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
There is a point on the line between the centres of the Earth and the moon where their gravitational fields have equal magnitude but are in opposite directions, effectively creating a point of zero gravity. Calculate the distance of this point from the centre of the earth...
Homework Statement
The Earth has a mass of 5.98x10^24 kg and the moon has a mass of 7.35x10^22 kg. The distance from the centre of the moon to the centre of the Earth is 3.84x10^8 m. A rocket with a total mass of 1200 kg is 3.0x10^8 m from the centre of the Earth and directly in between Earth...
Homework Statement
The gravitational field g due to a point mass M may be obtained by analogy with the electric field by writing an expression for the gravitational force on a test mass, and dividing by the magnitude of the test mass, m. Show that Gauss' law for the gravitational field reads...
So I was looking at the equation for Gravitation potential energy
U = - Gm1m2/r
This implies the energy is 0 as r→∞
However, if I lift a book above my head, wouldn't it have more potential energy than if it was lying on the ground, meaning as r (h) increases, potential energy increases? Where...
Hello, Is there any research available as to whether Newtons Law F = mg should include horizontal surface area as a factor (ie the surface area of opposing masses). Example a pole weighing exactly the same seems heavier when held at one end horizontally to the ground, compared to holding it...
I have a bit of intuition on microscopic structures, so I "easily" understand things such as chemistry, nuclear and particle physics and the such. I'm no expert in these subject or anything but I do have a easier time learning it.
But I REALLY have a hard time understanding some...
Homework Statement
The sun mass MS = 2.0 E30 kg revolves around the center of the milky way which has a total extension of 2.2 E20 m. The sun takes 2.5 E8 years to complete one revolution. Estimate the number of star in our galaxy based on this data.
Suppose that the distribution is...
I'm taking a course in general relativity, it's a beautiful theory and I personally have no reason to doubt it's validity. However, I also recently stumbled upon and alternative theory of gravitation which was worked out by Oleg Jefimenko and is published in the following book...
Homework Statement
What is the change in gravitational potential energy of a 64.5-kg astronaut, lifted from
Earth’s surface into a circular orbit of altitude 4.40 3 102 km?
The Attempt at a Solution
Ok, i know to find this i have to find the gravitational energy on Earth using...
Okay, i know people saw that Earth is pulling everything towards each other and infact every other object is attracting each other. So there must be a force. But how did they discover the law i.e. F = GMm / r^2.
They must have done some experiements to figure out this law and determine the...
Hello, I am trying to work out this exercise for my personal research connected with my bachelor thesis. The task is to compare equations (25.42) and (25.47) and express $u_0$ in terms of \tilde{L}. I have so far put the two equations together getting
\begin{equation}...
Dear Sir,
My name is Ashish R. Sai I am from India.I just appeared for 11th std.A few days ago I went through Gravitation.I completed my assignment.After completing assignments,I tried to find the gravitation between the moon and earth. During this i got a few doubts in this...
**Bonus Question** Gravitation
A 1000kg rocket sits on the surface of a Earth like (same mass and radius - no atmosphere) planet. When fired, the rocket engines produce a force of 25 000N. The rocket is designed to reach an altitude of 580 km before the fuel runs out. If 1/2 of the rockets...
Newton Law Gravitation - Multiple choice question??
Homework Statement
Newton’s law of gravitation can be applied to the Earth-Moon system. Which of the
following statements is not correct?
A The value of G at the surface of the Moon is the same as that at the surface
of the Earth...
Homework Statement
Three objects of equal mass (m) are located at three corners of a square of edge length , as shown in the figure below. Find the magnitude and direction of the gravitational field at the fourth corner due to these objects. (Use any variable or symbol stated above along...
Homework Statement
In the Bohr model of the hydrogen atom, the electron revolves around the nucleus. If the radius of the orbit is 5.8 z 10^-11 m and the electron makes 6.6 x 10^15 r/s, find;
a) the acceleration of the electron
b) the magnitude of the gravitational force of attraction...
Homework Statement
is there a point between the Earth and the moon for which the net gravitational force on an object is zero? Where is this point located? Note that the mass of the Earth is 5.98x10^24 kg, the mass of the moon is 7.35x10^22kg, and the distance between the centres of Earth...
Derive "Focusing Theorem" in Gravitation by MTW
I followed the logic in Chapter 22.5 from Misner&Thorne&Wheeler, trying to derive the focusing theorem, i.e. equation(22.37).
The problem that blocks me is the derivation of (22.36) for the cross section area. I already find the equation for...
I know physical bodies with mass cause gravitation.
But do massless particles, like photons, also cause gravitation ? I know they're affected by gravity, but would a cloud of photons bend space by itself?
Thank you
Why is gravitation still considered a Fundamental Force when General Relativity says that it is a geometric effect of inertia and space-time curvature?
Homework Statement
A 70 kg bungee jumper jumps from a bridge. She is tied to a bungee cord whose unstretched length is 13 m , and falls a total of 37 m .
Calculate the spring stiffness constant of the bungee cord, assuming Hooke's law applies.
88 N/M
Calculate the maximum...
Lets suppose that we setup two instances involving two masses m1 and m2.
m1 > m2
Case 1. The two bodies are separated by a distance r = 20.
Case 2. The two bodies are separated by a distance r = 10.
Suppose that in both setups, we were to release all restraining forces on these two...
Homework Statement
"At what height above planet B's surface (in meters) does the gravitational field intensity become 0.6 times its value on the surface of planet B, given that the radius of planet B is 6.40 x 10^3 km and that its mass is 5.97 x 10^24 kg?
Homework Equations
g=Gm/r^2...
At t = 0 a star of mass 5.0×1030 kg has velocity < 6.0×10^4, 7.0×10^4, -7.0×10^4 > m/s and is located at < 1.00×10^12, -4.00×10^12, 4.00×10^12 > m relative to the center of a cluster of stars. There is only one nearby star that exerts a significant force on the first star. The mass of the second...
Homework Statement
Please refer to the figures. (The first one is multiple-choice, the latter is structured).
Homework Equations
For the first problem:
u = √(2gH)
x = uxsinθt + \frac{1}{2}gsinθt2
uycosθt = \frac{1}{2}gcosθt2 and maybe others
u = initial velocity
x = x-displacement...
Homework Statement
I need to show that the first equation becomes the last. First sub in for r1 and r2 and then use the binomial theorem to expand to first order in d. Then use the assumption that d<<r1 and r2. To show it reduces to the last eqn
**In the first eqn it is NOT r3 is should be r2...
My book says r^3/t^2 was found constant by Kepler. What this constant is called?
How is acceleration equal to v^2/r in case of circular motion?
Why is rate of change of momentum or say product of mass and acceleration equal to force? Why not was it ma^2? How was it proved that it...
We know that
1. Mass causes bend in space-time and this is the how gravitation occurs.
2. The formula for gravitation (per the universal law of gravitation) is product of masses divided by the square of the distance between them and multiplied by the universal gravitation constant.
I...
Homework Statement
Homework Equations
2ΔEk=-ΔEp
The Attempt at a Solution
-Gm1m2(1/r1-1/r2)-Q=mv2
plug in given values solve for v.
my answer is 5.35x106m/s
given answer is 2100m/s
Gravitational waves are generated when the mass quadrupole moment changes in time.
We also know motion of mass contributes to its gravitation. Does the producing process of gravitational waves, which involves mass in accelerated motion, produce gravitation as well? If so, is it of less, equal...
while in downward motion or in an orbit astronomers experience weightlessness
their apparent weight (the mass they feel is m = (g - a)
where g is acceleration due to gravity and a is acceleration with which the person is going downwards.
now my question is what will the person feel if a>g?
if the Earth stops rotating , the value of 'g' will increase by Rω2 at the equator but will remain same at the poles.how does it happen?could you please explain me this?
Homework Statement
A space vehicle of mass 555kg, experiences a gravitational pull from Earth of 255N. The mass of Earth is 5.98x10 (to the power of 24) kg.How far is the vehicle a) from the center of the Earth, and b) above the surface of the Earth?
Homework Equations
FG = GM1M2/d squaredThe...
Its interesting that eventhough gravitation is a force, it cannot be measured. Literatures says that only gravitational gradient can be measured from gravity tensor is to be computed and by applying mathemaatical operations, derive the gravitational vector.
Can anyone help me to understand...
Homework Statement
Mars has a diameter of .54 times that of Earth and a mass of .11 times that of Earth. Suppose a rover was launched on Earth with the mass of 525 kg. Remember that g is -9.80 m/s/s
A) How much does the rover weigh on Earth?
B) How much does it weigh on Mars?Homework Equations...
Homework Statement
See Attachment
Calculate the force of gravity on the point mass due to the line mass in terms of the gravitational constant G, m, M, D, and L. The line mass has a uniform density.
Homework Equations
The Attempt at a Solution
Ok so apparently I'm suppose to...
Homework Statement
The question is presented as picture.
Homework Equations
We do not have the radius of the cavity and the position of the m. How can we find the force acted on it?
The Attempt at a Solution
r=1/(M-m)*Ʃmr=1/(M-m)*4/3ρR'^3*r where m is the mass of cavity ,R' is the...
a 120kg person stands on the surface of an asteroid of radius 600m. the person leaves the surface with 15J of kinetic energy and reached a maximum height of 300m above the asteroid's surface. what is the mass of the asteroid.
i am stuck please help me with the problem.
15-GMm/r(i) = 0 -...
Universe with only "e+", "e-", photons, and gravitation?
In theory could we have a universe with only electrically charged spin 1/2 particles and antiparticles of mass m and electrical charge e and that interacted only gravitationally and electromagnetically?
If so could we fine tune things...
Hello!
I need to find the relation between E^{2}-B^{2} and F_{\mu\nu} F^{\mu\nu}
Actually, I need to use this relation to determine that the first is a scalar.
What I can't understand is how these notations match the formal definition:
If I multiply a matrix by another (same size) I should...
Homework Statement
How deep would a mine shaft have to be for the gravitational acceleration at the bottom to be reduced by a factor of 5 from its value on the Earth's surface?
Homework Equations
g=r(GME/RE3)
G = 6.67 * 10-11
ME = 5.97 * 1024 kg
RE = 6.38 * 106 m
The Attempt at a...
Gravitation Potential Energy Problem of WHY?
Homework Statement
Energy is required to move a 1540 kg mass from the Earth’s surface to an altitude 3.12 times the Earth’s radius RE. What amount of energy is required to accomplish this move? The acceleration of gravity is 9.8 m/s^{2}...
Hello! I fail to understand this question... I don't even know how to approach it...
Given: m\frac{d^{2}x^{\mu}} {d\tau^{2}} =e{F^{\mu}_{nu}} \frac{dx^{\nu}} {d\tau}
I have to define u^{\mu}= \frac {dx^{\mu}} {d\tau^2}
and obtain:
u^0= cosh(\frac {eE\tau} {m}) u^0(0)+ sinh(\frac {eE\tau}...
Homework Statement
Standing on the surface of a small spherical moon whose radius is 6.00*104 m and whose mass is 7.50*1018 kg, an astronaut throws a rock of mass 2.05 kg straight upward with an initial speed 38.5 m/s. (This moon is too small to have an atmosphere.) What maximum height above...
I've worked out the inverse square law using centripetal acceleration and Kepler's law. But I can't quite see how Newton worked out for sure that the force is directly proportional to both masses. I know it's pretty intuitive, but I thought maybe there was a mathematical way of confirming that...
Newton's universal law of gravitation:
F=-G \frac{m_1 m_2}{r^2}
I'd like to set up the problem so the particle begins at t=0 at radius r=r0 and radial velocity vr=v0. And there is only a component of velocity, in the radial direction. (The particle is going straight toward the...
Homework Statement
what is the gravitational field strength on the surface of a star that has a radius of 5.0 x 10^6km and a mass of 6.0 x 10^33 kg
Homework Equations
i tried the F=G MM/r^2
The Attempt at a Solution
answer was rly weird and off
The asteroid 243 Ida has a mass of about 4.0×1016 and an average radius of about 16 (it’s not spherical, but you can assume it is).
A)Calculate the speed with which you would have to throw a rock to put it into orbit around the asteroid 243 Ida, near the surface. v= ?
B)How long would...
Homework Statement
NASA is considering solar sailing: using the momentum of light and of massive particles emitted from the sun to help push a spacecraft equipped with large, diaphanous sails. Assume that the density of the material from which the sails are made is about 1000kg.m^{-3}.
a)...
Ok so my physics teacher was telling us about the gravitation and he gave us an example of two people standing and he said that these two people are attracting each other. Then he calculated the gravitation force between them. It was a clear thing for me until this.
but then he said that they...