Calculating Distance in Two Different Methods

[stardrop]

Homework Statement

Show that we can calculate the distance of Sirius from us (in Ly) from the above data by two different methods.

If the positions of the Sun and Sirius are interchanged, what will be the m and M values of each?

Sun: m = -26.4; M = +4.6
Sirius: m = -1.4; M = +1.4

Homework Equations

M = m + 5 - 5logd
I = L/4pi d^2
I₁/I₂ = L₁/L₂
(d₂/d₁)^2

The Attempt at a Solution

M = m + 5logd
1.4 = -1.4 + 5 - 5logd
1.4 + 1.4 = 5 - 5logd
2.8 = 5 - 5logd
2.8 - 5 = -5logd
-2.2 = -5logd
-2.2/-5 = logd
.44 = logd

Thanks in advance for any help you can offer!

 

[andrevdh]

The absolute magnitudes will stay the same. They are per definition the apparent magnitudes when the object is located at 10 parsecs. Use the formula to calculate the parallaxes for the sun and Sirius and then recalculate their apparent magnitudes when their positions are swopped.

Also the inverse of the stellar parallax (in seconds of arc - the required units for p in the formula) gives the distance to it in parsecs.

 

[Kurdt]

Remember your laws of logs. $$a\log(b) = \log(b^a)$$. Also the equation you are using will give the distance in parsecs so you will have to convert to lightyears.

For the second, what do you know about magnitudes and brightness?

Edit: Beaten to it I knew I shouldn't have made that coffee

 

[andrevdh]

What is somewhat confusing is that one sometimes sees the equation

$$M = m + 5 + 5\ \log(p)$$

and at another time

$$M = m + 5- 5\ \log(d)$$

this is due to the fact that the stellar parallax of a star and the distance to it in parsecs are related by

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

I was referring to the first in my previous post while you seem to know the second.