Did Apollo's velocity slow down after TLI due to Earth's gravity?

I assume Apollo's velocity slowed down after it left Earth orbit, for how long was it decelerating. Did it start accelerating as it approached the Moon. What was the rate of deceleration due to Earth's gravity?

• What do you mean? Rate of deceleration at what point? Much of the lunar transfer is unpowered. Can you clarify. – Rory Alsop Jan 9 at 22:35
• @RoryAlsop I did not say powered deceleration. The velocity of Apollo changed from TLI to until Lunar orbit insertion due to the gravity of the Earth and presumably the Moon. What what that rate of change? – Bob516 Jan 9 at 22:56
• While the question could have been better formulated, I don't feel it merits being down voted, as judging on the basis of OP's record here, it was asked in good faith. What seems obvious to ourselves might not to somebody else, and that is something all of us ought to keep in mind when interacting here. – Happy Koala Jan 9 at 23:02
• @uhoh That would indeed be a rather awesome program... You're full of awesome ideas, you know? If you have an official fan club, could I pretty please be its president? There are lots of charting libraries out there so I could spin one up really quickly, but first the stars orbiting around the Saggie :D (my new nick name for Sagittarius A). – Happy Koala Jan 10 at 8:35
• @RoryAlsop Ah, fair enough, after all those Karman posts I've started equating down votes to "bugger off, you sod", but of course that's not the case. I'll keep that in mind next time around my eyes start tearing up at the sight of a post getting down voted :D – Happy Koala Jan 10 at 8:37

I assume Apollo's velocity slowed down after it left Earth orbit, for how long was it decelerating.

A pretty good analogy for TLI is throwing a baseball straight up into the air. The "throw" is the TLI burn; as soon as the ball leaves your hand it begins to slow down, trying to fall back towards Earth. The peak altitude of the "throw" is around where the moon will be three days later.

Did it start accelerating as it approached the Moon.

Yes, as noted in @PearsonArtPhoto's answer.

What was the rate of deceleration due to Earth's gravity?

The deceleration decreases the farther you get from Earth in an inverse-square relation:

$$a=-{G M \over r^2}$$

Where $$GM$$ (aka $$\mu$$) is the gravitational parameter of Earth (3.986e14) and $$r$$ is the distance from the center of Earth in meters. In LEO this is still 9.2 m/s2 or about 94% of Earth's surface gravity. By the time you're 3000 km up, though, it's only about 50% of surface gravity.

You can compare the results of the equations for the "downward"-pulling Earth component and the "upward"-pointing moon component, with the appropriate distances and gravitational parameters for the two bodies, to see what the crossover point is. Or use algebra if you're into that.

Yes, in fact it did slow down with time, until it approached close enough that the Moon pulled it faster. That happened at a point very close to the Moon. In a diagram on this page, for Apollo 8 we can see that point was just after the second full day, and the speed was about 3578 km/hr.

Borman, Lovell and Anders were the first humans to leave the Earth’s gravity. They also never felt any physical change when the spacecraft slowed down to 3,578 kilometres per hour relative to Earth and crossed over into the Moon’s gravity field at 55:38:40 GET (0629:40 AEST). They were 326,415 kilometres from Earth and 62,598 kilometres from the Moon.

• from your page: "At 2:50:37.79 GET (0141:37 AEST), the S-IVB stage burned for 5 minutes 17.7 seconds to boost the spacecraft’s velocity by 7,451.2 kilometres per hour, and Apollo 8 left Earth orbit and headed for the Moon at 38,959.4 kilometres per hour." – bitchaser Jan 10 at 1:39
• "Borman, Lovell and Anders were the first humans to leave the Earth’s gravity. They also never felt any physical change when the spacecraft slowed down to 3,578 kilometres per hour relative to Earth and crossed over into the Moon’s gravity field at 55:38:40 GET (0629:40 AEST). They were 326,415 kilometres from Earth and 62,598 kilometres from the Moon." – bitchaser Jan 10 at 1:52
• – uhoh Feb 17 at 21:48
• Just to nitpick, the statement "Borman, Lovell and Anders were the first humans to leave the Earth’s gravity" is incorrect. They never left earth's gravity. No one can, everything that exists and will ever exist is within earth's gravity (as long as earth exists). What the author probably meant is that they were the first humans to be subject to a gravitational field that was stronger than that of earth. – user2705196 Mar 16 at 18:41
• @user2705196 It's a direct quote, so... – PearsonArtPhoto Mar 18 at 9:48