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The James Webb Space Telescope is scheduled to launch in 2021 and be put in a halo orbit around Sun-Earth L2 soon after. The plan for the Wide Field Infrared Survey Telescope is a launch perhaps around 2025 to another halo orbit also around SE L2.

Both JWST and WFIRST have an approximately known angular resolution at this point in their designs, but is enough known about each planned orbit and their mutual phasing (if any) in order to estimate the minimum distance likely between the two during their possible operational lifetimes and therefore the largest possible angular size of each telescope as seen by the other?


Related but historical rather than future-looking (and lots of good answers!) Have spacecraft photographed each other beyond Earth orbit?

Information on the nature of JWST's planned orbit can be found at:

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Here's a partial answer to get things started. The JWST orbit around SE L2 is pretty big. If WFIRST was in a similar orbit and phased by 180 degrees (on the opposite side) they'd be about a million kilometers or $10^9$ meters apart. That's a rough upper limit to the distance between the two, it We can call a wavelength $10^{-6}$ meters.

Let's say both telescopes are spherical cows of sizes and apertures of 10 meters. Since

$$ \frac{10 \times 10}{10^{-6} 10^{9} } = 0.1 <1$$

neither telescope could begin to resolve the other when on opposite sides of the orbit, but only by a factor of ten. So the question really boils down to one of orbital mechanics, mission design, and perhaps telecommunications because they probably would always want to avoid the two telescopes fitting into the same ground station dish antenna's footprint.


From this answer:

JWST planned orbit JWST planned orbit JWST planned orbit

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