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Jake Blocker's excellent answer to How does one dogleg from Florida to a sun-synchronous orbit? explains what a dogleg maneuver is, what it's for, what it looks like, and even what a real dog's leg looks like for comparison!

A dogleg maneuver is done to change the inclination of a certain payload, and the reason it limits the payload capacity is most likely due to the cosine losses.

In my answer to it I mention an incident which might be the reason that doglegging to orbit was invented, but I don't know. I also describe it in this answer to History of multiple-payload launches?

Question: Which launch was the first to dogleg?

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    $\begingroup$ ...intentionally? ;) $\endgroup$
    – SF.
    Jun 5, 2018 at 14:21
  • $\begingroup$ @SF. ha! Yes let's say a planned trajectory $\endgroup$
    – uhoh
    Jun 5, 2018 at 14:25
  • $\begingroup$ Could this be it? en.wikipedia.org/wiki/Thor-Ablestar $\endgroup$
    – uhoh
    Jun 6, 2018 at 1:22
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    $\begingroup$ I think, ISRO mostly uses dogleg maneuver $\endgroup$
    – Amar
    Sep 8, 2018 at 13:59
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    $\begingroup$ Sputnik 2 had four... (sorry!) $\endgroup$
    – GordonD
    Aug 10, 2021 at 17:18

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Unsure if it was the first dogleg, but the launch of Telstar 1 was certainly an early one (July 10 1962).

Because of range safety considerations, when a Delta vehicle is launched from Cape Canaveral the launch azimuth may not exceed 108°. This establishes a path which crosses the equator at an angle of about 33°. The orbital inclination will have this value if all three stages are fixed in the initial flight plane, as they would be for maximum energy use. The desired higher inclination of 45° was attained by yawing the second and third stages to the south of the initially established ascent trajectory plane when the vehicle had arrived at a point where the range was clear to the south. Since the energy imparted to a spacecraft is reduced by such yawing, the final apogee or perigee or both will be reduced.

Source: Launching of the Telstar Satellite, included in NASA SP-32 Volume II

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    $\begingroup$ Addendum: Why didn't they just launch in a northwestern direction (like todays ISS launches)? Because it would have put the perigee of the elliptic orbit over the wrong hemisphere. Today that could be solved with a extended coasting phase, but this wasn't an option yet at the time. $\endgroup$
    – asdfex
    Dec 12, 2021 at 17:08

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