All Questions
Tagged with newtonian-gravity classical-mechanics
112
questions
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How much time does it take for an object to fall from space? [closed]
Let's say there's an object of mass $m$ in space, $h$ meters away from the surface of the Earth. $h$ is large enough that $g$ cannot be assumed to be constant. The acceleration varies according to ...
- 119
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Is quadrupole contribution to gravitational potential the sum of the contribution of all $m$ values?
Many of the sources I find on multipole expansions seem to be about electric potential and involve matrices. However, in my classical mechanics class we have not used matrices for multipole expansions ...
- 414
-4
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2
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117
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Is Newton's gravitational acceleration centripetal instead of attractive?
In 1845 W. R. Hamilton demonstrated [1] by the use of the hodograph representation that the velocity of any Keplerian orbiter is the simple addition of two uniform velocities, one of rotation plus ...
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2
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40
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Is there a way to express the collisionless boltzmann equation in terms of positions, velocities, times, without the distribution function?
Suppose I have data that represents a field of positions and velocities. If the distribution function (DF) for the data is $f(x,v,t)$, I know that the DF must obey
$$\frac{\partial f}{\partial t} + \...
-1
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1
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In one formula of orbital velocity for circular orbit it has inverse relation with radius while in critical velocity relation it has direct. Why?
In one formula of orbital velocity for circular orbit it has inverse relation with radius
$$v=\sqrt{\frac{GM}{r}}$$
while in critical velocity relation it has direct
$$v=\sqrt{gr}$$
Why?
2
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1
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266
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How to calculate the period of non-circular orbits?
How to calculate the period of non-circular orbits?
By conservation of mechanical energy:
$$
E = -\frac{GMm}{r} + \frac{1}{2}\mu \left ( \dot{r}^2 + r^2 \dot{\theta}^2 \right )
$$
By the conservation ...
- 1,515
-3
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1
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41
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Potential energy change is not negative? [closed]
$\Delta U = -(W_{earth} + W_{ball})$
$W_{ball}$ is almost 0, as earth's displacement by the falling ball is super small, so $\Delta y$ of the earth could be negligible and $W_{ball} = 0$. so:
$\Delta ...
- 137
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2
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221
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Laplace's equation doesnt reproduce Newtonian gravitational potential
Newton's law of gravitation describes the gravitational potential produced by a mass $m$ as : $G(r)=-k\frac{m}{r}$.However if you solve Laplace's equation for the gravitational potential in polar ...
user369585
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1
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107
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Measuring the effect of spin of a tennis ball on its trajectory
Upward spin (lift) applied to a tennis ball will shorten its trajectory.
Are mathematical calculations and actual experimental results on this available somewhere?
If not, does anyone know how to ...
- 17
1
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3
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182
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How to prove that a drop of water in the weightlessness of space is round in shape?
How to prove that a drop of water in the weightlessness of space is round in shape theoretically? More specifically, how to prove that a drop of water in the weightlessness of space is round in ...
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44
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How to obtain the equations of motion and trajectory of a particle from the effective potential?
In a certain problem regarding motion of a particle in a gravitational field with axial symmetry, I have an expression of an effective potential $\Phi_{eff}(r,\theta)$. Now, I am interested to study ...
- 2,015
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2
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158
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Why does the Lagrangian not show particle-interaction? Why are normal/tension forces not considered?
(1) For formulating a lagrangian for a system of particles compared to one free particle, we start with the kinetic energy and formulate a potential energy term that is in terms of each of the radius ...
- 17
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43
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Why is it important to release energy as quickly as possible to perform a vertical jump?
Let's assume that we create this mechanism, where we must decide if the actuating cylinders are double-acting hydraulic or pneumatic with a spring inside.
the goal is for the mechanism to suddenly ...
1
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1
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82
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Conic Section in Newton's Cannonball Problem
From the Classical Mechanics Lecture Notes by Helmut Haberzettl, we know that in Newtonian Mechanics, the solution to Kepler's problem can be parametrized as a conic section equation
$$r(\varphi)=\...
- 381
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6
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Free falling bodies in the absence of external forces
We know that if two balls $B_{1}$ and $B_{2}$ having masses $m_{1}$ and $m_{2}$ respectively and suppose $m_{1}$ is sufficient greater than $m_{2}$. In daily life observation, we see that both the ...
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