# The physics behind the Starshade

The Starshade is a space telescope with a large occulter that can fly off and block the light of a star so its telescope can picture the surrounding exoplanets:

I sort of understand the optics behind its shape; the light that bleeds around the edges their waves cancel each other out. But I can't get the math of the distance right. Say it wants to image the Trappist system, which is 4e17m away and its star is 7e7m in diameter and the shade is 10m. So the distance/size ratio would be 5e9, thus the shade would have to be 5e10m (50,000,000km) from the telescope right? Or is my math wrong?

Isn't that way too far?! Why is it so big? The orbital-mechanics behind it are also problematic. Will they orbit the Earth? Getting in an orbit 5e9m from the Earth is rather energetically expensive, not to mention the difference in orbital period they'd have to deal with.

I guess these are a lot of questions, but I can't find a proper explanation of the New Worlds mission (it's real name). So I'm hoping someone can explain the gist of it to me.

• @uhoh I would've if it was an answer. Asking for references in a comment is a bit too much in my opinion. Sep 1, 2017 at 14:42
• @ventsyv: It's about satellite sensors. It's on-topic. It is never correct to close on-topic questions just because they are also (probably) on-topic somewhere else. Sep 1, 2017 at 15:14
• @uhoh aren't you a negative Nancy. I don't see why you would doubt such uncontroversial, basic factual data as the size and distance of a star. Plus the source is rather obvious: Wikipedia. And it may be true that Trappist 1 is a particularly difficult system, but it's really close as well, so maybe that alleviates the challenges from its smallness. They found it after all. Sep 3, 2017 at 10:55
• @Herman et al. See Figure 2 in arxiv.org/abs/1204.6063 and Figure 1 (actually the entire paper) in arxiv.org/abs/0712.1105
– uhoh
Sep 4, 2017 at 2:42
• @uhoh Thanks! That is a very relevant paper. They assume a much larger 50-m starshade, at a distance of 70,000-100,000 km from the telescope located at the Earth-Sun L2 point. So that answers my question whether it will orbit the earth. And it seems indeed that imaging the Trappist system is not in scope of this mission. In fact they only hope to image 1 to 3 Earth-like planets in the entirety of its mission. That is a rather disappointing. Sep 4, 2017 at 8:35

Your math is wrong, the starshade operates at 50 000 km from the telescope. See the Exo-S starshade report, executive summary, page 4.

The physics behind the starshade are the following:

If there were no diffraction, putting the starshade in front of the star would compeletely block the light of the star, because when seen from the telescope it has a larger angular diameter than the star. However, due to diffraction, the light from the star is not completely blocked: it forms an Arago spot. This means the telescope still sees some light from the star, and that can hide the signal from the planets orbiting the star.

The shape of the starshade is designed to minimize the intensity of this Arago spot. The petals are a way to do that, and still use a completely opaque material (i.e. not using partially transparent materials). Here's an article deriving their shape.

• Thanks for that report! That it operates on a different distance doesn't mean that my math is wrong though. It might be because they pick other target stars. And then I still wonder, how is my math wrong? Sep 5, 2017 at 11:23
• It would be more helpful if you showed "the right math" in your answer. Right now your statement isn't so helpful; there are no numbers here, nor equations, and not so much in the way of explanations either. It would be better if you relied less on the links, and added a little more explanation here. Links tend to rot, and so the value of an answer can decay over time if it depends on the links to do the explaining.
– uhoh
Sep 5, 2017 at 11:49
• @Herman: the angular diameter of the starshade as seen from the telescope gives the inner working angle of the system, not to the angular diameter of the star. The IWA corresponds to the orbital radius of the closest planet the system can see, divided by the distance from the telescope to the star. See the drawing in page 4-2 of the report (page 65 of the pdf). Sep 5, 2017 at 14:51