# Homework Help: Radius of a star

1. May 25, 2006

### Brewer

How do I go about working out the radius of a star when I have the bolometric flux, the wavelength of the peak flux of its spectrum, and its parallax?

I've also calculated the temperature of its photosphere (Wein's law right?).

Or is it more to do with the parallax?

2. May 25, 2006

### SpaceTiger

Staff Emeritus
How does a blackbody's temperature relate to its area and luminosity?

What quantity does a parallax give you? How might you use this to derive a luminosity from a flux?

3. May 25, 2006

### Brewer

I haven't touched on luminosity for this question, as it asks for that in the next part (and I know how to get that).

As I understand it, radius of the star is d*tanP where d is the distance to the star, and P is the parallax. Is $$10^11$$ the correct order of magnitude for a star do you think? Its bigger than the sun, but its not overly huge for a star is it?

4. May 25, 2006

### lightgrav

you have its parallax? so it must be fairly close ... right?
that means it should appear fairly bright ... right?
Temperature determines how much light is emitted by each sq. meter of surface - not how much light comes off the entire surface.

Do you know how these are related?

5. May 26, 2006

### SpaceTiger

Staff Emeritus

You'll need it for this part.

1011 what? Meters?

6. May 26, 2006

### Brewer

Yes $$10^1^1m$$. Sorry about the double post

7. May 26, 2006

### SpaceTiger

Staff Emeritus
That's about the distance from the earth to the sun, so it's a bit too close for a star. I just noticed that you were associating the parallax with the radius -- actually, it gives you a distance. The distance, in parsecs, is given by:

$$d=\frac{1}{\theta}$$

where $\theta$ is the parallax angle in arcseconds.

8. May 26, 2006

### Brewer

Is it in metres if you use radians and parsecs if you use it in degress, arcmin and arcsec then?

I've just realised how its done though - distance can be used with the bolometric flux to find the bolometric luminosity. This is turn can be used with $$P = \sigma AeT^4$$ to find the raduis of the star right?

I'm a little confused how the question was intended to be worked out though - 2 marks for this, and a further two in the next part for writing down something you've already calculated in order to do this question (luminosity).

9. May 26, 2006

### SpaceTiger

Staff Emeritus
More generally, the expression is:

$$d=\frac{d_{earth}}{\theta}$$

where $d_{earth}$ is the distance from earth to sun. The expression I gave you is only valid in units in which the angle is in arcseconds and the distance is in parsecs. Use the above expression for meters and radians.

Yep.