# Did InSight take a "mean left" turn on its way to Mars? Is it an out-of-plane maneuver?

In the NASA JPL video NASA Launches InSight to Mars (part 1) after about 14:30 (currently) NASA's new Chief Scientist Jim Green (better photo here) explains:

Vandenberg is great for putting spacecraft into polar orbit. We fire straight south, and that way it goes over the ocean, goes under the south pole, comes up on the other side of the earth and then takes this &mean left*, and heads on out to Mars.

Was there a significant out-of-plane maneuver with respect to its orbit and is this what the "mean left" refers to? Would that vary depending on the launch time within the 2 hour launch window?

• Not a dupe of [Insight mission broken-plane maneuver needed? ](space.stackexchange.com/q/25825/12102) as that asks about a mid course plane correction.
– uhoh
May 6 '18 at 4:33
• Yep, Jim's comment is puzzling. The Atlas V 401 had plenty of launch capacity for InSight, but out-of-plane components are a bad way to waste ∆V if you don't need them. Instead of making a "mean left", just waiting an hour or so later to launch would have the same effect. As it was, the 2nd Centaur burn put the departure V∞ vector almost aligned (in azimuth) with Earth's orbit velocity vector, with a declination south of equatorial, maybe not too far from the ecliptic. I'll ask some of my JPL trajectory buddies about it next week. May 6 '18 at 6:10
• I just thought ... if you have a 2-hr launch window to a near-polar orbit, then coming over the N pole boost to a departure orbit more or less aligned with Earth's orbital velocity vector, it might be that launching at the center of that launch window orients the orbit for an ideal escape orbit injection maneuver, i.e. no out-of-plane component. But if you lauch as that window opens, 1 hr early, there's a 15° misalignment between the orbit plane and the departure V∞ vector, requiring a "mean left". Launching 2 hrs later requires a "mean right". May 6 '18 at 22:35
• @TomSpilker that's what I'm wondering too. Actually in the title I should probably change the two words "Was there..." to "Is it..." because that's what I'm really asking. In fact, I'll do that now (and fine-tune the last two sentences), thanks for helping me visualize this in 3D!
– uhoh
May 7 '18 at 0:34
• Good point @uhoh, I'll write a quick answer based on my comment above. May 7 '18 at 1:49

## 1 Answer

Jim Green's comment might have been a result of InSight launching at the very beginning of the launch window. If you launch from a given point on Earth's surface into a polar or near-polar orbit, the orientation of the orbit's plane depends on where the launch site was, considering Earth's rotation, when launch occurred. Every hour that launch site rotates 15° with respect to the Earth-Sun direction, so the resulting orbit plane rotates by 15° as well.

For now assume a perfectly polar orbit for the InSight parking orbit. It wasn't quite polar, but it was close enough that this approximation will aid understanding.

For maximum efficiency the V∞ vector of the intended Mars transfer trajectory should be close to parallel to Earth's orbital velocity vector in right ascension, and somewhere close to the ecliptic plane in declination. The ideal launch and parking orbit will have the intended V∞ vector in the orbit plane so the injection maneuver needs no out-of-plane component.

But that means you have a launch window of only instantaneous duration, not good for keeping a schedule.

InSight had a 2-hour launch window. If it were centered on that ideal launch moment, and they launch at the opening of the 2-hr window, then they are launching into an orbit plane that is 15° "early": Vandenburg is 15° farther west than it should be for the ideal orbit orientation, and the resulting orbit plane is offset 15° clockwise (as seen from the north). As it comes over the north pole for the trans-Mars injection (TMI) maneuver, it needs a significant out-of-plane component to that maneuver to meet the required departure V∞. And indeed, it would be to the left, if you're sitting upright on the Centaur, Jim's "mean left"!

Had InSight launched at the end of the launch window, 2 hours of planetary rotation would have moved Vandenburg 15 east of the ideal spot, and the out-of-plane component of the TMI burn would have been to the right — a "mean right".