[Steffen Clemmerson]

NASA claims they dropped a hammer and a feather on the moon and they equally "fell" in the exact same rate of speed. Proving mass doesn't matter. But yet gravity is bound by mass? Either way, if mass is truly (weightless) in a vacuum then I would assume that space itself is anti gravity. I mean, it follows the 5 criteria for "anit-gravity". And that being said, we obviously can't get into "space"

[Macarios]

Proving mass doesn't matter.

Nope.
Proving mass of small object doesn't change free fall ACCELERATION towards Earth, Moon, Mars...
But mass DOES change FORCE (weight).

Force is product of acceleration and mass.

What will fall faster: two weights of 5 lbs each glued together into one, or same two weights dropped together as singles?

[JohnAdams1145]

Steffen,

I suggest you take a physics class at your local high school or community college and then sign up for the AP Physics exam and pass it (it's only around $100 + free online study materials). It will clarify a lot for you, as you currently cannot distinguish between weight, mass, force, acceleration, and speed. Weight (here on Earth) is the magnitude of the gravitational attraction between Earth and an object. Weight on Jupiter is the magnitude of the gravitational attraction between Jupiter and the object. We ignore the gravity of other celestial bodies because they are negligible close to the surface (the magnitude drops with the square of the distance).

Therefore, weight on the Moon is the magnitude of the gravitational attraction between the Moon and the object. Gravity is an observed phenomenon that gives weight to objects with mass. A mass is not weightless in outer space because you haven't properly defined weight, unless you define it as the direction and magnitude of the net gravitational force, which is going to be minuscule if it is in outer space. A mass certainly has weight in any sort of orbit close to a celestial body. A mass also has weight on the Moon. It turns out that the weight is proportional to the mass. Therefore, by F=ma (Newton's Second Law), the acceleration is constant since F is the weight. Anti-gravity doesn't exist.

Your conclusion that we can't get into "space" is a non-sequitur. Rockets have been demonstrated to work at almost the same performance in the dense troposphere and the sparse stratosphere. There's no reason to believe that decreasing the density of the air further will suddenly make them stop working. Even basic logic contradicts your hypothesis. Of course, the physical explanation is conservation of momentum, which confirms that rockets work in space.

[douglips]

if mass is truly (weightless) in a vacuum then I would assume that space itself is anti gravity. I mean, it follows the 5 criteria for "anit-gravity". And that being said, we obviously can't get into "space"

You aren't making any sense. Mass isn't weightless in a vacuum. Vacuum is the absence of air - not the absence of gravity.
What, pray tell, are the "5 criteria for anti gravity"? I've never heard of such a thing, and I've studied physics for 4 years of college.

[Tom Bishop]

The poster has a point. Are we to believe that a feather would fall into a black hole as fast as two black holes colliding would?

[garygreen]

The poster has a point. Are we to believe that a feather would fall into a black hole as fast as two black holes colliding would?

this is approximately equivalent to the noobs who come here and say things like "but anyone can see curvature from an airplane!"  how seriously do you take their polemics?

acceleration is proportional to both force and mass.  yes, the black hole would experience a greater force than the feather.  it wouldn't experience a greater acceleration because it is proportionally more massive.

http://www.physicsclassroom.com/Class/newtlaws/u2l3e.cfm

[douglips]

Two black holes colliding would happen faster than a feather falling into a black hole, because in the case of two black holes, BOTH black holes are accelerating towards each other. In the case of the feather, the black hole's acceleration towards the feather is negligible.

The "different mass objects fall at the same rate" only refers to the acceleration of the single object under test. While a very very massive object would accelerate at the same rate, it would also cause the earth (or other surface) to accelerate towards it, making the apparent acceleration larger. When one object is several orders of magnitude more massive than the other, the more massive object doesn't accelerate much compared to the lighter one.

[Macarios]

The poster has a point. Are we to believe that a feather would fall into a black hole as fast as two black holes colliding would?

When feather falls to blackhole A we have barycenter 1.
When blackhole B collides with blackhole A there's barycenter 2.
From featrher to barycenter 1 is longer way than from blackhole B to barycenter 2.

In other words, blackhole A will intercept blackhole B faster than it will intercept feather.

EDIT: If feather and blackhole B fall together side by side, blackhole A will intercept them at the same point: common for all three objects, barycenter 3.

[JohnAdams1145]

The poster has a point. Are we to believe that a feather would fall into a black hole as fast as two black holes colliding would?

Tom, why is it you refuse to at least study the basics of physics? If you knew even a basic application of Newton's 3 Laws of Motion and his Law of Universal Gravitation, you wouldn't be saying stuff like this. Yet you're so quick to say that Newton was wrong, that gravity doesn't exist, and that most of modern science is garbage. This is a very simple derivation:

Two objects always lie on a line. We define L to be the object on the "left" and R to be the object on the "right" (the choice is arbitrary). We assume that space is Euclidean with the standard metric, as Newton did; this is a good enough approximation. We define i hat as the basis vector pointing to the "right". L has a mass of m_L. R has a mass of m_R. The force between them is Gm_Lm_R / d^2. Therefore the acceleration of L is Gm_R/d^2 times i hat, while the acceleration of R is -Gm_L/d^2 times i hat. So the closing acceleration (the time derivative of the closing speed) is G(m_R+m_L)/d^2. Now if m_L is much smaller than m_R (say, 1.6 x 10^23 times smaller -- that's a person vs the Earth), you can clearly see that the closing acceleration stays pretty much constant (what we see as "g" = 9.8 N / kg). This is the case with most fields, including electric fields; this is why test charges must be as small as possible. Of course the closing speed isn't constant; it is the acceleration integrated over time.

The fact that you cannot complete a basic Newton's Laws derivation to figure out what science has to say on your comment should demonstrate to you that you claim to refute science that you just simply don't understand.
In fact, I'll admit that I've been accused of the same on the FE hypothesis. But there's a crucial difference: FE assertions require a suspension of disbelief as they selectively follow logic, deduction, and demonstrable physical laws. In real science, most of the theory is supported by experiments and mathematics. It's not a lie to say that Einstein's Special Relativity is the product of two axioms. It's not a lie to say that Newtonian and Lagrangian mechanics can both be completely derived from Newton's Laws of Motion and Universal Gravitation, listed below:

1. In an inertial reference frame, objects at rest stay at rest and objects in motion stay in motion absent a net external force. (Defines an inertial reference frame)
2. In an inertial reference frame, the acceleration vector of an object is equal to the net external force vector divided by the mass of the object. (Acceleration, of course, is the time derivative of velocity, which itself is the time derivative of position).
3. Fa on b = -Fb on a. (The equal and opposite forces; combined with the second law, this implies conservation of momentum, the quantity mv)
4. Fg = Gm1m2/d^2 for point particles, and by 3-dimensional integral calculus, sufficiently distant spheres.
These 4 laws on their own are enough to completely debunk Flat Earth hypotheses while also having vast predictive power, from objects falling together to geostationary orbits to the Cavendish experiment to fluid dynamics to the various effects we observe on Earth as a result of being on a spinning ball. On the other hand, FE is constantly adding new assertions about perspective, shadows, distortion, maps, measured distances, invisible shadow objects in orbits around Earth, magical forces, cold light, etc to keep it viable. One can't be sure about its predictions because it needs fixing so often. It's exhausting to disprove all of these assertions until they reach the point of really making few testable predictions and thus become unfalsifiable.

As I've said before, I don't believe in discussions about the burden of proof, but I hope that each side can at least try to understand the arguments of the other. I've tried my best to read the wiki and understand what you believe (of course, I refuse to read ENaG because I know that the author is an imbecile -- I do, however, accept references to it if you're trying to explain what you believe). At the risk of exposing my own Dunning-Kruger, I probably understand the scientific implications of many FE assertions better than you do. The only FE who I've talked to on this forum who has demonstrated a good understanding of physics is Parsifal, and I learned a lot about how FE believes it fits in with currently accepted physics.

I didn't suggest you to take an AP Physics 1 practice exam to belittle you or to publicly prove that you knew nothing. I don't expect you to publish how well you did. But I hope that you give it a try, and see what you're missing. I just want you to recognize that there are significant gaps in your knowledge, and you can't just point to unintuitive things in physics that most people have a hard time understanding as disproofs of physics. There are always interesting physical explanations consistent with the 4 laws. And, if there's something that doesn't make sense to you, don't dismiss it outright as wrong, but instead feel free to ask anyone for clarification. I'll be the first to drop this boring cryptography and machine learning homework to help someone genuinely interested in improving his/her knowledge.


I'll give a non-obvious thing that Newton's laws predict: the braking distance of a vehicle (with everyday mass) depends little on how much mass it's carrying. The vehicle has a kinetic energy of (mv^2)/2. The frictional force is approximately f = mu * N, where N is the normal force, and mu is a relatively constant number dependent on the surface conditions (and also slightly on N, but that's why I say the distance depends little on the mass). Since the car doesn't accelerate vertically (oh dear, if it did!), N = mg. Then the frictional force is mu * mg. Then, to convert all of the vehicle's kinetic energy to heat, the vehicle has to travel a distance of (mv^2)/(2mu mg). Then, we see the masses cancel, and we get the stopping distance = (v^2)/(2 mu g). It turns out if you test this, the results approximately agree with this formula, and are nowhere near what we intuitively expect. Sometimes our intuitions are wrong. Newton's laws are very powerful and predictive.

[Tom Bishop]

Two black holes colliding would happen faster than a feather falling into a black hole, because in the case of two black holes, BOTH black holes are accelerating towards each other. In the case of the feather, the black hole's acceleration towards the feather is negligible.

The "different mass objects fall at the same rate" only refers to the acceleration of the single object under test. While a very very massive object would accelerate at the same rate, it would also cause the earth (or other surface) to accelerate towards it, making the apparent acceleration larger. When one object is several orders of magnitude more massive than the other, the more massive object doesn't accelerate much compared to the lighter one.

Great. So you admit that greater masses would appear to fall faster and that the OP is correct.

[Tom Bishop]

The poster has a point. Are we to believe that a feather would fall into a black hole as fast as two black holes colliding would?

When feather falls to blackhole A we have barycenter 1.
When blackhole B collides with blackhole A there's barycenter 2.
From featrher to barycenter 1 is longer way than from blackhole B to barycenter 2.

In other words, blackhole A will intercept blackhole B faster than it will intercept feather.

EDIT: If feather and blackhole B fall together side by side, blackhole A will intercept them at the same point: common for all three objects, barycenter 3.

Another agreement with the OP. He is on a roll.

[Tom Bishop]

The poster has a point. Are we to believe that a feather would fall into a black hole as fast as two black holes colliding would?

Tom, why is it you refuse to at least study the basics of physics? If you knew even a basic application of Newton's 3 Laws of Motion and his Law of Universal Gravitation, you wouldn't be saying stuff like this. Yet you're so quick to say that Newton was wrong, that gravity doesn't exist, and that most of modern science is garbage. This is a very simple derivation:

Two objects always lie on a line. We define L to be the object on the "left" and R to be the object on the "right" (the choice is arbitrary). We assume that space is Euclidean with the standard metric, as Newton did; this is a good enough approximation. We define i hat as the basis vector pointing to the "right". L has a mass of m_L. R has a mass of m_R. The force between them is Gm_Lm_R / d^2. Therefore the acceleration of L is Gm_R/d^2 times i hat, while the acceleration of R is -Gm_L/d^2 times i hat. So the closing acceleration (the time derivative of the closing speed) is G(m_R+m_L)/d^2. Now if m_L is much smaller than m_R (say, 1.6 x 10^23 times smaller -- that's a person vs the Earth), you can clearly see that the closing acceleration stays pretty much constant (what we see as "g" = 9.8 N / kg). This is the case with most fields, including electric fields; this is why test charges must be as small as possible. Of course the closing speed isn't constant; it is the acceleration integrated over time.

The fact that you cannot complete a basic Newton's Laws derivation to figure out what science has to say on your comment should demonstrate to you that you claim to refute science that you just simply don't understand.
In fact, I'll admit that I've been accused of the same on the FE hypothesis. But there's a crucial difference: FE assertions require a suspension of disbelief as they selectively follow logic, deduction, and demonstrable physical laws. In real science, most of the theory is supported by experiments and mathematics. It's not a lie to say that Einstein's Special Relativity is the product of two axioms. It's not a lie to say that Newtonian and Lagrangian mechanics can both be completely derived from Newton's Laws of Motion and Universal Gravitation, listed below:

1. In an inertial reference frame, objects at rest stay at rest and objects in motion stay in motion absent a net external force. (Defines an inertial reference frame)
2. In an inertial reference frame, the acceleration vector of an object is equal to the net external force vector divided by the mass of the object. (Acceleration, of course, is the time derivative of velocity, which itself is the time derivative of position).
3. Fa on b = -Fb on a. (The equal and opposite forces; combined with the second law, this implies conservation of momentum, the quantity mv)
4. Fg = Gm1m2/d^2 for point particles, and by 3-dimensional integral calculus, sufficiently distant spheres.
These 4 laws on their own are enough to completely debunk Flat Earth hypotheses while also having vast predictive power, from objects falling together to geostationary orbits to the Cavendish experiment to fluid dynamics to the various effects we observe on Earth as a result of being on a spinning ball. On the other hand, FE is constantly adding new assertions about perspective, shadows, distortion, maps, measured distances, invisible shadow objects in orbits around Earth, magical forces, cold light, etc to keep it viable. One can't be sure about its predictions because it needs fixing so often. It's exhausting to disprove all of these assertions until they reach the point of really making few testable predictions and thus become unfalsifiable.

As I've said before, I don't believe in discussions about the burden of proof, but I hope that each side can at least try to understand the arguments of the other. I've tried my best to read the wiki and understand what you believe (of course, I refuse to read ENaG because I know that the author is an imbecile -- I do, however, accept references to it if you're trying to explain what you believe). At the risk of exposing my own Dunning-Kruger, I probably understand the scientific implications of many FE assertions better than you do. The only FE who I've talked to on this forum who has demonstrated a good understanding of physics is Parsifal, and I learned a lot about how FE believes it fits in with currently accepted physics.

I didn't suggest you to take an AP Physics 1 practice exam to belittle you or to publicly prove that you knew nothing. I don't expect you to publish how well you did. But I hope that you give it a try, and see what you're missing. I just want you to recognize that there are significant gaps in your knowledge, and you can't just point to unintuitive things in physics that most people have a hard time understanding as disproofs of physics. There are always interesting physical explanations consistent with the 4 laws. And, if there's something that doesn't make sense to you, don't dismiss it outright as wrong, but instead feel free to ask anyone for clarification. I'll be the first to drop this boring cryptography and machine learning homework to help someone genuinely interested in improving his/her knowledge.


I'll give a non-obvious thing that Newton's laws predict: the braking distance of a vehicle (with everyday mass) depends little on how much mass it's carrying. The vehicle has a kinetic energy of (mv^2)/2. The frictional force is approximately f = mu * N, where N is the normal force, and mu is a relatively constant number dependent on the surface conditions (and also slightly on N, but that's why I say the distance depends little on the mass). Since the car doesn't accelerate vertically (oh dear, if it did!), N = mg. Then the frictional force is mu * mg. Then, to convert all of the vehicle's kinetic energy to heat, the vehicle has to travel a distance of (mv^2)/(2mu mg). Then, we see the masses cancel, and we get the stopping distance = (v^2)/(2 mu g). It turns out if you test this, the results approximately agree with this formula, and are nowhere near what we intuitively expect. Sometimes our intuitions are wrong. Newton's laws are very powerful and predictive.

Are you even talking about black holes and feathers here? The question is simple. Would two black holes intercept each other faster than a feather and a black hole?

[Tom Bishop]

The poster has a point. Are we to believe that a feather would fall into a black hole as fast as two black holes colliding would?

this is approximately equivalent to the noobs who come here and say things like "but anyone can see curvature from an airplane!"  how seriously do you take their polemics?

acceleration is proportional to both force and mass.  yes, the black hole would experience a greater force than the feather.  it wouldn't experience a greater acceleration because it is proportionally more massive.

http://www.physicsclassroom.com/Class/newtlaws/u2l3e.cfm

I looked at your link. Its wrong. That link does not account for the fact that under the theory of gravity the falling baby elephant in that example is also attracting the earth to it, moreso than the mouse would, however slight, as illustrated with my black hole example.

The statement from that article "all objects will fall with the same rate of acceleration, regardless of their mass" is blatantly incorrect, seeing that masses would mutually attract. Just look at the equations given in the article. It accounts for the pull of the earth but not the pull of the falling mass.

[garygreen]

I looked at your link. Its wrong. That link does not account for the fact that under the theory of gravity the falling baby elephant in that example is also attracting the earth to it, moreso than the mouse would, however slight, as illustrated with my black hole example.

The statement from that article "all objects will fall with the same rate of acceleration, regardless of their mass" is blatantly incorrect, seeing that masses would mutually attract. Just look at the equations given in the article. It accounts for the pull of the earth but not the pull of the mass.

tbh i slightly misread/misinterpreted your original statement as "two feather wouldn't collide as fast as two black holes."

that said, i'm now less clear about what criticism you're making.  can you elaborate?

[Macarios]

The poster has a point. Are we to believe that a feather would fall into a black hole as fast as two black holes colliding would?

When feather falls to blackhole A we have barycenter 1.
When blackhole B collides with blackhole A there's barycenter 2.
From featrher to barycenter 1 is longer way than from blackhole B to barycenter 2.

In other words, blackhole A will intercept blackhole B faster than it will intercept feather.

EDIT: If feather and blackhole B fall together side by side, blackhole A will intercept them at the same point: common for all three objects, barycenter 3.

Another agreement with the OP. He is on a roll.

Agreement? :-)
Would you be so kind to read the very second post in this thread?
Thanks.

About black holes, if their masses are in the same category bigger black hole will still fall towards smaller one, intercepting it.
If the feather is just next to smaller black hole, they will fall togehter into bigger black hole at the intercepting point.
You could see it already in the post you quoted.

[AATW]

I've honestly no idea how this got onto black holes. My physics is a bit rusty but I think this is correct. The formula for gravitational attraction is:

f = G (M1 x M2) / r2

G being a constant, M1 and M2 being the masses of the two objects. r being the distance between the two objects' centre of gravitys
So if M1 is my mass, M2 is the earth's mass then the above gives you the force the earth exerts on me (which is my weight, that's what weight is).

But we also know that

f = ma

F = force, m = mass, a = acceleration.

This can be arranged as

a = f/m

This, by the way, is what makes super sonic travel so expensive, the more "m" there is, the more "f" you have to provide to produce "a".

So the acceleration on me because of gravity is the force of gravity on me divided by my mass. Using the above two formulas that is:

(G (M1 x M2) / r2) / M1.

The two M1s cancel themselves out so it's:

(G M2 / r2)

Point being, this force is independent of MY mass, it only relies on the mass of the earth which pretty much remains constant and my distance from the earth's centre of gravity - which does vary slightly because the earth is not a perfect sphere. But the headline is that objects of different mass will fall at the same rate.

That is what Galileo proved by dropping cannonballs of different sizes out of high buildings and observing that they hit the ground at the same time. The reason this doesn't work with feathers and hammers on earth is air resistance which slows the feather's fall (and the hammer's, but not enough so's you'd notice because of the mass of the hammer). On the moon there is no atmosphere and so no air resistance so they fall at the same rate, hence the astronaut's exclamation "what do you know, Mr Galileo was right!"

The effect was recreated in a vaccuum chamber for a BBC series

[Tom Bishop]

I've honestly no idea how this got onto black holes. My physics is a bit rusty but I think this is correct. The formula for gravitational attraction is:

f = G (M1 x M2) / r2

G being a constant, M1 and M2 being the masses of the two objects. r being the distance between the two objects' centre of gravitys
So if M1 is my mass, M2 is the earth's mass then the above gives you the force the earth exerts on me (which is my weight, that's what weight is).

But we also know that

f = ma

F = force, m = mass, a = acceleration.

This can be arranged as

a = f/m

This, by the way, is what makes super sonic travel so expensive, the more "m" there is, the more "f" you have to provide to produce "a".

So the acceleration on me because of gravity is the force of gravity on me divided by my mass. Using the above two formulas that is:

(G (M1 x M2) / r2) / M1.

The two M1s cancel themselves out so it's:

(G M2 / r2)

Point being, this force is independent of MY mass, it only relies on the mass of the earth which pretty much remains constant and my distance from the earth's centre of gravity - which does vary slightly because the earth is not a perfect sphere. But the headline is that objects of different mass will fall at the same rate.

That is what Galileo proved by dropping cannonballs of different sizes out of high buildings and observing that they hit the ground at the same time. The reason this doesn't work with feathers and hammers on earth is air resistance which slows the feather's fall (and the hammer's, but not enough so's you'd notice because of the mass of the hammer). On the moon there is no atmosphere and so no air resistance so they fall at the same rate, hence the astronaut's exclamation "what do you know, Mr Galileo was right!"

The effect was recreated in a vaccuum chamber for a BBC series

https://www.youtube.com/watch?v=frZ9dN_ATew

That explanation is ignoring that under the theory of gravity the falling object is also pulling the earth towards it. "Mass doesn't matter" is clearly wrong.

[inquisitive]

I've honestly no idea how this got onto black holes. My physics is a bit rusty but I think this is correct. The formula for gravitational attraction is:

f = G (M1 x M2) / r2

G being a constant, M1 and M2 being the masses of the two objects. r being the distance between the two objects' centre of gravitys
So if M1 is my mass, M2 is the earth's mass then the above gives you the force the earth exerts on me (which is my weight, that's what weight is).

But we also know that

f = ma

F = force, m = mass, a = acceleration.

This can be arranged as

a = f/m

This, by the way, is what makes super sonic travel so expensive, the more "m" there is, the more "f" you have to provide to produce "a".

So the acceleration on me because of gravity is the force of gravity on me divided by my mass. Using the above two formulas that is:

(G (M1 x M2) / r2) / M1.

The two M1s cancel themselves out so it's:

(G M2 / r2)

Point being, this force is independent of MY mass, it only relies on the mass of the earth which pretty much remains constant and my distance from the earth's centre of gravity - which does vary slightly because the earth is not a perfect sphere. But the headline is that objects of different mass will fall at the same rate.

That is what Galileo proved by dropping cannonballs of different sizes out of high buildings and observing that they hit the ground at the same time. The reason this doesn't work with feathers and hammers on earth is air resistance which slows the feather's fall (and the hammer's, but not enough so's you'd notice because of the mass of the hammer). On the moon there is no atmosphere and so no air resistance so they fall at the same rate, hence the astronaut's exclamation "what do you know, Mr Galileo was right!"

The effect was recreated in a vaccuum chamber for a BBC series

https://www.youtube.com/watch?v=frZ9dN_ATew

That explanation ignoring that under the theory of gravity the falling object is also pulling the earth towards it. "Mass doesn't matter" is clearly wrong.

And the relative mass of the two objects, the cannonball and the earth?  Tom, please answer.

[JohnAdams1145]

Great. So you admit that greater masses would appear to fall faster and that the OP is correct.

Tom, reread what I wrote. You clearly don't understand limiting cases and orders of magnitude (ah, that actually makes sense, considering you don't understand why when you look out the window the ground looks flat). It's true that two black holes will converge faster toward one another because both of them are extremely massive; m_L and m_R are close in orders of magnitude.
You're either being willfully ignorant (not reading the formulae & derivation that I wrote) or extremely intellectually dishonest to say that a hammer would fall faster toward the Moon than a vacuum; technically, it does, but by a MICROSCOPIC, UNOBSERVABLE (due to the limits of microscopy + Heisenberg uncertainty principle -- that's how small it is) amount. Did you even try to understand what the formula for the closing acceleration is? It's G(m_L+m_R)/d^2. Now you tell me, if m_L is 10^23 kg and m_R is the object we're considering (feather or hammer), does it really matter whether m_R is 10 kg or 10000 kg? Of course the closing acceleration of the larger object will be a miniscule tad higher. This is NOTHING like the gibberish that the OP posted (completely unintelligible garbage masked with scientific and pseudo-scientific jargon); a hammer and a feather on the moon dropped on the moon will hit the ground at ESSENTIALLY EXACTLY THE SAME TIME.

Are you so dense to not know that 10^23 kg + 10000 kg is virtually the same as 10^23 kg + 10 kg or are you just being deliberately dishonest? I assume the latter.

The lack of effort you put into actually understanding the other side is stunning. This is basic math; there are plenty of third graders who can understand this, and yet you refuse to understand it.

[AATW]

That explanation is ignoring that under the theory of gravity the falling object is also pulling the earth towards it. "Mass doesn't matter" is clearly wrong.

Not clear what your point is there.
The mass of the two objects is not relevant to the speed they accelerate towards earth (ignoring air resistance) for the reasons I've given.
The two objects do indeed exert some force on the Earth but because their mass is so small (relative to the earth's mass) it doesn't cause the earth to move

(because f=am so a = f/m - and when the 'm' as as big as the earth's the f has to be pretty big to produce any significant 'a')