What is Gravitation: Definition and 913 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.
Homework Statement
A. The mass ratio of the Earth and the moon is 81:1 and the earth-moon separation is 3.8x108m. At which position between the Earth and the moon is the gravitational potential at a maximum?
B. Which of the following statement about a communication satellite in parking...
Homework Statement
Please give an example when the following condition is true-
Gravitational Potential is zero and gravitational field intensity is non-zero.
Homework Equations
The Attempt at a Solution
Homework Statement
1.A satellites are placed in a circular orbit that is 1.43 × 10^8 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance
Homework Equations
1.I used G*mE/r^2
The Attempt at a Solution
1. Got an answer of .0195m/s^2 I...
I'm trying to understand the basics of gravity. Newtons law of universal gravitation gives us : F1 = F2 = G (m1m2)/r2
Now on Earth you can simply that down to
F = mg where g = G (mearth/R2)
But using f = mg, a heavier object say a tennis ball should fall faster than a cannon ball. But...
Homework Statement
Which of the following statements about Newton’s Universal Law of Gravity is false?
A. The heavier mass exerts a force on the lighter mass that is equal but opposite to the force the lighter mass exerts on the heavier mass.
B. A heavy mass from far away can exert the...
I'm working on a problem on relating gravitation and simple harmonic motion. The idea is that a mass dropped in a hole drilled through the Earth will oscillate (no friction, etc).
The question asks this:
"Show that the motion of the mass is simple harmonic motion and find a formula for r(t)"...
hello, I'm not saying that Newton's law of universal gravitation is really wrong but there are phenomenons which i don't think the law is really correct and i want someone to help me. There might be explanations but i don't really know any explanations right now so an explanation would be...
Homework Statement
At what distance from teh Earth will a spacecraft on the way to the Moon esperience zero net force due to these two bodies because the EArth and Mon pull with equal and opposite forces?
Homework Equations
net force = m a
a radial = r^-1 v^2
Fg = r^-2 G M m...
I don't understand the physical meaning of one of my dimensions/variables.
Let there be a gravitational potential \phi (x_a), a=1,2,3.
Equation of motions of a freely falling particle is:
\frac{d^2 x_a}{d t} = - \frac{\partial \phi}{\partial x_a}.
If there are 2 particles falling, family of...
Hi there,
I don't understand why the equal of Newton's law of gravitation F = Gm1m2/d(squared) is different for no spherical objects.
In the image of my attachment there are one spherical object and a no spherical object. So why if there are not very distant the equal used is F =...
Hi all,
Does Newton's law of universal gravitation depend on the geometry of the manifold? For example, what happens to formulas if we take the projective plane as our universe? How can one model "the mass" on the projective plane or on torus?
I am a math grad with very elementary...
What does strength mean exactly in this context below. Is this the acceleration imposed by M on m?
Strength of gravitational field created by a mass M: g = F/m = -G(M/r^2)r^unit
In the Einstein's theory of general relativity, the gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies.
But the quest for the famous graviton does not presume that gravitation is due to a force?
Is the quantum gravity conflicting with the...
Homework Statement
The three spheres in Fig. 13-45, with masses ma=80g ,mb=10g and mc=20g, have their centers on a common line, with L=12 cm and d=4cm. You move sphere B along the line until its center-to-center separation from C is d=4cm. How much work is done on sphere B (a) by you and (b)...
Hi,
I have attempted a basic gravitation question from “Classical Mechanics” R. Douglas Gregory (1st ed). I get the answer provided at the back of the book, but it doesn't make sense to me. Can someone help me interpret the answer?
Question: Pg 71, Q3.3
A uniform rod of mass M and...
Homework Statement
In Fig. 13-41, a particle of mass m1 = 0.23 kg is a distance d = 84 cm from one end of a uniform rod with length L = 6.4 m and mass M = 2.4 kg. What is the magnitude of the gravitational force on the particle from the rod?Homework Equations...
Homework Statement
Figure 13-39 shows a spherical hollow inside a lead sphere of radius R = 4.5 m; the surface of the hollow passes through the center of the sphere and “touches” the right side of the sphere. The mass of the sphere before hollowing was M = 380 kg. With what gravitational...
I am trying to learn more about General Relativiity. We had Newton's Law of Gravitation. When does it not work? I heard at very high speeds, high mass bodies, and when the distance to a high mass body is very short (Mercury for example, I think)? How does Newton's Gravitation differ...
I'm trying to figure out these two problems and I'm so lost!
1. Two planets are circling a star. The second planet has an orbit 4 times the size of the first planet. By the time the first planet revolves once, how many times the second one will?
My solution: the formula is T=2PiR/v... so...
Hi all! It is often said that Newton deduced from Kepler's laws the theory of gravitation. Particularly from (T^2)/(a^3)=const for differnet planets he deduced that gravitational force must look like '1/(r^2)'. I can also do that by writing F=ma and integrating it in spherical coordinates, but...
Homework Statement
A 450kg satellite is to be placed at an altitude of 2.45 x 10^6m above the Earth surface. Calculate the period the satellite will have when orbiting at that altitude.
Homework Equations
m2g = Gm1m2/R^2 = m2v^2 = m2(4pie)^2 R /T^2 = m2 2pie v/T
Ac=4pie ^2 R / T^2...
Here is the succinct story of apple which fell on Sir Newton. Since both apple and Earth attract each other with a force equal in magnitude from both sides but apple move faster towards Earth because of its greater acceleration than negligible acceleration of earth. So Newton derived the...
Combining quantum mechanics with general relativity supposedly yields infinite gravitation, between the gravitons if I have understood this correctly (correct me if I'm wrong). String theory supposedly does away with this infinite gravitation -- my question is, how does it do this...
Homework Statement
Comets travel around the sun in elliptical orbits with large eccentricities. Suppose the comet has an initial speed of 1.17*10^4 m/s when at a distance of 4.9*10^11 m from the center of the sun, what is its speed when at a distance of 5.9*10^10 m? Give your in m/s in...
Homework Statement
A rocket accelerates to speed v0 near the Earth's surface,and then coasts upwards. Show that if
v0 = 2sqrt(gR)
where R is the Earth's radius, then very far from the Earth the rockets speed will be
v = sqrt(2gR)
Homework Equations
The only equations I have thought...
Homework Statement
A 11 kg satellite has a circular orbit with a period of 1.0 h and a radius of 4.9 × 10^6 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 41 m/s^2, what is the radius of the planet?
The attempt at a...
So, I'm going over this bit in the beginning of MTW's Gravitation where they give an equation for changing acceleration from time coordinate t to time coordinate T(t):
\frac{{d}^{2}x}{{dt}^{2}} = \frac{d}{dt}(\frac{dx}{dT}\frac{dT}{dt}) = \frac{{d}^{2}T}{{dt}^{2}}\frac{dx}{dT} +...
Homework Statement
How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?
The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2
Homework Equations
The Attempt at a...
Homework Statement
If a uniform sphere of mass M and radius R, is height h above an infinite sheet of uniform density \rho_{s}, what is the gravitational force of the sphere, on the sheet.
Homework Equations
F=\frac{GMm}{R^{2}}; \Phi=\frac{GM}{R}; \nabla\bulletg=4\piG\rho; U=m\Phi...
Homework Statement
Starting with Newton's law of gravitation, determine the height h one person has to go from the surface of Earth in order for the person's weight to be reduced to 1/5 of their weight at the surface of the Earth. The only information you are given is that the radius of the...
The other day I was reading a simple experiment to determine (yes, very roughly) the constant of gravitation, all using simple tools in your basement.
http://www.fourmilab.ch/gravitation/foobar/"
What struck me about this experiment is another that I remember from childhood cartoon...
I was reading this very small section in my physics book and can't seem to come to grips with its concept.
It starts off with Newtons shell therem being applied to a particle located inside a uniform shell and that the shell exerts no 'net' gravitational force on a particle inside it.
It...
Homework Statement
A square of edge length 19.0 cm is formed by four spheres of masses m1 = 5.10 g, m2 = 3.00 g, m3 = 1.20 g, and m4 = 5.10 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 3.00 g?
Homework Equations...
If the distance between two objects is zero, won't there be infinite gravitational attraction force between them? How would the objects can get separated?
classically, acceleration towards the Earth's surface is described by
a=G*m/r^2
usually we think of using this formula to calculate the force of gravity as we rise away from the Earth's surface. but consider what would happen if if you traveled through a tunnel to the center of the earth...
Homework Statement
Each mass is 4kg find the magnitude and direction of the net gravtitational force on mass A due to the other masses. each side of the square is 10cm
http://img13.imageshack.us/img13/3815/1012447.jpg
I am having trouble with (b) the square
Homework Equations
F =...
Hi everyone. I know about the equations of gravitation but something is still bothering me.
The equation for total energy of a satellite in an orbit is -GMm/2r
However, when the satellite suddenly lose control and heads to the Earth, why does the total energy in the system change according...
Homework Statement
In an old-fashioned amusement park ride, passengers stand inside a 5.4-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all...
I have searche many general relativity texts and have not found an answer to the following question: How does curvature translate into the Newtonian idea of gravitation? For example, how is Newton's law of gravitation, where all matter attracts all matter, an approximation to the idea of...
Homework Statement
Mars travels around the Sun in 1.88 (Earth) years, in an approximately circular orbit with a radius of 2.28 x 10^8 km
Determine
a) the orbital speed of Mars (relative to the Sun)
b) the mass of the Sun
Homework Equations
acceleration centripetal = 4(pi^2)(r) /...
Homework Statement
The mass of the Moon is 7.36 x 10 ^ 22 kg. At some point between Earth and the Moon, the force of Earth's gravitational attraction on an object is canceled by the Moon's force of gravitational attraction. If the distance between Earth and the Moon (center to center) is 3.84...
I've had this on my mind for a while. I'm pretty confident that I have the right idea, but I can't find a formula that I could use to prove it to someone. So, here it is.
Imagine a sphere of space-time with absolutely nothing inside of it. It is a large sphere, sun-size large. Now, take...
Suppose an object is dropped from height h, where h < R but gravity is not constant). Show that the speed with which it hits the ground, neglecting friction, is approximately given by:
v = sqrt(2gh)(1 - (h/2r))
where g is the acceleration due to gravity on the surface of the Earth.
HINT...
Do higher energy photons have the same trajectory around planet/gravity as low energy photons? I.e: If you were shooting photons from the same position wrt a planet would their path be the same?
Homework Statement
Given
if:
(1) Fsm + Fem = Mm x Ams
(2) Ams = Ame + Aes
(3) Res ~= Rms
Show that (4) Fem ~= Mm x Ame
Where:
'Fsm' is the force between the sun and moon, 'Fem' the force between Earth and moon, etc.
'Mm' is the mass of the moon, 'Ams' the accelleration of the...
(Offtopic from another thread)
So I have a super-duper laser which can emit a very short but extremely powerful pulse in some direction. This pulse is so powerful that the energy of light is say 1Kg * c**2, or the relativistic mass of light is 1Kg.
What is a gravity from that light...
Homework Statement
Two satellites are launched at a distance R from a planet of negligible radius. (Yes, that's what the problem says...) Both satellites are launched in the tangential direction. the first satellite launches correctly at a speed v_0 and enters a circular orbit. The second...