One theory about the behaviour of moths states that they navigate at night by keeping fixed angle between their velocity vector and the direction of the Moon [or some bright star]. A certain moth flies near to a candle and mistakes it for the Moon. What will happen to the moth?

Hints: in polar coordinates (r,θ ), the formula for the angle ω between the radius vector and the velocity vector is given by

Use the formula to solve for r as a function of .

I do not know how to set up the necessary equations. I tried sketching a diagram,but I cannot seem to find a relation between ω and θ necessary to solve the formula given. Is my diagram correct? Thank you for your help.