- #1
Xyius
- 508
- 4
Homework Statement
An observer 5pc away observes the sun in the plane of Jupiter orbit. He cannot resolve either object but he notices a slight dimming of the star when Jupiter passes across the sun in his vision. Find the magnitude of the sun with and without Jupiter in front of it.
Homework Equations
Magnitude formula
[tex]m_1-m_2=2.5log\left( \frac{\Phi_1}{\Phi_2} \right)[/tex] (Where Phi is the flux)
I do not know if this is the only equation or not.
Absolute Magnitude of Sun = 4.77
The Attempt at a Solution
So the case when Jupiter is NOT crossing over seems simple enough.
[tex]m_1-m_2=2.5log\left( \frac{\Phi_1}{\Phi_2} \right)[/tex]
[tex]=m-M=2.5log\left( \frac{d^2}{10^2} \right)[/tex]
[tex]=m-4.77=2.5log\left( \frac{5^2}{10^2} \right), m=3.26[/tex]
So now I just need to find the magnitude when Jupiter is crossing the sun. My professor said to find the area of the solar disk that is visible when Jupiter is crossing by simply doing..
[tex]\pi (R_{sun}^2-R_{Jupiter}^2)[/tex]
But I do not know where this fits into the above equation. How can I relate this to the flux ratio? Any help would be appreciated :]