I thought that the Apollo spacecraft would have to have accelerated up to at least the escape velocity of the Earth, which is around 25,000 mph. The moon is approximately 240,000 miles from the Earth, so they should have been able to get there in aroung 10 hours. Yet it took 3 days.
I have searched here and on Google for an answer to this but can find nothing.
What am I missing?
Just a guess, but I believe the number you quote is the escape velocity from the surface of the earth. The Apollo missions left for the moon from earth orbit where escape velocity would be greatly reduced.
Well, for one thing they didn’t want to crash into the Moon at 25,000 mph. You’re missing the gravity of the Earth, the gravity of the Moon and the trajectory taken to end up in a nice orbit around the Moon.
Let’s see… firstly, if they reached escape velocity, there would probably have been a danger of overshooting the moon. Escape velocity from earth would have given them enough speed to leave earth and everything close to it behind. The moon is still in earth’s orbit, therefore they do not need ‘escape velocity’ to reach it (though they probably need to get a significant fraction of it.)
Second factor is that they were accelerating gradually. It probably took at least 10 hours just for the apollo spacecraft to reach ‘top speed’ as far as that term has any meaning in space. (After they spent the huge Saturn booster rockets simply getting up into earth orbit, of course.) And, as other people have pointed out, they needed to slow down and avoid hitting the moon at high speeds and wouldn’t be able to thrust with high force on the deceleration end, either.
Out of curiosity, does anybody know of a place where we can actually find a relatively full apollo flight plan, indicating how much they were able to accelerate at what times, what speed they were travelling when, and so on? That would be fascinating reading I think.
No, the point is that if you hit 25,000mph in low Earth orbit you are then going fast enough to reach an indefinite distance away from the planet without further need for acceleration - not that you will continue moving at 25,000mph because you have magically escaped all influence from Earth’s gravity.
When you fling an object upwards it immediately starts accelerating downwards under gravity. The higher its initial upward velocity, the higher it will reach before this acceleration brings it down. For slow moving objects close to Earth acceleration due to gravity can be considered a constant 32ft/sec/sec; for fast moving objects you have to factor in the lesser effects of gravity as altitude increases. But there’s still plenty of Earth gravity about the place by the time you get as far out as the Moon; enough to constrain the Moon to a 29-day orbit about the planet.
Bottom line: Crank your rocket up to 25,000mph and you’ve enough velocity to slip the surly bonds of Earth all right, but you’re slowing down steadily as you move away - you decelerate quickly at first, more slowly the further away you get, and at this particular speed it will take until you reach an “infinite” distance from Earth before you slow all the way down to zero. So most of the trip to the Moon was made at a speed a good deal less than 25,000mph.
It didn’t take that long to reach this speed. They got up to Earth orbital speed - 17,000mph - in just a few minutes starting with a brutal 4g acceleration from the first stage that gave them over 5000mph in a couple of minutes IIRC. (Accelerating at that speed you’re adding 80mph to your speed every second.) So they had only to add the remaining 8000mph, and at a modest 1g acceleration that would take only does the sums six to seven minutes or so. I’m not sure what the actual figures were, but there is info about all this somewhere on the Web.
Was it a spiral orbital path that got them to the moon rather than a ‘direct line of sight’ path?
In pedestrian terms, you are not travelling between two points whose locations are static to each other. One point is in orbit around the other point. You have to travel to where the other point is going to be, not where it appears at any given time. Think in terms of a quarterback passing to a wide reciever who is running a set pattern.
If memory serves me, the Appolo astronouts did a few earth orbits before blasting out towards the moon. They then went into moon orbit. Therefore, the path of the spacecraft was circles and spirals, not nice straight lines.
a) You might want to contact the Air and Space Museum. They’re a great resource. To my surprise, they’ve answered emails when I doubted if they would. Give it a try!
b) Also, if you’re in the area, check out the books in the gift shop. Beyond the “gifty” type books, I’ve found some discarded NASA reports on the old missions and such. It’s worth a look!
Well yes, but a lot of the velocity that generated that spiral was a result of the earth’s velocity around the sun.
Addendum: Oh, I should have added - If you do find anything, please come back and share with the class! I’d like to see that, too!
As a hijack, I wanted to ask about the pros and cons of different flight paths to the moon. The subject has come up now that the US is considering manned flights to the moon again.
The Apollo program started by placing the vehicles in Earth orbit, then going into a very high elliptic orbit that brought the spacecraft into the moon’s vicinity. The path was planned so that if insertion into lunar orbit didn’t happen (as in Apollo 13), the moon’s gravity would whip the spacecraft into a return trajectory with only minor course corrections necessary. This flightplan was dictated by the choice of having a separate lunar lander with lunar orbit rendezvous, the weight limitations of the Saturn 5, and to maximize the safe return to Earth options if a critical failure took place anywhere.
In articles I’ve read about about returning to the moon, I’ve seen proposals for direct ascent (no preliminary earth orbit) and using the L1 earth-moon gravitational balance point as the rendezvous site. How would these flight paths be more desirable than the one used for Apollo?
Um, I don’t think so. For example Apollo 11 went from the Earth to the Moon (I love typing that) when the Moon was near first quarter. That put he moon 90 degrees from the direction to the sun. In this position Earth’s velocity around the Sun is actually away from the position of the Moon.
The point is that regardless of the position of the two their velocities aournd the Sun are both approximately equal and their motion around the Sun is of no help or detriment to a body travelling between them.
I suppose that the the TLI (trans-lunar injection) path could be considered a “very high elliptical orbit.” When drawn to scale, however, it looks like a fairly straight line leading out from Earth orbit along a line 30 or so degrees ahead of the Moon’s position at the time of burn in Earth orbit. In scale the Earth and Moon are a golf ball and a garbanzo bean four feet apart.
Actually, the answer is really much simpler than has been presented: they didn’t have enough fuel to go that fast.
The Saturn V assembly uses almost all of its fuel getting into Earth orbit. The various other stages of transit to and from the Moom use an amount of fuel that, for obvious reasons, had to be limited only to what they absolutely needed.
You COULD get to the Moon faster, but you’d need more fuel, so that you could burn the engines longer. And if you went much faster than they were going, you’d have to turn the ship around and fire the engines to slow down when you got there - another waste of fuel. (The escape velocity of the Moon at its surface is about 5300 MPH, and it’s a bit lower at altitude, so you can’t be going faster than that or you’ll shoot on by.)
So to go faster they would have had to build an even bigger rocket to carry more fuel. It was easier to just take their time.
I interpreted springears post as meaning that the path from the earth to the moon was a long spiral in space when viewed from a position “above” the planetary plane. That spiral would largely be a result of the velocity of the earth-moon pair in orbit around the sun. There was no intention to imply that part of the velocity in going from the earth to the moon was provided by the orbital velocity.
Just because they reached escape velocity didn’t mean the spacecraft was totally beyond Earth’s gravitational influence. Much as with a thrown rock slows down near the top of its trajectory, the gravity of the Earth gradually slowed down the spacecraft as it neared the gravitational balance point between the earth and moon. Achieving escape velocity only means that you will keep travelling upward or outward instead of being pulled back to Earth like a projectile, but gravity will still slow you down.
Then the spacecraft sped up slightly as it “fell” toward the moon.
Yes, the earth, moon and spacecraft are all gravitationally interconnected and are orbiting the sun as an ensemble.
Also, remember, it is all uphill.
You can find full details of the Apollo program at the NASA website. The log for Apollo 11 specifically is here: http://history.nasa.gov/ap11-35ann/apollo11_log/cover.htm