# Apollo 11's velocity is dropping. Why?

I’m following the Apollo 11 mission at http://www.wechoosethemoon.org and I’ve noticed something that has surprised me.

I have always heard that, due to the lack of friction in space, once a vehicle gets going out there, you can shut the engine off and the vehicle keeps right on going. But what I’ve noticed since the Command and Service Modules left Earth orbit yesterday is that the velocity has dropped. As I type this, it’s at 5,356 feet per second.

So what is causing the decline in speed? I doubt the vehicle is using propellant to slow itself at this point in the journey. There isn’t supposed to be any friction out there to slow it down. Earth’s gravity maybe? But that’s supposed to be awfully weak at a distance, and we’re talking about a small ship 100,000 miles from the planet.

How much of a drop in velocity? Over what time period?

That big honkin’ sphere called ‘The Earth’ is still just a-steady tugging on it. At a certain point (maybe 40K miles from the Moon?), the Moon will have a greater influence, and it will start accelerating again.

Yes, gravity. The size of the ship is irrelevant. The velocity will continue to drop until the point where the Moon’s gravitational attraction is stronger than the Earth’s, and then it will speed up again.

I’d put my money on this. Gravity does get weaker at distances, but not that weak. Acceleration due to Earth’s gravity (or decceleration, if you’re going away from it,) at 100,000 miles distance, would be 0.015 of a meter per second squared, if I’ve used this calculator right: Gravity Equations Formulas Calculator - Gravitational Acceleration

That would add up to 1296 meters/second, or 4252 feet/second, over the course of 24 hours. (Of course, it’s not going to be at that distance for 24 hours, but I think it gives you an idea.)

ETA: Beaten to the point, but I brought the numbers.

This how I got about the same rate of acceleration:

1. Distance from Earth’s center at the Earth’s surface is about 4,000 miles.
2. The rate of acceleration due to gravity at Earth’s surface is about 10m/sec squared.
3. 100,000 miles is 25 times this distance.
4. 1/25 squared = 1/625.
5. The rate of acceleration at 100,000 miles is about 1/625 of what it is on the earth’s surface.
6. 10/625 = 0.016.

This doesn’t take into account the fact that the gravitational force between the Moon and the ship is increasing the closer the ship gets to the Moon.

And this is all by design, because they’ve given that ship just enough of a boost to match orbits with the Moon - they don’t want it to go whistling past, or have to do a big burn to slow down when it gets there.

“Small ship” is irrelevant - its lesser weight is exactly counterbalanced by its lesser momentum, and if it had been an Imperial Star Destroyer at the exact same speed, it would have been decelerating just the same. Think cannon balls and Leaning Towers.

Oh, do you mean Galileo’s thought experiment?
Or the experiment that never happened: Galileo's Leaning Tower of Pisa experiment - Wikipedia

I just have to say that www.wechoosethemoon.org is very cool. It’s a shame that the weekend gets in the way. I was enjoying it playing in the background in my cubicle.

And I’ll be on the road on Monday

Just imagine what would happen if Apollo didn’t quite have escape velocity. It would slow down, stop, then fall back to Earth. If it has just slightly over escape velocity, it will slow down, almost stop, then be captured by the moon’s gravity and start accelerating again.

Only in the absence of external forces, such as gravity.

Absoutely it’s Earth’s gravity. And while the force of gravity does get weaker with distance, it has an infinite range.

Realize that the Moon is about 240,000 miles from the Earth, and gravity keeps it in orbit around the Earth.

nevermind

Note that Earth’s gravity is strong enough to hold on to the moon itself, and so far 11 isn’t nearly that far away.

But this one did.

–Cliffy

BTW The New Horizons space probe launched to Pluto a few years ago left earth with the highest velocity of any previous spacecraft around 36,000 MPH. It shot past the moon in less than 8 hours.