Wait... I know how. Of course. If they record its position in the sky over the course of a year, it will make a sinusoidal pattern against the distant background. In the same way as if you watch a bullet flying past you in a straight line and you jump up and down, if you could do that. Because we know how far away the sun is, through simple trigonometry the distance can be calculated very easily. It's the same method used to calculate the distance of the nearest stars, after that they start to use Hubble red shift law, and some other crazy shit. I still think its pretty difficult to measure P from the data they have since its distance to the earth is not the same as its MEAN distance to the sun.