Solving Planet A's Semi-Major Axis Ratio To Planet B's

[zeromaxxx]

Homework Statement

You are one of the first astronomers in a civilization on Planet B in another solar system. With your unaided eye, you follow planet A in the same solar system and note that it never gets further away than 16 degrees from the star (around which both planets orbit).

What is the ratio of the size of Planet A's semi-major axis
to that of Planet B?

Homework Equations

The Attempt at a Solution

I seem to have trouble visualizing this scenario and so I don't know how to approach the problem...

 

[Delphi51]

Sketch a star and the orbits of two planets in circular motion. With such a small angle, we must be on the planet of the larger circle; mark its position anywhere on the circle. Mark the points where the inner planet will appear furthest away from the star. With a bit of trigonometry you should be able to find the answer.

 

[livegong67]

Would it be sin(16) = Ra/Rb
I know that gives that the ratio of the radius' but I'm not to sure how to find the semi-major axis

 

[Delphi51]

For circular orbits, the radius IS the semi-major axis.
Perhaps the use of the term implies you are to consider elliptical orbits. I suspect that would result in the same answer.

 

[gneill]

For circular orbits, the radius IS the semi-major axis.
Perhaps the use of the term implies you are to consider elliptical orbits. I suspect that would result in the same answer.

It gets quite a bit more complicated when the orbits are elliptical and the perihelion directions are not aligned (the major axes are not collinear). Mutual distance plays a big role in the observed angular size, and the "width" of the orbit varies with viewing angle.