How would 2 spacecraft be launched to be in sync in opposite directions?

Question

How would 1 spacecraft be launched to have a prograde orbit and the another be launched retrograde to have a mirrored orbital path around the sun or otherwise? Would the 2 spacecraft launch together at one launch site or at different sites on Earth be more efficient?

Related:How would 2 JWSTs make stereo pictures?

How will JWST manage solar pressure effects to maintain attitude and station keep it's unstable orbit?

Answer 1

STEREO A and B, 2006-047A and B, (29510 and 29511) were launched together from "Cape Canaveral Air Force Station in Florida on a Delta II 7925-10L launcher into highly elliptical geocentric orbits".

The elliptical orbits intercepted the Moon's trajectory, and because of a small but carefully design difference in their two positions, one was thrown "forward" into a faster heliocentric orbit, while the other was sent back, not quite free from Earth's gravity field, to meet the Moon again when it was moving in the other direction. There it received a second gravitational assist in the retrograde direction, putting it in a slower heliocentric orbit, relative to Earths.

From this answer to the question Gravitational assists from bodies other than planets:

The Moon has been used as a gravitational assist in different ways.

NOTE: As @notovny pointed out elsewhere these orbits go in the opposite direction in the rotating frame of Earth's orbit, but in the "normal" inertial frame, they both travel around the Sun the same way, in orbits very similar to that of Earth. It's just that one goes slightly faster and the other slightly slower relative to Earth.

But in the rotating frame, they do go in opposite directions. One moves towards Earth's L4, the other towards L5.

See this answer, which links to this NASA page. The first video shows the two STEREO spacecraft use two and three passes by the Moon to leave Earth orbit and enter into an orbit around the sun.

The trajectory is also described in some detail (but sans cool GIF) in this answer.

It would certainly be quite a challenge to fit two JWST-class telescopes on one rocket, but if they were somewhat smaller than JWST, it could be done again in a similar way.

Here is a GIF made from the frames of that .mov file:

See also this answer and the video: