# What percent of time is a rocket to the moon on the right trajectory?

I heard the following quote: "A rocket to the moon spends only 7% of the time on the correct course, the rest of the time it is off course and needs to be corrected and put back on course."

This is a nice anecdote in relation to how important it is to keep correcting your own course in life, have a destination in mind but keep checking if you are on course and correct.

Examples of similar quotes:

The Apollo moon rockets were off course 97% of the time. Yet they still reached their chosen destinations – and returned to earth – with pin-point precision and timing.

Did you know that an Apollo rocket is actually on course only two or three percent of the time? At least 97% of the time it takes to get from the earth to the moon, it’s off course. Put another way, for every half hour the ship is in flight, it is on course for less than sixty seconds.

Source: Better Networker

They are nice examples but are they really true. Where would these percentages come from?

• Actually (if I listened to those silly sentences) to me that would mean that you don't really need to have a destination in mind at all most of the time, because at the end someone will guide you to the Moon anyways. :P
– nico
May 2 '12 at 13:26
• Describing a system in the normal fluxuation of it's feedback loop as "off course" just proves that they guy who wrote the book was a business major because he couldn't hack it in a slipstick course. May 3 '12 at 2:31
• How is "the right trajectory" defined? Given a narrow enough definition, one could probably claim that the Apollo rocket was off course until the final adjustment was made when entering lunar orbit. With what I expect would be a more useful definition of "moving closer to the target," it was probably on course close to 100% of the time. May 3 '12 at 4:31
• I guess the author defined "the right trajectory" as having its nose pointed at the target rather than being on the calculated trajectory designed to intersect the target at the desired future location in space along the target's trajectory in orbit :) May 3 '12 at 9:19
• I think the main message you can get from these quotations is "business analysts have no idea of rocket science". Jul 21 '15 at 9:24

This image shows the Apollo 13 timeline, derived from the official log:

.

As you can see, they only course-corrected four times over the course of the 143-hour mission.

The Apollo 11 mission had five scheduled course corrections, three of which were considered unnecessary by mission control when the window arrived. Of the two course corrections that actually occurred, one was only a three-second burn and the other doesn't specify how long it lasted.

So no, I wouldn't say they were only on course 3% of the time.

• +1, but given Apollo 13 did not go according to plan nor complete its mission, can we meaningfully include it? Apr 30 '14 at 1:44
• @Oddthinking - Well, they still went to the moon, right (and back, thankfully)? The question really only mentioned getting to the moon, after all. If anything, I'd expect a craft with serious issues to need more course corrections, to be off-course more often (whether from just being off in the first place, or having some mid-transfer trouble). So this makes a nice counterpoint to a "no problem" run. Apr 30 '14 at 13:46
• @clockwork depends on the kind of failure. Anything that doesn't make the ship lose mass into space (or to lose mass in a different way than desired) can't change the ship's trajectory either. You can miss a maneuver, accidentally fire less or more or in the wrong direction, but an oxygen tank rupture that doesn't leak air into space doesn't cause a need for a course correction Jul 25 '15 at 15:49
• @JanDvorak: A discovery that the craft cannot be relied upon to use its rockets in the intended fashion could cause a need for a course correction to ensure that the craft's actual abilities will suffice to get it where it needs to go. Aug 1 '15 at 3:35
• I would expect that in some sense the original claim could be accurate if "correct course" is interpreted to mean "a course which would result in its reaching the surface of the moon", since most of the time the LEM would have been attached to the command module which was, of course, never on a course to actually reach the moon's surface since that wasn't its job. Aug 1 '15 at 16:32

Because of the incredible cost of getting propellant out of the Earth's gravity, I am pretty certain the moon rockets were almost always perfectly on course, with occasional corrections.

According to NASA, the launch phase gets the Apollo rockets to Earth's orbit, then there is a burn to join what they call the Trans Lunar Coast Phase, during which no propellant is expected to be fired. The next burn is at the Moon end to join a Lunar orbit.

The calculations on that page are all about making sure the phases line up with the minimum burn required to transition from one to the next, which is why launch windows are so critical.

One of the indicative diagrams from that page.

A comparison of lunar landing strategies can be found here. Again, it is heavily focused on savings in propellant, or as they state it, delta V (change of velocity):

... the TLI maneuver for the WSB is greater than for the standard ballistic transfer, there can be a lunar capture DV savings of about 25% when capturing into a Lunar orbit. The Hiten mission 17 (originally called Muses-A) performed such a capture in October, 1991

• Rory, I find this surprising, so I just want to make sure I understand it. You are saying the Apollo rockets did not undergo frequent corrections, but instead there were only three, relatively short, periods the rockets were used - to launch, to head toward the moon, and then to stop when they got there. That's remarkable. May 3 '12 at 1:04
• @Oddthinking, I'm wondering if the correct interpretation of the statistic isn't that the rockets were only 'pointing at' the moon for 7% of the trip... May 3 '12 at 5:30
• I think we can count this myth as busted based on this information. There are in fact not frequent corrections just a couple of points at which the burn happens, presumably during this burn there may be many mini corrections going on. But the general idea that you are making constant corrections is wrong. May 5 '12 at 8:51
• @Oddthinking, why do you think it's remarkable? It seems intuitive to me. Gravity is an extremely weak force, and space is a near-perfect vacuum; with no significant gravity perturbing your course and no friction to speak of, there would be no reason to continue to fire the rockets. In fact, continuing to fire the rockets would be a bad idea, as you'd have to apply approximately the same amount of force in the opposite direction to land. This would cost a lot of fuel, and rockets are already 90+% propellant! Apr 30 '14 at 14:16
• @Brian: Just to be clear: I am not at all suggesting the answer is wrong, just that it was a pleasant surprise to me. While I didn't expect that gravity or friction would drive the craft significantly off-course, I am shocked at the precision involved. It strikes me as hard to get your trajectory right to within a degree, and any error of a degree early in the flight would be easily corrected early and catastrophic later, encouraging the use of frequent small corrections rather than infrequent large ones. I reiterate: My intuition was clearly wrong. I love it when that happens. Apr 30 '14 at 14:42