Questions tagged [newtonian-gravity]
This tag is for questions regarding the Newtonian model of gravity in which the force between two objects is given by $~GMm/r^2~.$ It is a natural phenomenon by which all things with mass or energy – including planets, stars, galaxies, and even light – attract one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides.
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Initial positions and velocities for the three-body problem
I have made a simulation of the three-body problem, it follows the euler's method of solving differential equations. I have tried some initial positions and velocities of the bodies and have observed ...
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Einstein's equation of gravitation field [duplicate]
I'm looking for the reason why there is the number eight $8$ at the r.h.s. of EI:
$$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c^2}T_{\mu\nu}.$$
My attempt was to take the limit of this equation ...
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Can we treat the entire mass of the spheroid as being concentrated at its center?
I know that to find the gravitational force between two objects, if either of them is a sphere, we can assume its mass to be concentrated at its center and use the formula for gravitational forces for ...
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Deriving expression for gravitational potential energy around a mass, $M$, using vectors
(I think my question will be somewhat related to this one: Deriving gravitational potential energy using vectors .)
I know the change in the potential energy associated with a conservative force, $\...
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Speed of satellite in elliptical orbit [closed]
A satellite $S$ orbits a planet of mass $M$ in an elliptical orbit. At perihelion, $S$ has a tangential velocity of $v_1$ and is distance $r_1$ from the planet. At aphelion, $S$ has a velocity of $v_2$...
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Why is velocity proportional to radius in a spherical explosion?
While doing problems on spherically symmetric explosions, I noticed I had been intuitively assuming that velocity scales linearly with radius of the "shell" under consideration. To be more ...
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Can an Ideal Lever Balance in a Non-Horizontal Position?
I recently came across an interesting question while reading Feynman's Lectures on Physics. In chapter 4–2 "Gravitational potential energy," there's an illustration that made me wonder about ...
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With what vel. would you have to launch an object vertically up from the earth's surface for it to land back again at it's initial launching point?
[Can skip reading this part] First of all, Newtonian gravity shall be considered whilst trying to solve this question. It's been on my mind for a long, long time and has been bothering me since. I ...
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Why is the uncertainty of the Gravitational Constant $G$ many orders of magnitude larger than that of other important fundamental constants?
Why is the numerical range of uncertainty of the Gravitational Constant $G$ many orders of magnitude larger than that of other important fundamental constants?
What are the challenges in precise ...
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Gravitational potential due to arbitrary shape
Outside the uniform sphere, the potential is expressed as if all the masses are concentrated in the center of the sphere.
Is it also true for arbitrary shape?
That is, outside any body, is potential ...
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Terminal velocity gravity against first-order drag force
Let's say that we have a falling object with two forces acting on the object:
gravity $F_g = mg$ and a first order drag force $F_d = kv$.
Terminal velocity will be reached when gravity is equal to the ...
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Why do higher objects have a greater force?
We did an experiment in class today using a spring scale, a plastic bag, and a variety of other objects. Essentially, we attached the bag to the spring scale and measured the force, in newtons, of ...
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In an $n$-body system, do all bodies accelerate towards center of mass?
I've been building an $n$-body simulator as a way to learn a new game engine, and I've come across something that isn't necessarily a problem, but has intrigued me. Most other simulators I'm seeing ...
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Dropping a stick down with an angle
Let's say that we drop a stick down with an angle, meaning that the stick is not parallel to the ground. Assume there is only gravity. Is it correct that the orientation of the stick will not change ...
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Gravitational binding energy of a sphere with radially-dependent density
As stated here, the gravitational binding energy of a uniform sphere is:
$$U = \int_0^R -\frac{G}{r} \left(\frac{4}{3}\pi r^3\rho\right) \left(4\pi r^2\rho\right) \mathrm{d}r.$$
I want to know if the ...
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