxy) in which the standard candle is found. The most important standard candle in recent cosmology is stellar supernovae (more specifically, what is called a "type Ia supernova"). They are so bright that they can be seen in extremely distant galaxies. Observations of these supernovae in distant galaxies led to the recent discovery that the expansion of the universe is accelerating.

Sorry to go on so long. It's a big topic, and I've only scratched the surface.

Answer 4

Aero...
Great answer!
I could not have stated it better myself, so I defer!
Thumbs UP!!!
Bobby