There's one piece of bad math that I've encountered relatively frequently in conversations. It's
incredibly frustrating to me, because it's just so crazy - but the way we teach math and physics, far to many people just don't have enough of a clue to see how foolish it really is.
This comes up in conversations with lay-people whenever a new space probe is launched. It's generally presented in the form of a question; something like "That TV announcer said something about a point between the earth and the moon where gravity cancels, so there's no gravitational pull towards either the earth or the moon. How can the moon cause tides if its gravity is cancelled all the way out there?"
I've never found a form of this that was sufficiently mockable - in general, people who ask the question know that there's something wrong with the question; they know that it's stupid, but they don't know why. I don't like to make fun of that: people who ask a question because they know that their ignorant about something, and they're trying to fix that patch of ignorance - they don't deserve to be mocked. So I've avoided this. Until now: I've found the perfect mockable presentation of this problem. And wait till you see the wonderfully insane form I found it in!
No one would quarrel with the fact that there is a relationship between what the Moon does and what the Tides do. The Bible, after all, says that the Moon was designed to serve mankind through "signs" (which could certainly include Tidal phenomena), and through "seasons", and by giving light.
However, to say there is a relationship or connection between the Moon and Tides is one thing; to say that the Moon causes and controls Earth's tides (as the whole world has been taught is a scientific fact) is quite another thing.
In the first instance--since God has said that one of His purposes for making the Moon and having it behave as it does is precisely for man's aid in such things as gauging tides, planting, harvesting, etc.--we see the relationship as supernatural. These are "signs" and they have always worked and they work now for those who read them. Thus, there is a relationship or connection between the Moon's behavior and supplying useful and necessary knowledge for man.
In the second instance, however--since "science" has said it will explain everything in natural terms without God and will designate all supernatural explanations as superstitions held by unenlightened people--we find that the obvious connections between the Moon's behavior and certain phenomena such as Tides must be explained naturalistically by the science establishment.
So, God gave His supernatural explanation for Tides, which man has rejected. In its stead, man has come up with a purely naturalistic explanation for the tidal phenomena. In short, man's "science" has declared that the Moon's gravitational pull (assisted by the sun's pull) causes the Tides. This declaration is now counted as a "fact" of science.
Vern, one of these explanations is the Truth and one is a lie. Let's see if we can find out which is which.... First, let us look at some facts and see where they take us logically. For instance, there is a real fact about a neutral gravity zone between the Earth and the Moon. I quote from a letter from NASA dated April 5, 1990 addressing this matter:
"...On a direct line from the Earth to the moon, equal gravitational effects would be found at approximately 216,000 miles, given a mean
distance of 240,000 miles between the two bodies...."20 (Emph. added)Other sources confirm this understanding. Figures XIV & XV {reproduced in book only} are taken from one of famed rocket scientist Werner von Braun's books. They illustrate this neutral gravity zone.
OK. So all we are describing here is something that must logically be true if the statistics about the Earth and Moon gravitational pulls are fairly accurate. Earth's gravity is said to be six times as strong as the Moon's gravity, or said the other way, the Moon's gravitational attraction is 1/6 or about 17% that of Earth's gravity.
Somewhere between the two bodies the pull of one body has got to be overcome by the pull of the other
one. At this point (which NASA says and von Braun confirms averages c. 216,000 miles from the Earth) there
is a neutral gravity zone where the Earth's gravitational pull becomes weaker than the Moon's gravitational
pull and, at this same point, the Moon's gravitational pull becomes weaker than the Earth's gravitational
pull.This circumstance is demanded by the gravity concept and all the supposed facts and laws that describe the Earth and Moon gravitational fields. OK, Vern? Now keep that in mind as we read what "science" says about Tides on Earth....
What "science" says is that the Moon's gravitational pull reaches out thru the neutral gravity zone (where it couldn't attract a balloon full of feathers, a dead horse, or the Astrodome) and goes on beyond 50,000, 100,000, 216,000 miles and sucks the big ole Earth toward it like stretching a rubber ball! I know it's incredible; I know it's insane, but that's what the naturalistic (i.e., "scientific") explanation demands that the Moon must do. Read it for yourself from these examples (which are repeated in every book on the subject):
"Strange as it may seem [yeah!], what we normally think of as
the solid body of the earth is also affected by the moon, so that it
too [the Earth, that is] has a tide. The landmass of the earth is elastic
and actually rises and falls about 4 1/2 inches. We do not feel these
land tides...but they do take place." 23 (Emph. added)In his book, The Lunar Effect, author Lieber says:
...the pull of the moon distorts the earth as if it were a rubber
ball. The North American Continent may rise so much as a foot
when the moon is overhead."24The famous "science" writer Asimov says:
"...the earth, so to speak, is stretched in the direction of the moon.
The solid earth does not stretch much, however (only about nine inches
on each side), and only delicate measurements can show this stretch."25He's lying about the "delicate measurements", of course. No measurement shows this (and what the others said) or could show it. Mathematical decorations derived from and supportive of this crazy hypothesis might show a 9"stretch (twice what the other guy just said), but no measurement has or can show it.
In a kid's "science" book we read:
"Now the land of the earth does not move easily, but the waters do.
The waters on the side of the earth closest to the moon pile up in a
"bulge", causing a high tide. But at the same time there is a high tide
on the other side of the earth. What do you suppose is the reason for
this? The answer is that, as the moon's gravity pulls the water nearest
to it a little away from the earth, it also pulls the whole earth a little
away from the waters in the ocean on the farthermost side, setting up a
second high tide there."26In The Moon: Earth's Natural Satellite, author Branley says the same thing in explaining his diagram on the tidal phenomena:
"...the ocean at E [the furthermost from the moon], because it is so
much farther away is not pulled toward the moon as much as the solid
earth; the earth is pulled away from the water; and the water is therefore
deeper during this part of the tidal cycle."27 (emph. added)Branley then gets into some numbers which grow out of the myth he believes, numbers so contradictory as to be comical if the world weren't mesmerized by this deception:
"The tide-raising force of the moon is very small indeed, compared
to the force of gravity. The tide-raising force of the moon is about
1/9,000,000 that of the earth's gravity...."28Wow. One nine millionth Let's see; that means the earth's pull toward its own center on its own crust and oceans and seas is nine million times as great as the Moon's pull on the same features, doesn't it? Nine million to one. Whew! Amazing, isn't it that nine million mule power could be pulling something one way and one mule power could overcome all that every hour of every day and stretch the Earth and cause zillions of cubic feet of water to shift around everywhere! Yes, just amazing, especially when that one mule power stopped out there at the 216,000 mile neutral gravity zone! Momma mia...
Now that is truly first class insane crackpottery. Just off the wall.
Yes, it's an ultra-fundie geocentric lunatic. (A particularly appropriate term given the subject.) See, the lunar tide thing is part of an elaborate conspiracy by
scientists to deny God's role in causing the tides. In fact, it's all tied in to evolution. But we won't get to that bit today.
This doesn't even need me to mock it. Just read it yourself, and when you manage to pick yourself up off the floor, I'll explain the math behind the error.
It's crazy, but it does contain that gravity question - just stretched out beyond the breaking point. But what makes it break in that loony-tune universe is the same thing that causes confusion back here in the real world.
The "zero point" isn't the point at which the moons gravity stops. It's not the point at which
the earths gravity overcomes the moons gravity so that the moons gravity can't come any closer to the earth. It's just the point at which things balance.
Get two large springs - like a slinky. Attach each of them to opposite ends of a rubber ball. Then attach the other end of the springs to opposite walls of a room, and let go of the ball. The ball will
oscillate back and forth for a while, but eventually, it will stop, in a configuration like the figure to the right: the two springs will each by stretched to the point where the force that each stretched spring applies to the ball is the same. The place it stops is the equilibrium point for the two springs in that space - it's the point where the force exerted by the two springs is equal, and so they cancel out - the ball is effectively under no accelerating force.
But - more importantly: the walls that the springs are attached to are still being pulled towards each other, even if the springs are in equilibrium. The fact that the tension in the springs
create forces that cancel out at the equilibrium point doesn't mean that the forces have disappeared.
Gravity operates in the same way. As you move away from the moon, the force of the moons gravity decreases - every time you double the distance from the center of the moon, the moons force of gravity on you decreases by a factor of four. But it never disappears. The force doesn't stop at equilibrium - it just balances there. If you move closer to earth than the equilibrium point, then the earth's attraction is stronger than the moon's. But it still exists.
Just to hammer the point home a bit more, let's look at the math. Let's look at the gravitational forces on a person on the surface of the earth. We'll just do it approximately, to keep the calculations simple, so we'll do it for a person standing on the equator, and we'll pretend that the moon orbits right above the equator.
We'll start by just laying out the basic data that we'll need to do the calculation. I'll use my own weight for the person; I weigh about 84 kilograms. The radius of the earth at the equator is about 6,350 kilometers. The mass of the earth is about 6.0×1024. The mass of the moon is about 7.4×1022. The distance from the earth to the moon (surface to surface) is about 384,000 kilometers. The radius of the moon is about 1,700km.
Newton's equation for calculating the gravitational force between two objects is F=Gm1m2/r2, where the ms are the masses of the two objects, r is the distance between their centers of mass, and G is the gravitational constant 6.7×10-11m3/(kg sec2).
So - the force of gravity from the earth on the person (with all numbers rounded to two significant figures) (6.7×10-11)×(6.0×1024)×84/(6.5×106)2 = 800 newtons.
The force of gravity from the moon is calculated the same way. But we need the distance from the center of the moon to the surface of the earth, and our distance figure is surface to surface, so we need to add the radius of the moon - so the distance is 385,000km. So - the gravitational force from the moon on the person is (6.7×10-11)×(7.4×1022)×84/(3.9×108)2 = 2.7×10-3 newtons.
The force of the moon on the person on earth is very small - on the order of 1/300,000th the gravitational force of the earth on that same person. But it's definitely there - real, and measurable. And that kind of force is more than enough to produce the very modest effect of tides.
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If you're standing on a pair of bathroom scales, in front of the sink, and you press down very slightly on the sink, then you seem to weigh a little less. Isn't it odd how lightly pressing down like that overcomes your entire weight, and causes the scales to wobble ever so slightly (although by an amount that would seem enormous to an ant). That funny author must never add one and one together.
Good post, Mark.
If their "logic" were true, the moon wouldn't revolve around the earth, and the earth wouldn't revolve around the sun. Past the equilibrium point, no extra-terrestrial gravitational force can penetrate!
Like you said, the error is in their assuming the equilibrium point is where, somehow, the gravitational force from each body is zero, instead of the correct assumption that their sum is zero.
minor nitpick, you dropped the units for the masses of the earth and moon.
So why do we have high tide on both sides of the earth at the same time, as asserted by the "kids science book"?
Wouldn't gravity cause water to "bulge" only on the side closest to the moon? Maybe the cause of high tide on both sides of the earth is due to the earth spinning? I'm not buying the explanation provided by the kids science book.
Or, maybe it is a sign that God is controlling the tides.
I think there's another error in the "argument" in the last paragraph worth pointing out, and it's a kind of "look at the big numbers produced by the scientific explanation!" fallacy. The claim is that since the moon exerts 1/9M of the force on the oceans as the earth, it couldn't possibly displace millions of cubic feet of water.
If you really want godly 'signs' from the moon, should they not be in kilometer-long Aramaic characters, scratched into the lunar dust? Probably too obvious. I should stick to math, and avoid theology.
David:
I'll assume that's a serious question, and not just snark making fun of the whole argument.
Tides are caused by differentials in the effect of gravity between the liquid in the seas and the solid bulk of the earth. The solid is stretched toward the moon, but it's not very elastic, so the distorting effect of gravity is quite small. For the most part, the earth acts as a rigid body. So for the earth, it behaves almost as if the earth were a fully rigid point-mass with the entire mass at the center of gravity.
Liquid, however is not rigid. So on the close side to the moon, the liquid can flow so that it builds up the tide. That's the easy part to see: the earth is pulled towards to moon, and reacts to that pull as a single rigid body; the water flaws, and so it builds a bulge pointing at the moon.
On the opposite side of the earth, the pull of gravity from the moon is *smaller* because of the greater distance. But the earth is behaving as if it were a rigid body - so the gravitational effect on the rigid earth is the gravitational force on the mass of the earth at the center of the earth - so it's *closer* to the moon that the water on the far side. So the earth is effectively being pulled towards the moon harder that the water opposite the moon is; so the earth is pulled away from the water - effectively creating a bulge opposite the moon.
Wikipedia has a good article on tides:
http://en.wikipedia.org/wiki/Tidal_force
I suspect that a lot of the confusion about gravity comes from the constant media insistence that the Space Shuttle is in zero gravity, complete with pictures (of floating astronauts, etc.) that seem to prove it.
Gahh! The Stupid! It burns!
I think part of your problem here is that you have used those Satanic metric units instead of Godly standard units. Anyone can lie with meters and newtons. Who really knows what they represent? They make your whole argument very suspicious. ;^)
I have to think there is an easy explanation for the zero gravitation point our "non-science" gentleman would understand.
Here's an attempt:
A man is being tortured in the gallows (he's on the rack). As they tighten the chains that hold his arms over his head and his feet at the ankles equally, the man does not move. Since the man is not moving he is not being pulled by one chain over the other. There is zero-pull like our 216,000 mile point in space. So why does the man scream in pain?
"Zero pull" does not mean "no pull," it means the object at that point is being pulled equally by the two forces.
I'm stopping here before thick sarcasm sets in...
Thanks, Mark. It really was a serious question (although my comment about tides being a sign from God was pure snarky).
The kids science book provided the same explanation you just provided. However, I am not sure that I completely accept this explanation. The size of the tide created by the moon pulling water away from the earth is fairly significant. In order to have a similar high tide on the non-moon side it would mean that the non-moon side of the earth would need to be pulled away from water to a similar degree. I certainly may be wrong, but I didn't think this was actually the case.
It may help to realize that the moon doesn't revolve around the earth; instead, the earth and moon both revolve around the center of gravity of the earth/moon system, which is slightly on the moon side of the center of the earth. The water on the far side of the earth is not constrained to follow.
No amount of mockery can make up for the teeth-grinding stupidity of that piece. I feel soiled.
The thing that these anti-science it's-all-a-conspiracy rants always seem to have in common is that they somehow simultaneously assume that certain bits of science (the existence of gravity, the equilibrium point in the right place, etcetera) are unquestionably correct, while assuming that the people that discovered all of that somehow simply didn't see some incredibly obvious 'fact' which has occurred to them and them alone. In every case, their argument seems to go along the lines of "well if there's gravity, why don't we fall into the sun, smart guy?" and they honestly expect some scientist somewhere to go "wow, you know, I never even thought of that!"
Myself, when I see something incredibly obvious that seems to have been missed by the rest of the world, I generally start out assuming I'm not getting some crucial bit of information, and set out to find out what that is.
Here's a good site for explaining the different forces that cause the tides: http://co-ops.nos.noaa.gov/restles3.html
Here's the weak point: "No one would quarrel with the fact that there is a relationship between what the Moon does and what the Tides do. The Bible, after all, says that the Moon was designed to serve mankind through "signs" (which could certainly include Tidal phenomena), and through "seasons", and by giving light."
I would certainly quarrel with the claim that the Bible says there's a relationship between the Moon and the tides. "Signs" do not include tidal phenomena. Since tides occur approximately twice a day, there is no obvious reason why they should have anything to do with the Moon. And seasons have nothing to do with the Moon, yet according to this guy, the Bible claims they do. And of course there's tidal phenomena all over the universe, which the Bible is strangely silent on.
By the way, since this is a site about math, why not discuss the tides in mathematical terms? Why all the hand-waving?
I think the simplification to Newton gravity with field and forces fits the purpose of debunking bad math.
But if we are going to extend the discussion to full-blown general relativity, we should also note that the above terminology is void. Instead masses move in curved spacetime and the forces are fictitiuos when moving in non-inertial frames.
The general force description is recovered by using four-forces and four-acceleration in spacetime.
This is similar to that we shouldn't speak of "relativistic mass" anymore, but recognize only invariant mass. [I often slip back into old habits because I was taught that way myself.]
But it can also be annoying when it should be emphasized, see the lack of a reasonable free fall description Tom Jackson identifies as a problem in comment #8.
Correct link and spelling: the forces are fictitious.
And to think one can hear this, when the latest IIRC instantaneous measurements is down to mm on Earth radius. (By long baseline interferometry to reference stars, I think.)
:-P
Actually we have pretty good ad hoc checks. Why not remember the fact that most people are closer to 2 m long?
And, although it was inconvenient in the context of the post, normally we use a flat approximation close to a large sphere such as Earth. (For example to easily extract potential energy as mgh, for different heights h.) The gravitational acceleration g here happens to be roughly 10 m.s-2, an easy to remember number ;-), so for example our mass m of 84 kg is roughly 800 newton as force mg.
Very minor nitpick (and we all knew this would come up again :-):
The SI standard shorten to s, not "sec". Also we write "800 newton" since the number express the plural and the unit is always singular. (This makes all sorts of things simpler, except possibly in everyday texts.)
Like David, I am not sure I buy the explanation for the high tide on the opposite side that you gave. It doesn't jive with either my intuition nor my understanding. However, I am willing to believe that my understanding is wrong or your explantion is somehow equivilent.
As I understand it, an objects orbit is determined at its center of mass. However, portions of the object that are closer to the primary will experience a slightly higher pull, while those portions further away will have a slightly lower pull. Since the object is nominally rigid, the closer portions will be forced to move slower than they would need to remain in the orbit they occupy meaning that they have the extra force pulling them toward the primary. The further portions are forced to move at a speed faster than the orbit they occupy and thus experince an outward force. Thus a rocket shaped object in orbit will have a tendency to have its long axis point through the primary. A great story written around this is Neutron Star by Larry Niven.
So, am I wrong, or is this just another way of saying what you said?
I'm going to join the nitpick brigade here. Your mass is 84 kilos. Your weight is approximately 9.8 times that in newtons. This is not something I could overlook in this context. Mass is invariant (modulo Einstein), but weight depends on the gravity at an object's location, and is, in fact, measured in units of force.
David / Brian:
Consider if you had three point masses orbiting the Earth/Moon center of gravity, one at the Earth's center of gravity, one at that distance plus one Earth radius, and one at the distance to the Earth's CoG minus one Earth radius (plus the Moon, which need'nt be a point mass). In the normal case, if all three point masses were in orbit, we would observe a higher velocity for the outer one, and a lower velocity for the inner one, and they would only align every XX thousand years. If they all had the same velocity, then the inner one would begin to fall towards the orbital center of mass, and the outer one will begin to drift away, since their velocities are respectively too low and too high for their orbital distance. That is exactly the situation for free-flowing bodies of water (or very slow-lowing bodies of rock) with respect to the Earth, when all are in orbit around the Earth/Moon CoG... On Earth, we see that falling inwards or drifting outwards as, respectively, a tide rising towards the Moon, or away from the Moon.
Is that better?
Bonus question...
MarkCC-C writes:
Now let's consider the gravitational pull of the Sun on Mark.
Distance = 1.5 x 10^11 m
Mass (of the Sun, not Mark) = 2 x 10^30 Kg
F = (6.7Ã10^-11)Ã(2Ã10^30)Ã84/(1.5 x 10^11)^2 = 0.5 N.
So given that F exerted by the Sun on Mark is about 180 times that exhibited by the Moon (barring math errors on my part), why does the Sun only account for about half the tidal force of the Moon?
"So given that F exerted by the Sun on Mark is about 180 times that exhibited by the Moon (barring math errors on my part), why does the Sun only account for about half the tidal force of the Moon?"
Isn't the "tidal force" the difference between the pull felt at your head and that felt at your feet? And since that difference is such a smaller percentage of the distance to the sun than to the moon, wouldn't that account for the Moon's larger "tidal force"?
Mark,
Yes, I do like that explanation better. If I understand you correctly, the entire body of water around the earth can be viewed as orbiting the Earth/moon CoG, and it is the velocity of this orbit (which is affected by the position of the moon) that causes the tides. So the moon isn't so much pulling on the water closest to the moon side of earth, but is instead affecting the 'orbit' of the earth's water. At least, I hope that is close to what you were saying.
Well I didn't read ALL the posts so it may have come up already, but I think I have the "laymanest" explanation:
Imagine 2 wedges made of wood equal in length. One wedge has a much greater width at one end than the other and it represents earth's gravity. The other with a much thinner fat end of the wedge (hehe) represents the moons gravity. If you place them one on top of the other with thin ends in opposing directions then at some point along the wedge the widths will be equal and this would represent said area while demonstrating that while gravity weakens it does continue passed that point.
David - yes, that is one way to view it, and it makes the cause of the tides more apparent, at least in my mind. I think the distinction between "pulling" the Moon-side water and "relatively less pulling" the away-from-Moon-side water and "affecting the orbits" is a distinction without a difference; it is the (difference in) relative attraction to the Moon that creates those different orbits for the two bodies of water (if the water were not bound to the Earth by the much stronger attraction of Earth's gravity). In the end, though, that's just a matter of how you describe it...
In general, any non-point mass will experience a 'stretching' tidal force when moving under the influence of the gravity of another mass. This arises from the fact that only the center of gravity of the mass is actually moving at the "right" velocity for its orbit. The parts that are closer to the gravitating body moving a bit too slow for their orbit, and thus experience a force directed toward the gravitating body. The parts that are further from the center of mass are moving a bit too fast for their orbit and will tend to "fly away," experiencing a force directed away from the gravitating body. This is the basis of the Roche limit, which is the distance at which an orbiting body will be torn apart by tidal forces, because the tidal forces exceeds the body's own gravitational cohesion.
Yes - and to get all mathy about it, this difference calculation means that the tidal force is proportional to the derivative of the gravitational force. That is, it's proportional to one over the distance cubed.
So, the ratio between the sun's gravity and the moon's gravity is:
[ (mass of sun) / (sun distance)^2 ] / [ (mass of moon) / (moon distance)^2 ]
= 177 (what Dave S calculated)
But the ratio between the sun's tidal force and the moon's tidal force would be:
[ (mass of sun) / (sun distance)^3) ] / [ (mass of moon) / (moon distance)^3 ]
= 0.45 (close to the one-half value you read about)
So the sun's tidal force is definitely smaller than the moon's; but it's large enough in comparison so it should be noticeable (which in fact it is - it makes the difference between a "spring tide" and a "neap tide").
I remember the terminally stupid GCSE question which went something along the lines of "why would it be advantageous to put a satellite in the point where the gravity cancels?" And you are supposed to write that it would stay in the same place relative to the Earth and Moon. You are not supposed to know that the orbital motion of the Moon would quickly wreck this configuration, and the term "Lagrange points" is probably unknown to the examiner, so you'd probably lose marks for mentioning them.
Sea tides are even more complex when you add in the constraints caused by the tidal 'bulge' being contained in ocean basins.
That tidal 'bulge' (in principle) gets pulled across an ocean basin as a wave, and then between 'pulls' it retreats as a wave, and so on. That is, lunar gravity causes is a cyclic input to water in the basin, a wave 'sloshing' back and forth as it were.
When that kind of rythmic sloshing happens in a closed basin (the world oceans, more or less) what happens is that you tend to get standing waves, often circling the basin. The location and height of that standing wave at any time is a function of lunar tidal attraction, AND of the geometry of the ocean basin.
This is the reason that high tide is not always just when the moon is overhead - it can lead or lag that time depending on the geometry and motion of the standing wave pattern in the basin.
It is also the reason some locations in the ocean don't have appreciable tides. The tidal range at Tahiti, for example, is typically less than an inch or two. Tahiti is very near a node at the center of the Pacific tidal standing wave pattern - the point around which the tide revolves. The further from that node, the greater the amplitude of the tide as the pacific tidal standing wave rotates in the basin - which is why Alaska has a much higher tidal range than Los Angeles. It is further from the node near Tahiti.
This is also why some places have only one high tide a day, and others have two. It depends on whether the standing wave pattern in that ocean basin has two tidal bulges radiating from the node, pointing opposite each other and causing two high tides a day as they rotate, or a single bulge rotating around the basin.
Just one question. Are we sure that the guy is not making fun of us? I checked his site and the main point behind the site is that:
The Earth is not rotating...nor is it going around the sun
I think it is only a joke.
What do you think?
"The Earth is not rotating...nor is it going around the sun"
Why are you so sure that the earth IS rotating, and that it IS going around the sun? Sounds like ancient jewish mysticism to me.
:)
Why we are sure that the Earth is rotating:
(1) We can see other planets, moons, and asteroids rotating, by telescope, spacecraft, radar...;
(2) Earth's measured polar flattening and equatorial bulge;
(3) Foucault pendulum
http://en.wikipedia.org/wiki/Foucault_pendulum
This is not mysticism. The point here is to oppose Logic to Faith, observation to denial; eyes open to see the cosmos versus eyes closed to pray.
It is, of course, possible to apply Logic and Faith, observation and meditation, appreciation of the universe with appreciation of a hypthetical Creator.
There is a tide in the affairs of Men...
Actually I think that the guy of the tide has a point there. I may be wrong but he may just trying to show that if you question scientific theories (for example evolution) on the basis of what it is written on the bible then you should also question the fact the the earth is rotating. While it is easier to fool people on evolution because it is a difficult theory, it is more difficult to fool people on earth revolution because everybody has seen it.
If you make people realize that if they question scientific theories because of their holy scriptures they end up believing the stupidest things, they may reconsider their stance.
Am I making any sense?
PhD Stud: If I'm reading you correctly, you're basically thinking that the guy's entire site is a satire meant to lampoon people who take the scripture over science?
The problem with that statement is the demonstrable number of people who *do* take scripture over science, and have access to the internet.
Great to see the discussions here. The 1969 issue of Times magazine gave a different figure for the neutral point and quoted Werner von Braun as the source. The distance given was 43,495 miles from the moon.
Your quote: "Somewhere between the two bodies the pull of one body has got to be overcome by the pull of the other one. At this point (which NASA says and von Braun confirms averages c. 216,000 miles from the Earth) there is a neutral gravity zone where the Earth's gravitational pull becomes weaker than the Moon's gravitational pull and, at this same point, the Moon's gravitational pull becomes weaker than the Earth's gravitational pull."
The moon hoax conspiracy theorist have take von Braun's figure as gospel and use it to determine the moon's gravity to be 64% of earth's. They're extrapolating that to mean there is an atmosphere on the moon.
I did the simple calculation using F=Gm1m2/r^2 = Gm2m3/R^2
Where:
m1 = earth mass
m2 = mass at neutral point
m3 = moon mass
r = distance from earth to m2
R = distance from moon to m2
The result is that the neutral point is 90% the way to the moon. Or about 23,9000 miles from the moon.
So the question is: What is von Braun's figure?