Astrophysics: Magnitude of sun when Jupiter crosses over it.

[Xyius]

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
$$m_1-m_2=2.5log\left( \frac{\Phi_1}{\Phi_2} \right)$$ (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.

$$m_1-m_2=2.5log\left( \frac{\Phi_1}{\Phi_2} \right)$$
$$=m-M=2.5log\left( \frac{d^2}{10^2} \right)$$
$$=m-4.77=2.5log\left( \frac{5^2}{10^2} \right), m=3.26$$

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..
$$\pi (R_{sun}^2-R_{Jupiter}^2)$$
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 :]

 

[Andrew Mason]

Start with the definition of flux: $\Phi$. How is flux related to area of the source?

How does Jupiter passing in front of the sun affect the effective area of the light source (ie the sun).

AM

 

[Xyius]

Start with the definition of flux: $\Phi$. How is flux related to area of the source?

How does Jupiter passing in front of the sun affect the effective area of the light source (ie the sun).

AM

Okay so Flux is..

$$\Phi=\frac{L}{4\pi d^2}$$ Where d is the distance from the star to the observer.

I guess the only thing that changes here would be the Luminosity. Luminosity is defined to be..

$$L=4\pi R^2 \sigma T^4$$ Where R is the radius of the star.

So would this be on the right track? My concern is this isn't a "disk" as my professor hinted towards. :\

 

[Andrew Mason]

Okay so Flux is..

$$\Phi=\frac{L}{4\pi d^2}$$ Where d is the distance from the star to the observer.

I guess the only thing that changes here would be the Luminosity. Luminosity is defined to be..

$$L=4\pi R^2 \sigma T^4$$ Where R is the radius of the star.

So would this be on the right track? My concern is this isn't a "disk" as my professor hinted towards. :\

It may not be a disk. But a sphere's cross-sectional area is what one sees from a distance. How is the viewable cross sectional area of the sun affected when Jupiter passes in front of it? When does the effect reach a maximum?

AM