How Do You Determine Maximum Angular Separation in Vector Problems?

[MSU Student]

So I was given this on a recent physics problem.

http://prntscr.com/5s8u0u

I understand vectors completely, I just don't know where to start. Specifically where it mentions maximum angular separation am I confused. Any type of hints/assistance is appreciated.

 

[Nathanael]

If the orbit of Venus had a larger radius than the orbit of Earth, then the maximum angular separation would be 180 degrees.
Draw the orbit of Venus. Imagine Earth as being in a fixed position with Venus going around it's orbit. When would the angle (as measured from Earth) between the sun (the center of orbit) and Venus be the largest?
It's difficult for me to explain without a picture, but hopefully this helps.

P.S.
Next time it would be helpful if you just copied the problem over here instead of providing a link.
(Some helpful people may skip your problem if they see just a link.)

 

[MSU Student]

It would be 0 degrees would it not? You would basically have the vector running from Earth, through the sun, and then to Venus. At least that's how I imagine it.

Also, sorry for posting this question in the wrong sub-forum.

 

[Nathanael]

When Venus is directly behind or directly in front of the sun (as viewed from Earth) then the angular separation would be zero degrees, but that is not the maximum. I suggest drawing a picture of the orbits.

 

[Chestermiller]

The problem is poorly posed. I think that they want you to place the Earth as the center of your coordinate system, and place the sun along the + x axis. Then, I think they want you to move Venus to various locations in its orbit around the sun and draw the line from the Earth to Venus. Depending on where Venus is placed, the line makes an angle with the x axis. They want you to focus on when the angle is maximum. At least that's my spin.

Chet