Force of gravity during translunar flight

Assuming we measure distances in units of earth-to-moon distance, and masses in units of Earth's mass, we can write a simple piece of code to calculate the net acceleration (or force, it doesn't matter since we are using arbitrary units) of a craft in translunar flight. We assume that Earth is located at (0,0) and the Moon at (1.0). We also use the data indicating that the mass of the Moon is 0.0123 that of Earth.


function funForce(x,y)
rEarth=sqrt(x**2+y**2)
rMoon =sqrt((1-x)**2+y**2)

sinEarth=y/rEarth
sinMoon=y/rMoon

cosEarth=x/rEarth
cosMoon=(1-x)/rMoon
fx=(cosEarth/rEarth**2-0.0123*cosMoon/rMoon**2)
fy=(sinEarth/rEarth**2+0.0123*sinMoon/rMoon**2)
funForce=sqrt(fx**2+fy**2)
end


Now, we can plot the net absolute force as a function of (x,y) in the plane containing the Earth, the Moon and the craft. Since this is a 2D function, let's use contour lines to plot it:



The red dot correcponds to the so-called "neutral point", where the gravity of Earth is canceled by that of the Moon. Let's take a look at the slice of that 2D function through the X-axis:



Indeed, cancellation happens where it should (roughly 23k miles from the Moon).

Note, however, that the Apollo craft could have never passed through the neutral point thus defined, as the trajectory was much more complex. Assuming that it passed within 10% from the X-axis (which connects the centroids of Earth and Moon), we assume that the craft passed the blue point on the first graph.

Now, if we take a slice of that 2D function through the blue point, we get this:



Note that there is a minimum point in that graph. One would be tempted to say that this is about the place when the Moon's gravity starts to win out (while the net force is NEVER equal zero).

That point is located appoximately 43k miles from the Moon.


[edit on 3-12-2007 by buddhasystem]

[edit on 3-12-2007 by buddhasystem]

By the way is anybody finds an error in the posted material, please let me know. This was done quickly, so it may deserve a check.

Excellent presentation buddhasystem

Joins all the dots that a simple linear application of newton's principles misses due to the dynamics of matching the moon's orbital speed to allow orbit of that body to be achieved.

BS, your screaming at a deaf crowd, sir. But good work anyway, even though your wasting your time. The foolish theories presented in this section are more of a religion for the ignorant and uninformed, who want to remain ignorant and uniformed at all costs. There is nothing you can do or say that will change a single mind that believes this utter nonsense of the moon's gravity, bases on the moon, "NAZA" truth serum (did you here that one? I fell out of my chair laughing), people living on Venus and Mars, soul catchers on the moon.......and of course don't forget about the wonderful story of Element 115, etcetera.

But, those casual browsers might at least see a little common sense in this section and maybe, just maybe won't get sucked into the black hole and paranoia and ignorance.

Thank you Pilgrum and ITF.

I'm worried that I made a mistake somewhere (in which case I will promptly re-do the calculations), so I'm just waiting for John Lear to comment. I'm sure the issue of "neutral point" is of utmost importance to him.

John, if you are reading this,
I would love your comments.

Still no reponse from John Lear. The point that he's so fond of strumming, about his "neutral point" and how it relates to the Moon's gravity, is suddently neglected. Oh well, what do you expect...

Originally posted by buddhasystem

Still no reponse from John Lear. The point that he's so fond of strumming, about his "neutral point" and how it relates to the Moon's gravity, is suddently neglected. Oh well, what do you expect...

Sorry for the delay BS. The reason that I am delaying is that 2 retired former Lockheed scientists are coming to my birthday party tonight and I am going to share my response with them to check for accuracy before I post it.

Thanks for your patience.

reply to post by johnlear



Thanks John, I'm anxiously waiting to make necessary corrections.

Originally posted by buddhasystem

Thanks John, I'm anxiously waiting to make necessary corrections.

Thanks for your patience BS.

I had the birthday part of the century.

Bob Lazar called about 5 pm and said that he wouldn't be able to make it but wished me a Happy Birthday.

Everybody arrived about 6 and Bob walked in at about 6:30.

I was in total shock and he said, "I wouldn't have missed this for the world".

Jim Tagliani was also there with Shelly. Jim worked at TTR when Bob was at S-4.

Ron Blackburn (retired, 20 years at Lockheed Skunkworks) was there along with about 40 of my friends, many of them former Groom Lake workers.

We all talked about the old days and what we remembered..

Much of the party was videotaped by Ron Garner. At one point several asked that the video tape be turned off. And it was turned off.

The last people there at midnight were Zorgon, Ron and Sue Blackburn, Bob Lazar, Jim and Shelly Tagliani and me.

I mentioned my theory about the gravity on the moon and a breathable atmosphere.

Bob supported your position that the moon has one sixth of the earth's gravity and that there is no possibility of a breathable atmosphere.

He explained that the Bullialdus/Newton law of inverse square had no relevance and he explained why.

I disagreed but I did not argue the point. Bob did not believe flying saucers existed when I first met him either, and to this he did admit.

So you don't need to correct your calculations according to Bob Lazar.

But he is still my best friend.

this makes me realize thaat you have way to much time on ur hands =]