All Questions
Tagged with newtonian-gravity integration
45
questions
3
votes
1
answer
204
views
How to calculate the gravitational binding energy of a uniform cube of length $L$ and mass $M$?
The functional form is known already (as attached). But what is the solution for this integral?
- 425
0
votes
1
answer
51
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Nonlinear GPE of a solid block seems wrong
I am trying to calculate the gravitational potential of a solid block, and I have a nonlinear answer which strikes me as wrong.
A block with horizontal surface area $A [m^{-2}]$ and uniform density $\...
- 5,148
1
vote
1
answer
82
views
How to find gravity field of a solid square body?
I was programming gravity simulation and stumbled upon a problem, that Newton's formula for point masses is not enough for me, I need gravity field formula of a solid square body (2D).
To simplify ...
- 141
1
vote
2
answers
416
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Gravitational force of point mass on a rigid body - Integral proof
Assume a point mass $m$ located at $\vec{x}$. Assume also a solid body whose coordinates $\vec{x}'$ belong to a connected subdomain $\vec{x}' \in \Omega$. The solid body has a non-uniform mass density ...
- 201
0
votes
2
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708
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Integrating a dot product gives wrong sign for work done [duplicate]
Consider a point mass which creates a gravitational field. The gravitational force pulls a 'test mass' towards the point mass. Since the displacement and gravitational force are in the same direction, ...
12
votes
2
answers
22k
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Gravitational potential energy of any spherical distribution
The general formula to get the potential energy of any spherical distribution is this :
\begin{equation}\tag{1}
U = - \int_0^R \frac{GM(r)}{r} \, \rho(r) \, 4 \pi r^2 \, dr,
\end{equation}
where $M(r)$...
- 7,592
0
votes
1
answer
899
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Period of a pendulum [closed]
In the book 'Calculus the Early Transcendetals' at page 776 (7th edition) they give that the period of a pendulum with length $\text{L}$ that makes a maximum angle $\theta_0$ with the vertical is:
$$\...
- 291
2
votes
3
answers
832
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What's my $\mathrm dM$? Gravitational Potential inside a circle of mass
I'm trying to find the gravitational potential for an arbitrary point within a ring of uniform mass density. The point is constrained to be in the same plane as the ring.
So we start with:
$$\Phi=\...
- 53
0
votes
1
answer
91
views
How to find an equation for $x$ in terms of $t$ for a particle falling under gravity with resistance given by $mkv^2$? [closed]
Okay so I have determine the velocity $v$ and displacement $x$ as functions of $t$ for a particle falling under gravity with resistance given by $mkv^2$.
I have set up the equation of motion divided ...
- 35
1
vote
1
answer
1k
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From Paris to ... London [closed]
(Excuse the pun in the title, couldn't resist)
Paris and London are connected by a straight underground tunnel, as shown in the diagram below. A train travels between the two cities powered only by ...
- 3,569
4
votes
1
answer
3k
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Newton's original proof of gravitation for non-point-mass objects
Suppose we have two bodies, one very large (Earth), and one very small (a cannon ball). If the cannon ball is some distance away from the Earth, to find out the force produced on the cannot ball, we ...
- 143
4
votes
2
answers
326
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How do you know which way to choose the limits of an integral?
I am reading http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S4
In the beginning of equation 13.18, in which Mr. Feynman calculates the potential energy of an object outside a spherical shell, ...
- 527
2
votes
1
answer
11k
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Gravitational force exerted by a rod on a point mass
I have doubts with the solution of a certain problem. I will give the entire solution below and will lay out my doubts as well.
A point mass $m_1$ is separated by a distance $r$ from a long rod of ...
- 383
8
votes
3
answers
6k
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Integrating radial free fall in Newtonian gravity [duplicate]
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 ...
- 93
2
votes
0
answers
123
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What is the correct way of integrating in astronomy simulations? [closed]
I'm creating a simple astronomy simulator that should use Newtonian physics to simulate movement of plants in a system (or any objects, for that matter). All the bodies are circles in an Euclidean ...
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