What is Gravitation: Definition and 915 Discussions
Gravity (from Latin gravitas 'weight'), or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are attracted to (or gravitate toward) one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing and forming stars and caused the stars to group together into galaxies, so gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become weaker as objects get further away.
Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915), which describes gravity not as a force, but as a consequence of masses moving along geodesic lines in a curved spacetime caused by the uneven distribution of mass. The most extreme example of this curvature of spacetime is a black hole, from which nothing—not even light—can escape once past the black hole's event horizon. However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them.
Gravity is the weakest of the four fundamental interactions of physics, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a consequence, it has no significant influence at the level of subatomic particles. In contrast, it is the dominant interaction at the macroscopic scale, and is the cause of the formation, shape and trajectory (orbit) of astronomical bodies.
Current models of particle physics imply that the earliest instance of gravity in the Universe, possibly in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch (up to 10−43 seconds after the birth of the Universe), possibly from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a currently unknown manner. Attempts to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory, which would allow gravity to be united in a common mathematical framework (a theory of everything) with the other three fundamental interactions of physics, are a current area of research.
I have tried simplifying the integral (turning into an integral in terms of position variables) using the equation of motion. It's easy to show:
$$\frac{1}{x^4}=\frac{(\ddot{x})^2}{(GM)^2} $$
And therefore one can write:
$$\frac{1}{(GM)^2}\int_{t=0}^{t_f} (\dot{x}\ddot{x})^2 dt =...
Why does the text saying that the Newton's framework doesn't require the two masses to be equal? If using f = ma give us inertial mass then how is f = Gm1m2/r² a different things? Isn't the law defined as the force is directionly proportional to the product of the masses and we calculated the...
It is assumed that gravitation in n dimensions would follow an approximate 1/d^(n-1) law. In our 3D world the attraction of a uniformly dense sphere is the same as if all the mass were concentrated at its center. I have read for n>3 this is not so. I want to find out what the result would...
I believe that this is due to context of application, but now, I'm starting to doubt myself. For example, a helicopter lifting itself has positive PE change. I really don't intuitively understand how this works. Can someone kindly explain this to me?
From the International Society on General Relativity and Gravitation (http://www.isgrg.org/)
there were some 50-year anniversary celebrations and a 100th birthday celebration:
This post is primarily about items related to "Gravitation" by Misner Thorne Wheeler.
Go to ISGRG to see
a 50-year...
Dark Energy puts a constrain on the size of overdensities (like clusters and superclusters of galaxies) and their growth.
A higher Dark Energy density would reduce the radius of the zone where matter would be gravitationally bound, because more Dark Energy density would mean that objects would...
I'm trying to make a 2D game on Unity similar to Universe Sandbox 2. I currently am working with a star and planet, both with roughly the masses of the sun and earth respectively for comparison and at a distance of 31,000,000km.
My current model uses Newton's formula for gravitational force (F...
I have a doubt about gravitation. Suppose the mass of the Sun halves in an instant, after how long does the Earth ''notice'' it?
That is, does the gravitational force also decrease instantaneously?
Instinctively I would say yes, but I don't understand why it should be so. If, for example, we...
I solved the math using vector rule
R= \sqrt{F^2 +F^2 +2F^2cos\frac{\pi}{3}} =\sqrt{3}\frac{Gm^2}{a^2}
But the answer is showing: \sqrt{3}\frac{Gm^2}{a^2} (-\hat{j})
My question is:
Why is (-\hat{j}) added here? Why is it negative?
I am having a discussion with a couple of very obtuse individuals on another forum who think they know celestial mechanics, but do not. These two have long promoted themselves to be something they are not, and since I am rather new on the forum they are unwilling to even listen (or heaven...
TL;DR Summary: Express through the Hubble constant the force that acts on the hydrogen atom due to the expansion of the universe
We have a hydrogen atom, in a gravitationally bound system nothing interesting happens to it. Let's put it in an empty world with only an electron and a proton...
1: There is a universal gravitational force between two 1 kg iron balls, and the energy generated by their mutual attraction is so small that it is difficult to observe; there is also an attractive force between a 1 kg neodymium magnet and 1 kg of iron, but the energy generated by their...
What I did was just sub in the numbers and convert km to m. So (6.67E-10)(1000)(5.98E24)/(1,000,000+6.37E6)^2 * (1,000,000+6.37E6) So it's just (6.67E-10)(1000)(5.98E24)/(1,000,000+6.37E6). I thought this was a straightforward problem, but it seems that it is not. What am I missing?
When we observe distant time dilation effects, usually indicated by redshift, there are three possible explanations:
1) The speed of light, is slower there and then;
2) Space, is contracted for light there and then;
3) The frequency, of specific light is slower there and then.
However, it is...
Diagram : I draw a picture of the problem situation and paste it to the right.
Attempt : Let me assume that the position of the smaller mass ##m## at a given instant of time ##t## is ##x(t)##.
(1) Gravitational potential energy ##\frac{GMm}{x} = \frac{1}{2}mv^2(x)##, where ##v(x)## is the...
First, please excuse my english first, Does anyone know who already had invented or built such a machine ?, which it can float in air by gravitation change (It can also be move up and down and move back and forth by manipulate and changes gravity force inside the machine. I have an idea but...
In describing the spacetime around a massive, spherical object, one would use the Schwarzschild Metric. What metric would instead be used to describe the spacetime around multiple massive bodies? Say, for example, you want to calculate the Gravitational Time Dilation experienced by a rocket ship...
Newton arrived at "there is a force that drives a planet around the star by examining kepler's laws but how did he arrive to inverse square law by kepler's third law (##T^2=\frac {4\pi r^3}{GM}##)?
Thank you.
Electrons flowing through a resistor are dissipating electrical energy. The electrical energy is transported from the battery to the electrons along the curved field lines of the Poynting vector. It seems like a meaningful idea that electrical energy necessarily travels from the source to the...
Supposedly, the retarded wave solution to Maxwell's equations applies to gravitation as well as electrodynamics.
The space station doesn't fly off into the distance because every object in the universe (at whatever distance) focuses gravity through the mass of the station. Every object on the...
This is a continuation of this post, which has been closed to replies:
I am also really curious to better understand Jefimenko's theory of gravitation; I have the book, which apparently is no longer available on amazon, and I updated the wikipedia page to include his generalized gravitation...
Hi everyone! Hope your day is going well. I’m an ex-physics student who recently wanted to go back to studying the subject (as a hobby, mostly). So I picked up Zee’s GR book since GR is the thing I’m the most interested in. I expected to hit a wall on some basic things since I’m rusty, and did...
I want to determine the normal flow depth in a perfectly horizontal circular conduit. The system characteristics are known (Internal pipe diameter, Mannings roughness, Discharge). However, I am not sure how to calculate the normal flow depth. When using Manning's equation one can find the normal...
I recently encountered this problem on a test where the solution for the above problem was given as follows:
$$F= \frac{Gm_1m_2} {r^2} $$ (1)
but
$$ m=\frac{4}{3}\pi R^3 $$
substituting in equation (1)
$$F= \frac{{G(\frac{4}{3}\pi R^3\rho})^2 }{2R^2} $$
where r=radii of the two spheres
m=mass...
In Gravitation by Misner, Thorne and Wheeler (p.139), stress-energy tensor for a single type of particles with uniform mass m and uniform momentum p (and E = p2 +m2) ½ ) can be written as a product of two 4-vectors,T(E,p) = (E,p)×(E,p)/[V(E2 – p2 )½ ]
Since Einstein equation is G = 8πGT, I am...
Hi,
my daughter saw my MTW copy on the desk and she asked me about the picture with the apple in front. To introduce her to the idea of gravitation as curved spacetime I answered like this:
Consider you (A) and a your friend (B) at two different spots on a garden each with a firecracker. Take...
I'm trying to understand what the time dilation looks like when moving through space and then approaching a planet's gravity field. So I have the broad understanding that if you are moving near the speed of light in a spaceship, your clock ticks normal but the clocks on other stationary objects...
An asteroid of mass M explodes into a spherical homogenous cloud in free space. Due to energy received by the explosion, the cloud expands and the expansion is spherically symmetric. At an instant, when the radius of the cloud is R, all of its particles on the surface are observed receding...
I would like to exercise the formulations in the book. I have read Gravitation and many others but I need to do more exercises. I get very bogged down in writing out the symbols. Are there electronic solutions for writing and exercising these equations? I have used Mathcad to perform...
I was reading Einstein's 1911 paper named "On the Influence of Gravitation on the Propagation of Light" when stated the formula for frequencies measured by observers at different fixed positions (heights) on Earth surface. One observer is at the origin of some coordinate system and measures a...
Assumptions
1. General Relativity is the modern and most complete widely accepted theory of gravitation, formulated in a background independent, geometric way.
2. General Relativity is formulated in a manner consistent with Special Relativity and I could imagine that it might be possible to...
Are you aware of the 3-article series of Wiesendanger's quantized extension of GR?
This is open access: C Wiesendanger 2019 Class. Quantum Grav. 36 065015 and the two sequels linked to in the PDF. The question is if this work counts as a quantization of a reasonable extension or reformulation...
Hello,
I would like to calculate the orbital velocity using the geometrical way of reasoning. But I have a hard time to understand and apply some basics into my calculations.
The reasoning is pretty simple. After some time: dt ,the particle travels the distance: Vtot1 * dt = R*sinθ (see the...
In the famous book, Gravitation, by Misner, Thorne and Wheeler, it talks about the stress-energy tensor of a swarm of particles (p.138). The total stress-energy is summed up from all categories of particles. Is summation meaningful in the non-linear theory of Einstein gravitation? Thanks.
I need help with understanding this problem. I had initially chosen B, that the two satellites had the same speed because the mass does not effect the velocities of each of the satellites considering they are in orbit. But that answer was marked incorrect by my instructor. What other answer...
Consider only the Earth-Moon system, where both the Earth and Moon are spheres. A horizontal line joins the centres of the Earth and Moon. Consider a point P that lies on the surface of the Earth. The line joining P and the centre of the Earth meets the horizontal line joining the centres of the...
Hello everyone.
Probably this question is trivial, but nevertheless I am confused about Newtons law of motion:
$$F=G\frac{m_1m_2}{r^2}$$
Now, some sources say, that F is the force between the two masses m1 and m2. Other sources say, that F is the force that m1 exhibits on m2. But isn’t this a...
Suppose a rocket is moving at radial velocity vr and tangential velocity vt in the Sun's gravitational field. At some time, the rocket enters the gravitational field of Mars (with the above mentioned velocities), and gravitation effects due to the Sun can be ignored. After more time, the rocket...
Hi,
I was reading Wikipedia article on Newton's Law of Gravitation and I couldn't make sense of the following section.
Source: https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation#Limitations
How could the improved law of gravitation be written? Like as shown below? Thank you...
The speed of star on the outer of are solar system is not according to the visible mass.
Change the law of gravitation F = 1/r^2 to fix this.
Galaxies far away are moving away with increasing speed.
Change the law of gravitation F = 1/r^2 to fix this, include a repulsive force to fix.
Would this...
From one point of view the charged particle is accelerating and should emit electromagnetic waves.
But from the equivalence principle, I think, it should not.
Does anybody know the answer?
For question A, I know that I am supposed to input the numbers given into the Universal Gravitation Equation, but I do not know how to solve for it beyond that.
For question B, I know that the astronauts weight depends on the mass and gravity of the new planet but I do not know how to prove it...
I was recently working on the two body problem and what I can say about solutions without solving the differential equation. There I came across a problem:
Lets consider the Kepler problem (the two body problem with potential ~1/r^2). If I use lagrangian mechanics, I get two differential...