Apparently, Aristotle reasoned (without experimentation) that heavier objects must fall to Earth faster than lighter objects.  For example, a 1,000 kg ball of iron would fall faster than a 1 kg ball of iron.  Galileo is reputed to have disproved this experimentally by dropping two differently heavy objects from the Tower of Pisa, and they were observed to hit the ground at the same time.  Case closed, right?  Well, it suddenly occurred to me this morning that Aristotle was actually correct, and Galileo's experiment was incapable of discerning any difference in arrival times between the two weights he dropped.  And I wonder if our measuring devices today could discern the difference in arrival times in this case?    The formula for force due to gravitational acceleration is:  $$F = \frac{Gm_1m_2}{d^2}$$  For both the 1000kg and 1kg masses, the product of them both with the Earth's mass is clearly the Earth's mass, so $F$ will be virtually the same for them both.  But if we take the 1000kg mass out to the Moon's orbit, and we stop the moon in its orbit so it stands still with respect to the Earth, the force $F$ will clearly be much larger between the Moon and the Earth than between the 1000kg mass and the Earth.  The result of this is that the Moon and the Earth will meet much faster than the 1000kg mass will meet the Earth.  Am I right, and is Aristotle vindicated, or is there something I'm missing here?
612
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.
15882
As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates due to gravity. It can reach a point where its velocity is high enough to keep falling but also keep missing the object it is falling towards. What keeps it from accelerating (because of gravity) and eventually reaching escape velocity? I feel like I'm either looking at things the wrong way or I have the entire thing wrong.
39543
The principle of equivalence - that, locally, you can't distinguish between a uniform gravitational field and a non-inertial frame accelerating in the sense opposite to the gravitational field - is dependent on the equality of gravitational and inertial mass. Is there any deeper reason for why this equality of "charge corresponding to gravitation" (that is, the gravitational mass) and the inertial mass (that, in Newtonian mechanics, enters the equation $F=ma$) should hold? While it has been observed to be true to a very high precision, is there any theoretical backing or justification for this? You could, for example (I wonder what physics would look like then, though), have the "charge corresponding to electromagnetic theory" equal to the the inertial mass, but that isn't seen to be the case.
104570
In most of the mechanics textbooks , the  is stated without any justification or an experiment to confirm this law. Also after introducing this law forces are also decomposed without any justification. Please suggest any links or books related to this. Any help will be appreciated. Thanks in advance.
35762
While it is fairly established that both fast movement and the presence of gravity make time pass slower as compared to a system at rest / free of gravity, does that mean that there is no way for time to pass faster than in vacuum, or does general relativity also have "faster" metrics?  To be more precise, is there any frame into which one could go for a while, and on returning to vacuum less time would have passed there?
2714
Some people say that mass increases with speed, some people say that the mass of an object is independent of its speed.  I understand how some (though not many) things in physics are a matter of interpretation based on one's definitions. But I can't get my head around how both can be 'true' is any sense of the word.  Either mass increases or it doesn't, right?  Can't we just measure it, and find out which 'interpretation' is right? e.g.: (in some sophisticated way) heat up some particles in a box and measure their weight?  ------------------------------  UPDATE  Right, so I've got two identical containers, each with identical amounts of water, each on identical weighing scales, and each in the same g field. If one container has hotter water, will the reading on its scale be larger than the other? If the answer is yes, and g is constant, does this mean that the m in w=mg has got bigger?
122606
Ok,this is a silly question. But for quite long I have been thinking about this. What is gravitation all about?? My book directly writes since force of gravitation is directly proportional to the masses and inversly proportional to the square of the distance ie. $$F = G\frac{M_1 . M_2}{r^2}$$ . So is this gravitation all about? What is the cause of it? The book then says     We are not in the scope in classical approach so as to discuss the cause of this. However,as a matter of fact that if there are more than one mass,then there is gravitation as it is their fundamental property.( Cause of gravitation can be attributed to exchange of non-classical particles between the masses) .    Then it ended the talkings. What are those non-classical particles? Why and how are they exchanged? So far I have studied physics , I never found such weird phenomenon like this. I want to know what is the cause of gravitation and what is the cause of exchange of those so-called non-classical particles? And how do they do it?
62225
On , it is written that      So, we see things falling with an acceleration which we call the acceleration of gravity,and thinking that we live in a straight line , uniformly moving or stationary inertial frame, we attribute that acceleration to a force, the force of gravity. Whereas in reality,objects falling towards the Earth are moving along geodesic paths with no acceleration and according to modified version of law of inertia, have no force acting on them. They fall simply because the curved space-time near the Earth ...   Now, why do the objects falling towards the Earth move along the geodesic paths with no acceleration? That means the objects don't have any force acting on them, but why? A body in a free-fall moves with acceleration $g$, so, why is it written like that? Why does the author use Law of inertia on freely falling body?? Law of Inertia can only be applied when no external force acts on the body. So, is the freely-falling body accelerates under force of gravity or moves uniformly while moving through geodesic paths as quoted by the author?
32211
Since humans are not large in mass, do we exert enough gravitational force for a small object to orbit around us? (Assuming that the only gravitational force acting on the object is from the human). Using Newton's law of gravity and using myself as the human mass, I exert a 10^-8 force on a 1 kg object .5 meter away, but I am not sure if even this small of a force will be acceptable. What is the baseline "force" between two objects for 1 to orbit another?  Edit: I am not sure if this is a SpaceExchange question.
71566
Is there a difference between Weight and Force of Gravity or they just mean the same thing? My textbook does not clarifies this point.
71284
Possible Duplicate:          Today we were in our Literature class talking about the Renaissance and the Enlightement and our teacher also said that scientific experiments were being conducted, and she gave as an example the experiment in which they dropped objects with different mass from a tower to see which object would land first. She then said that she herself didn't know the outcome and since I'm known in my class as the #1, they asked me and I said that they landed at the same time (to my shock many classmates even disagreed with me about this fact). The teacher asked me to explain why and we haven't had anything about inertia in our physics class, so I was forced to use my own self-thought knowledge of physics: I said gravity does pull harder on heavier objects, but heavier objects have more resistance to move, in other words, they have more inertia. The entire class except for the teacher disagreed with me even though they usually don't. One fairly annoying kid asked me to explain why a feather falls way slower than a bowling ball, and I explained why and I also made the claim that in a vacuum they would fall at the same rate. Was I right or my class? Of course I know my explanation is lacking, but it has truth to it, right?
9305
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?
59620
I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving math, which would be all of them.  So lets say we drop an object from a height, $R+r$, it falls toward earth. This height, $R+r$, is far enough away that the $g$ it experiences is a fraction of $g$ at sea-level. Let's just say that air resistance is negligible, and it wouldn't be that complicated to just integrate from $0$ velocity to the terminal velocity piece wise and deal with the rest of it later.  So the key here is that acceleration is changing with time. I thought I could simplify this by saying it changes with distance, and it has nothing to do with time, but this didn't really help, my guess is that maybe time is important (doh).  I tried integrating acceleration with time, and ended up nowhere. I tried integrating $a=GM/R^2$ with respect to $R$ from $R+r$ to $R$ and ended up with a negative function.  I saw somewhere someone tried to expand with taylor series, they even have something similar on hyperphysics, but I can't figure out how to obtain the polynomials that precede the variables.    This is the hyperphysics site where they use polynomials to find the distance.   Maybe I can't solve this because I haven't taken a course in differential equations yet. What I want to know is how to calculate the distance at any time.
45008
While learning about motion of centre of mass, I came across this statement online,      It is also more accurate to say that the Earth and Moon together revolve about their common center of mass.    I am not able to understand this. Can anyone please explain this statement?
7628
I'm wondering if it's possible to send a man to the Moon using equations consistent with Newtonian gravity and without the elaborate tools of Einstein gravity. Are the predictions made by Newtonian gravity sufficiently precise to plan a successful voyage? If not, where would the Newtonian equations fail and how does Einstein gravity correct for these deficits?
49958
I've been pondering the precise mechanism of time dilation for the example of a simple pendulum in two different situations:   The observer and ground are at rest in one frame of reference;  the pendulum is moving at high speed with respect to that frame. The observer is at rest in one frame of reference; the pendulum and the ground together move at high speed with respect to that frame.   user8260 has pointed out that in situation 1, in the pendulum's frame $g$ is greater by $\gamma^2$ compared to $g$ in the observer's frame. Thus in the pendulum's frame the period is less than it is in the observer's frame by a factor of $1/\gamma$, just as one would expect from time dilation.  But what about situation 2? Here, compared to the pendulum frame, the observer sees the pendulum with the same length in a stronger gravitational field, yet observes a longer period. Does the inertial mass of the pendulum change differently than its gravitational mass? Also, does the analysis depend on whether the plane of swing is perpendicular or parallel the direction of motion?
82301
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?