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From NASA Spaceflight's article SpaceX Falcon 9 launches first NRO mission with NROL-76:

The NROL-76 launch was not to be targeting a sun-synchronous orbit, typically used by the NRO’s optical imaging satellites. While it is possible to reach such orbits from the Kennedy Space Center or Cape Canaveral, the rocket would have to perform a series of dogleg maneuvers that would severely limit its payload capacity.

What does this mean? Is there a diagram illustrating what these maneuvers might look like? Why a series of them instead of one, presumably longer maneuver? Has this kind of thing been done recently?

update: I have found dogleg mentioned in this blog.

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    $\begingroup$ Before anyone adjusts my spelling of dogleg, lets wait and see what happens here: english.stackexchange.com/q/387446/217285 $\endgroup$
    – uhoh
    May 2, 2017 at 11:47
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    $\begingroup$ An early shuttle DOD mission (32?) flew a dogleg ascent to reach a high inclination orbit without busting the "no overfly of inhabited areas" rule too badly. Very expensive performance-wise, only done that one time in the program. Don't know if the same rationale applies to this launch. $\endgroup$
    – Organic Marble
    May 2, 2017 at 13:04
  • $\begingroup$ @OrganicMarble I just tried to look in JPL Horizons for "mission" or "shuttle" or "STS", but have a hunch that's not going to work in general, neither would TLEs for initial ascent. $\endgroup$
    – uhoh
    May 2, 2017 at 13:07
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    $\begingroup$ Oops, it was STS-36. en.wikipedia.org/wiki/STS-36 $\endgroup$
    – Organic Marble
    May 2, 2017 at 13:14
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    $\begingroup$ I don't have a graph handy or enough background information to warrant a full answer, but the tl;dr of it is essentially a series of plane change maneuvers (i.e., yawing off of your initial trajectory) during and/or after ascent. Plane changes become more expensive the faster you go, so anything you can do in the early stages of ascent pays you back in spades compared to making the adjustment once you're in a stable orbit $\endgroup$
    – Tristan
    May 2, 2017 at 15:16

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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 order to perform such a maneuver a rocket has to yaw in a certain direction in order to change the direction of flight. However, this yaw comes at a cost, as the more you stray the direction your rocket is pointing in from prograde, the less efficient your rocket will become. For example, if your rocket was only 10 degrees stray from prograde, you would still get 98% if the total Delta V. However, in certain missions a large inclination change is necessary, so if you want to stray 45 degrees away from prograde to achieve a large inclination, you would only get 70% of the total Delta V for that stage.

The reason it is called a dogleg maneuver is the resembles the path of travel has to a dogs leg.

Here's a picture of a falcon 9 launch, I do not believe it's from NROL-76. The maneuver occurs towards the center of the screen.

enter image description here

And here's a picture of a dog's leg just to compare :)

enter image description here

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  • $\begingroup$ Oh - that's not what I expected at all! The map I mean, the other image I had a hunch already ;) The numbers for "loss of delta-v" are for maneuvers late in the ascent, aren't they? Wouldn't the loss be reduced for maneuvers executed early on? See for example this comment by @Tristan $\endgroup$
    – uhoh
    May 2, 2017 at 18:41
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    $\begingroup$ Those numbers are just cosine losses strictly due to moving your thrust away from the prograde direction. It doesn't include the delta-v cost of successfully altering your path -- basically zeroing out that portion of your velocity vector that is out of your desired plane of travel. That's where the early-vs-late difference comes in: the later you are in ascent, the more velocity you have to null out. You get bitten twice in that regard. $\endgroup$
    – Tristan
    May 2, 2017 at 19:29
  • $\begingroup$ another "Florida dogleg maneuver" you might want to include: space.stackexchange.com/a/36296/12102 $\endgroup$
    – uhoh
    Jul 24, 2019 at 0:51
  • $\begingroup$ I've linked to your answer and borrowed your images in Most dog-legged launch? $\endgroup$
    – uhoh
    Aug 10, 2021 at 1:42
  • $\begingroup$ I suspect the term dogleg originates from the many golf courses in Florida and California, which is where the two primary US launch sites are located. A golf course of any repute will inevitably have at least one hole, oftentimes many, with a dogleg. The dogleg hole in golf almost certainly gets its name from the curve in a dog's leg. $\endgroup$
    – David Hammen
    Apr 6, 2022 at 10:25
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Supplementary information. After asking this question I saw the photo below. The item on top is called GRAB 1 for Galactic Radiation and Background. However that's a cover:

Galactic Radiation and Background (GRAB) was the covername for Project Dyno ELINT intelligence satellites operated by the U.S. Naval Research Laboratory (NRL) shortly after the Cold War U-2 incident of 1960. The satellites carried two sets of instruments: an unclassified experiment (called Solrad) and a then-classified payload to collect electronic intelligence (ELINT) (called Tattletale). Of five attempted launches, two missions were successful. The program is also known by the later codeword Canes.

Reading further:

Incidents

During the second launch attempt, the Thor booster shut down 12 seconds early, and the flight was subsequently terminated by Range safety. As fragments fell on Cuba, subsequent launches from Cape Canaveral flew a dogleg trajectory to reach 70 degree inclination.

I'm not yet sure if this is the origin of doglegging to orbit, so I've asked Which launch was the first to use a dogleg maneuver?

enter image description here

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