The angular size of stars - prac astronomy

[RoosterPhil]

Hi, I am writing a project on ways to measure the angular size of our sun and distant stars.

I've been given a list of ways this can be done and have been told to research them. However I am having trouble finding information on 2 of the methods.

Using the transit of planets: I am assuming this can only be applied to our own sun as other planetary systems are difficult to find - only through variations in the intensity of light output from the star as the planet passes across it, this also has the problem of finding a system where the orbital plane lies perpendicular to the line to the observer.

So using the fact that planets in our own solar system (mercury and Venus) pass between the Earth and the sun how can you use this to find the angular size of the sun?
Is it by again determining the variation of intesity output - this doesn't seem right to me, the size of the sun relative to the planet in this case is much too big and would be difficult to get an accurate reading.
Which leaves one method i think. Knowing the radius of the planets orbit, its angular size, distance to the Earth etc, you can measure the time it takes to pass across the sun - therefore knowing the angular size of the sun. N.B ignoring that the orbits are circular etc.
Is this correct?

The second way:
Stefan's Law. This one i don't have many ideas for - the law itself
P = (sigma)AeT**4
Stars are black bodies = e = 1
I = P/A
So I = (sigma)T**4

Now we can find the intesity of light from a distant star. If we can find the distance to the star and assume that it is main-sequence, then we can anticipate the angular size of the star?

Thanks for any help, very much appreciated
Phil

 

[Nereid]

Welcome to Physics Forums Phil!

Using planetary transits to measure the angular size of the Sun seems an odd thing to do, IMHO. I mean, you can make a direct image of the Sun, and so can measure its angular size directly.

Planetary transits *are* one method for measuring the angular size of distant stars! If you can determine the orbital parameters of the distant planet, the timing of the transit gives you some idea of the size of the star (some caveats of course).

In the second case: if you know the distance and observed intensity of a star, you can calculate its 'absolute' intensity. From its spectrum, you can determine the temperature of the star's photosphere. Can you now use Stefan's Law to calculate the star's radius? What other factors do you think you'd have to take into account?

 

[RoosterPhil]

I understand how to use stefans law now thanks
i take it just use the parallax method to find the distance, so this limits stefans law to find the angular size of close'ish' stars. other factors taking inot account. hmmm you could estimate spectral changes through doppler shifting using that proper motion and tangential stuff I am supposed to know about, but i don't need that much detail luckily. lol

i didn't realize we were able to accurately find data on orbits of other planetary systems. If you did know the orbit of the planet how would that tell you the angular size of the star? would you need to know the type of planet it was and so estimate the mass, using that to determine the size of the orbit? Or is it just directly through timing - planets in our own solar system have different orbit times obviously - so is there a direct link between distance from the sun and the speed at which the planet moves?
oh yeah what does caveats mean? lol
thanks Phil

 

[Nereid]

Parallax is a good method for determining distance, but certainly not the only one. So far as applying Stefan's Law is concerned, it doesn't matter how the distance is determined, merely that it is (and that you have a good understanding of the likely errors in the estimate).

For other factors, think about the other elements that go into a determination using Stefan's Law - intensity, temperature, ... what might affect your estimate of these?

This page has some good material on extrasolar systems, including tutorials on how such planets are detected and orbits determined. You might also google "Kepler's Laws"