Help With A Problem: I'm Confused

[astronomystudent]

I am trying to solve the following problem, and I have done one step that I think is right but I don't know what I am doing, and I am very confused.

4. If Jupiter were really 7.52 A.U. from the Sun instead of 5.20 A.U., what would the affect be on the energy it gets from the Sun? What would be the affect on its appearence (size and brightness) from Earth? Careful, these are two different questions!

This is what I have done thus far...
I used the following equation: (apparent distance (near)/apparent distance (far)) = (distance (far)/(distance (near))^2
therefore i did: (apparent distance (near)/apparent distance (far)) =(7.52 A.U./5.20 A.U.)^2.
That equals = 2.091360947.
That is all I have.

 

[Astronuc]

The flux from a point source falls off as 1/r². This is because, assuming the total energy is uniformly distributed in a 4pi solid angle, as one travels out a distance r, the surface area through which the energy/light is distributed inreases at 4pi*r².

Now the brightness of Jupiter or any other planet has is related to the solid angle subtended by the planets area. As the the distance to Jupiter increases, the solid angle subtended by its area, decreases.

I am not sure about your equations.

In the first part, simple find the ratio of the spheres corresponding to Jupiter orbit, and the sunlight should decrease by the square of the ratio of the closer/further, or (5.2/7.52)² = 0.478, which is the inverse of your 2.09.

As for the earth, one has to consider the position of the Earth at 1 au from the sun. So the light from the sun is less, and the reflected light received is less.

 

[astronomystudent]

Wow! So what I calculated has nothing to do witht his problem? Sweet!
How do I calculate the ratio? Is there any math involved in the second part of this problem or is just stated like you said? I am so confused, I am going to need a step by step process here. If you can help me with that?

Thanks

 

[Astronuc]

Let's say a source A has intensity I in all directions of a solid angle 4pi. The flux at r is given by Flux = I/Area(r) = I/(Area of Sphere of radius r) = I/(4pi*r²).

So at B which is r from A, the flux is I/(4pi*r²).

Now B reflects light back to C, which is at distance s.

The intensity of light I_B from B is just Flux * Area receiving Flux, which one can assume is unidirectional. One could just treat the projected area which is simply pi*r_B² and determine what proportion of incident light is reflected to point C.

Then Flux at Point C is the just the I_B (indirection of C) divided by the area at distance s from B = I_B/(4pi*s²).