I am an extreme novice in Physics, I am also a beginner in Physics Stack Exchange, and I'm not fluent in English, so please bear with me, consider my question with indulgence. I request indulgence especially because $99\text{%}$ of my question is a well-known question with an evident and well-known answer, but the important thing of the question is the remaining $1\text{%}$ which I will try to explain the best I can. This well-known question is:  &quot;On the Moon, drop a feather and a hammer, will they touch the ground at the same time?&quot;  (and the question is the same on Earth if we exclude the air density/shapes of bodies that fall). This question is always answered by the strict affirmation that &quot;yes they do&quot;, and confirmed by astronaut . I agree with that. I agree that it's a strictly equal time, if we consider that the Moon is not attracted by the feather or the hammer. It may sound obvious to many people that the Moon is not attracted by so much light objects, but theoretically it is because these objects have a mass, even if the feather/hammer mass is around 1E-23 times of the Moon mass. (It's like the Earth which is 100 times more massive than the Moon, so the Earth is also attracted and the effect is its &quot;oscillation&quot; around the  which is at approximately $4,670$ to $6,380\ km$ away from the geographical center of the Earth.) And here comes my question, which may look identical, but there is a change in the conditions and in the enunciation, especially I say &quot;body&quot; instead of &quot;Moon&quot;, and I say &quot;mutually attracted&quot; rather than &quot;one object falls on the body&quot; so that you better understand how my question is 1% different from the previous question:  &quot;In space vacuum, a feather and a body are both initially positioned at the same distance and with no relative movement, and are mutually attracted because of their masses and will collide in a given amount of time. Let's repeat the same experiment with a hammer instead of the feather, will they collide in exactly the same amount of time?&quot;  (even if there's a tiny difference of 1E-20 second, I consider that it's not the same time) My assumption is that the hammer and the feather will be both attracted identically by the body, BUT at the same time the body will be more attracted by the hammer than by the feather (because the hammer is heavier than the feather). So, the body and the hammer will collide quicker than the body and the feather. Am I right or not? Where am I wrong? Of course, my question is related to the first well-known question, and my assumption is that there is a difference, although extremely small, maybe 1E-20 seconds, but theoretically it's different because the Moon is attracted. What do you think? Do you know any document which talks about that? (I searched a lot but I couldn't find anything) Thank you very much for your interest in this question.
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The common understanding is that, setting air resistance aside, all objects dropped to Earth fall at the same rate. This is often demonstrated through the thought experiment of cutting a large object in half. The halves clearly can't then fall more slowly just by being sliced in two.  However, I believe the answer is that when two objects fall together, attached or not, they do "fall" faster than an object of less mass alone does. This is because not only does the Earth accelerate the objects toward itself but the objects also accelerate the Earth toward themselves. Considering the formula: $$ F_{\text{g}} = \frac{G m_1 m_2}{d^2} $$  Given $F = ma$ thus $a = F/m$, we note that the mass of the small object doesn't seem to matter as when calculating acceleration the force is divided by the $m$ term, its mass. However, this overlooks that the force is actually applied to both objects, not just to the smaller one. The acceleration on the second, larger object is found by dividing $F$, in turn, by the larger object's mass. The two objects' acceleration vectors are exactly opposite, so closing acceleration is the sum of the two:  $$ a_{\text{closing}} = \frac{F}{m_1} + \frac{F}{m_2} $$  Since the Earth is extremely massive compared to everyday objects, the acceleration imparted on the object by the Earth will radically dominate the equation. As the Earth is $\sim 5.972 \times {10}^{24} \, \mathrm{kg} ,$ a falling object of $5.972 \, \mathrm{kg}$ (just over 13 pounds) would accelerate the Earth about $\frac{1}{{10}^{24}}$ as much, which is one part in a trillion trillion.  Of course in everyday situations, we can for all practical purposes treat objects as falling at the same rate because of this negligible difference—which our instruments probably couldn't even detect. But I'm hoping not for a discussion of practicality or what's measurable or observable, but what we think is actually happening.  Am I right or wrong?  What really clinched this for me was considering dropping a small Moon-massed object close to the Earth and a small Earth-massed object close to the Moon. This made me realize that falling isn't one object moving toward some fixed frame of reference, but that the Earth is just another object, and thus "falling" consists of multiple objects mutually attracting in space.
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For years I have been very fascinated by the "mystery" aspect of gravity. Functionally, we understand it for our applications, but in my (limited to my 3 quarters of undergrad general physics) understanding, we don't know why it exists or how the "pull" works.   To provide an example of what I mean: there has to be some "measurable material" of gravity between, say, the earth and the moon -- some kind of 'graviton' (not that it needs to be a particle or anything, I have zero claims as to the nature of how gravity does what it does). The [butchered] saying of "pluck a flower and move the furthest moon" originates because gravity in theory, has an infinite range (right?) and moving a flower on earth could maybe move an atom on Jupiter ever so slightly.  Anyway, similar to how we had "very good" hypotheses about the existence of Higgs boson that the LHC 99%+ confirmed, do we have any "very good" hypotheses in regards to the fundamental way how gravity does what we have long-known it to do?
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In  I describe the >30 years of laser ranging between lasers on Earth and the retroreflector arrays on the Moon. Amazingly, after comparing this data to simulation of all of the orbital mechanics and tidal effects, the residual is only a few centimeters.   If $\text{H}_D$ is about 70 $\text{km}\ \text{s}^{-1} \text{Mpc}^{-1}  $ (or about 2.3E-18 $\text{sec}^{-1}$), then with a semi-major axis of 3.84E+08 meters, over 37 years the effect would be of order 1 meter. Since these measurements are consistent with zero to the level of a few centimeters, this is taken as experimental evidence that metric expansion is not taking place locally compared to the rate seen between galaxies.  If I understand correctly this is "suppression" is due to the large amount of mass in our galaxy, even though it is thousands of light years away. So I am wondering - if a similar experiment were done in a similar solar system associated with an isolated star alone in an intergalactic region, what does current theory predict - would metric expansion be detected, or would the mass of the one star be enough to suppress it?  Then what if it were just a planet and a moon without the mass of the star, or even two smaller masses?  I'm looking for an answer at a level similar to  and , where time was taken to note the the specific relevant concepts and work from the paper linked in the first answer.
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The moon orbits Earth at about $380,\!000 \,\mathrm{km}$  away from it, at around $3,600 \,\mathrm{km}$ an hour.  I was thinking, with light traveling at $300,\!000 \,\mathrm{km/s}$, how close to earth (probably in the $\mathrm{nm}$ range is my guess) would light have to be to Earth to orbit it?  Update: After reading the below answers, here's my reasoning to why I thought it would be in the nanometre range.  I thought that if light was as close as possible to Earth (like, a planck length away or something), Earth's gravity would make it hit Earth immediately, but I forgot that the pull of gravity gets weaker when one is further away from Earth (i.e. at the surface of Earth is still somewhat "far away").
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I know this question has been asked in other forms, generally regarding the balance of forces.  This time I want to focus on motion.  I've got a laser accelerometer on my desk.  It tells me that I'm accelerating at $9.8~\rm m/s^2$.  For the first experiment I'm travelling in space.  I pick a nearby star and discover that I move about $490$ meters in $10$ seconds from that star.  For the next experiment I'm on the surface of Earth.  I measure the same acceleration with my laser accelerometer.  I pick a spot (the center of the Earth) and discover I don't move at all in $10$ seconds.  How is acceleration without motion possible?
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If two bodies are close, both will get attracted to each other and collide. Under what conditions will the two bodies start revolving around their common center of mass? I understand that such bodies represent the gravitional two-body problem, but I want to know what are the initial conditions that allow it so settle into such a configuration (without going into the maths)
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Or does it exist mathematically?  Is it really inconsistent with a common-sense, mathematics or known physical laws?   As far as I understand, if it exists, it must be far away from the "positive" matter because of repelling force, so it explains why there is no observations of such matter.   It would be also very consistent with the idea that the total energy of the Universe is zero. Doesn't it imply that the total mass of  the Universe is zero?   Can you please clarify the statements below that seem to contradict each other?  1)  -Max Tegmark.  2) Despite being completely inconsistent with a common-sense approach and the expected behavior of "normal" matter, negative mass is completely mathematically consistent and   3) Such matter would  and show some strange properties, stemming from the ambiguity as to whether attraction should refer to force or the oppositely oriented acceleration for negative mass.
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My book says:     For most of the small objects, both are same. But for mammoth ones, they are really different ones. And in a gravity-less environment, COG is absent; COM still exists.   Ok, what's the big deal when things are small and big? How these two :  &amp; ?
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Non-metal objects are attracted to the Earth due to gravity. So the weight of non-metal objects can be only dependent on their mass.   On the other hand metals can be attracted to the Earth's magnetic field, with the Earth acting as a giant magnet; causing metals to weight more than they normally should.   In other words the weight of metals and magnetic objects would be the sum of the magnetic force plus the gravitational force, is that correct?  If that effect is true, would it be more clear as we go closer to the magnetic poles, and metals would weigh different in different locations on Earth?
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I've read a lot of conflicting answers in these forums. However, today saw the awesome announcement of gravitational waves. Two black holes merged:   Not only that, they merged FAST. In 1/5th of a second revolving around each other 250 times a second. The entire event was quicker than a heartbeat. Moreover, we observed this happening as distant outsiders. So now we can say for sure:   Objects approaching the event horizon DO NOT appear to slow down Black holes CAN merge in a finite (and quick) amount of time And all this is wrt a frame of reference far, far away   To quote the NYTimes article:  One of them was 36 times as massive as the sun, the other 29. As they approached the end, at half the speed of light, they were circling each other 250 times a second.  And then the ringing stopped as the two holes coalesced into a single black hole, a trapdoor in space with the equivalent mass of 62 suns. All in a fifth of a second, Earth time.  However, everything I've read so far has let me to believe that an outside observer should never be able to measure the collision happening in a finite time. So what exactly is happening here? I must have read at lest 5 different versions of this so far everywhere in these forums over the past several years.
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Using a "successive impact model" (as if each ball were seperated from the other ones), I produced the following animations:    You can see any combination of balls with masses of 1 or 2 (left) or 1 and 4 (right).  Unfortunately, I do not have any Newton cradle to make some experiments, and I'd like to compare my results with observations. I contacted the author of , which is the most instructive one I found about asymmetric Newton cradle. In particular, he writes that the "OoO" configuration behaves as the "ooo" one, which is not what I simulate. But the author is not sure whether who is wrong because he did the experiments a long time ago.  I am especially interested in asymmetric Newton cradle with simultaneous impacts: left and right balls collinding at the same time.   Please let me know if you have any idea on where to find such experimental data.  Edit Just of few general remarks to avoid extending the comments.    Energy and momentum are conserved. However, they are sufficient to ensure uniqueness of the post-impact velocities only when there are 2 balls. The successive impact model precisely consists in propagating the impact ball after ball, and therefore leads to a unique solution (which conserves momentum and energy globally). From the waves point of view, changing the mass of a ball can be done by increasing the diameter, or the density (or a combination of both). This simple model cannot account for such subtleties of course, but maybe it does not matter when the balls are "small enough". Even if I think it's quite basic, following WetSavannaAnimalakaRodVance's comment, I am ready to hand out my Mathematica code to anybody who wants it. I'll check for good ways to share it.
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I once saw on TV that the moon is slowly drifting away from the earth, something like an inch a year. In relation to that the day on earth what also increase in time. I wonder why is that?
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I'm having trouble understanding how a  (not the  that is generated as a result but the material itself) work. The particles are aligned in a specific direction to give rise to force but I don't see how this alignment gives rise to "attraction" or force.
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I know plus pushes another plus away, but why, really, do they do that? On the other hand, molecules of the same type are attracted to each other. I find that weird.  I do know some stuff about four universal forces. But why in general the general "rule" is that opposite charges pull each other?   Yes, I do realize this could be connected to very basic stuff that science is still trying to figure out, and can be traced to the Higgs,  but still, there must be something to tell.
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According to , there are 5 equilibrium, or  of the Earth-Moon system and only 2 of them are said to represent stable equilibrium points.     This made me think if there is an equation that describes this system, and from which Physics Laws was it derived?
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There is always one point in introductory mechanics that has been continuously bothering me ever since I had taken my freshman physics course - Why does a massless rope have its tension equal on both ends?  I have been searching for a good explanation on various textbooks at different levels, but none of them provided me a satisfactory explanation. They either   State directly "we assume the string is massless and the pulley has no friction, therefore the tension must be the same throughout the string" without further any elaboration and continue the calculation, Claim without any reasons that "whenever the rope and the pulley are massless and frictionless, the tension will be the same on both sides", or Explain using a lot of hand-waving arguments regarding infinite acceleration, non-zero moment of inertia, etc. , in one line or two.   Although those hand-waving arguments of type $(3)$ do sound quite reasonable to me and will convince me for a while every time I review them. But after a while, I will start feeling not well about this whole tension concept again.  Therefore, I am looking for a rigorous (in the physicist's sense) proof of exactly why and when do the tension in rope will be uniform, and hopefully from that I can clean up all of my conceptual difficulties.
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Intro:  In completing , he presents an experiment (go to 42:44) which leaves me baffled.    Experiment:  (I recommend watching the video; see link above.)   There is a $2$ kg block with 2 identical strings attached to it: one at the top, the other at the bottom. The top string is attached to a "ceiling", and the bottom to a "floor". Professor Lewin "stretches" the system (by pulling on the bottom string) with the block not accelerating. One string snaps.     Prediction:   Initially, the top string has a tension of approximately $20$ N, to counter the force of gravity. The bottom string has no tension at all. Then, when Lewin pulls the bottom string, it gains some tension $n$ N. To counter act the force exerted by the bottom string, the top string exerts now $20 + n$ N. I assume that the string with more force will give out sooner, leading me to conclude that the top string will break.     Results:  (This was conducted by Lewin, not me; see link above.)   Trial 1: Bottom string breaks. Trial 2: Top string breaks. Trial 3: Bottom string breaks.     Additional Notes:  The results don't seem consistent. If I was right, I'd expect all 3 experiments to be right; conversely, if I was wrong, I'd expect all 3 experiments wrong, with one exception: the results are more-less random and one result isn't preferred over the other.    Question:        Why was my prediction incorrect?   Was there a flaw in my logic?   Why were the results inconsistent?