All Questions
Tagged with newtonian-gravity classical-mechanics
112
questions
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3
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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 ...
- 117
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1
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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
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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 ...
0
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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
$$\frac{\partial f}{\partial t} + \...
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1
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51
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In one formula of orbital velocity for circular orbit it has inverse relation with radius while in critical velocity relation it has direct. Why?
In one formula of orbital velocity for circular orbit it has inverse relation with radius
$$v=\sqrt{\frac{GM}{r}}$$
while in critical velocity relation it has direct
$$v=\sqrt{gr}$$
Why?
2
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1
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267
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How to calculate the period of non-circular orbits?
How to calculate the period of non-circular orbits?
By conservation of mechanical energy:
$$
E = -\frac{GMm}{r} + \frac{1}{2}\mu \left ( \dot{r}^2 + r^2 \dot{\theta}^2 \right )
$$
By the conservation ...
- 1,525
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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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224
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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
answer
111
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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 ...
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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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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 ...
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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 ...
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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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95
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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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How much time after will two oppositely charged particles collide for both gravitational force and electrostatic force?
Suppose two point objects charged with opposite charges $q_1$ and $q_2$ at a distance $r$ in a vaccum.
So, the net electrostatic force on both objects $= F_c = \frac {q_1q_2}{4π\epsilon_0r²}$ [$\...
- 1,070
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3
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178
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Why gravitational potential away from a planet increases?
textbooks----
"potential increases towards infinity and is maximum at infinity"
But that is true only when we are seeing potential w.r.t Earth
EXPLANATION---------
So , as we know that ...
- 444
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57
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If the change in potential enegry is equal to the negative of the work done, then this principle isn't consistent here in the case freely falling body
Let us assume that a body of mass $m$ falls from height $h_1$ to $h_2$ :
Here the Work done by gravitational force (Conservative force) is :
$$\mathrm{Force \ ×\ Displacement} = mg \ (h_2-h_1) \tag1$$
...
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114
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What is the effective potential for photons in Newtonian gravity?
I am confused about the movement of photons and their trajectory, I hope you can help me:
What kind of path does light follow in Newtonian gravity?
What is the effective potential for photons in ...
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3
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224
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Equation of motion of a classic inverted pendulum in free fall
I was thinking in this interesting problem:
Suppose we have this inverted pendulum:
But without this control force $F$ and the system would by loose from a height $h_0$, with initial velocity $0$ ...
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2
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3k
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What happens when the PE equals to zero in the potential energy vs intermolecular distance graph? [closed]
In the potential energy versus inter molecular distance graph, we know that atoms/molecules/particles want to be at optimum distance from each other ie $r_0$ and to the left of this position in the ...
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699
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Why in binary star system the 2 bodies revolve around their center of mass?
Can you prove it mathematically?
Is it just an observation?
I know the force between them is $\frac{Gm_1m_2}{r^2}$.
Centripetal force on any one of them is $\frac{mv^2}{r_1}$, where $r_1$ is radius of ...
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120
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How do you find the position at which three particles obey $m_1 a_1 = m_2 a_2$ if two of the particles form a composite body?
From Classical Mechanics by Kibble:
Consider a system of three particles, each of mass m, whose motion is
described by (1.9). If particles 2 and 3, even though not rigidly bound
together, are ...
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1
answer
648
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Newton's first law - elevator lift upward and downward force [duplicate]
Why does $F_c$ is equal to $F_g$ and why $F_c$ isn't greater than $F_g$? $F_c$ is moving it upward right, so the force must be greater than gravity to pull it upwards I think.
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188
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Physical interpretation of the symmetry for the Runge-Lenz vector
In the post What symmetry causes the Runge-Lenz vector to be conserved?, and based on the results of https://arxiv.org/abs/1207.5001, it was it was discussed that the Runge-Lenz vector is the ...
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1k
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When is the effective potential equal to the total energy?
I have a question about the energy of a particle in orbit due to a gravitational attraction. The effective potential given by the gravitational force is defined to be
$$
U_{\text{eff}} = \frac{L^2}{...
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82
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Exact distance travelled by an object due to gravity only
I am aware of the fact that for two point masses in space, the time that it will take for them to collide is, T=$\pi \sqrt{\frac{r_i^3}{8GM}}$, where M is the sum of the 2 bodies' masses, $r_i$ is the ...
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Justification for the nature of planet's orbit in gravitational field!
In kleppner Mechanics in the chapter central force he derived the polar form of orbit for gravitational force as illustrated below: (first two equations are derived from fundamentals of central force)
...
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1
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43
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Variable mass of orbiting body
Considering an object orbiting earth at radius $R$ and speed $v$, at one moment in time the mass of the object starts to decrease, what will happen to the object in terms of speed and orbit?
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54
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A thought experiment to prove that Newtonian gravity is incomplete [duplicate]
A particle is at rest in one frame having mass $m$. It'll attract another mass proportional to its mass ( newtons law) .
We jump into another frame moving close to speed of light. In this frame it's ...
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253
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What is definition of weight of person in elevator moving with acceleration?
I have a question, I need your help with understanding definitions. Let's recall the famous problem:
What is the weight of the person mass m, if the elevator moving up with acceleration a?
of course,...
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435
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How to calculate the sphere of influence of a planet?
I'm making an orbit simulator, and to make it simpler, I'm only simulating one celestial object(planet, moon, sun) acting on each object(sattelite).
So that the sattelites and rockets can switch ...
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Virial theorem for two particle inelastic collision
Consider two point masses separated by a large distance R so that their initial potential energy can be considered 0. They are both at rest with respect to the Centre of Mass (COM) reference frame so ...
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2
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741
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Can the equivalence principle be safely used in non-relativistic mechanics?
Imagine an ideal pendulum in a train. While the train is in uniform motion, Newton's laws apply within the train, and we can easily write down the equations of motion for the pendulum. Now assume the ...
- 9,304
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Is it the gravitational field created by an object which exerts force on another object or the interactions between their fields that exerts force?
We are taught that Gravitational force exerted by an object is a two-step process:
The object creates a field around it.
The field exerts a force on bodies present in the field.
Now, since we know ...
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1
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84
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Why does this volume integral vanish?
I am stuck on this problem concerning the gravitational potential of a body. The body has a mass density $\rho(\mathbf x)$ and I have to calculate a contribution to the total gravitational potential ...
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2
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582
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Expression for force of gravity on an arbitrary curve with endpoints fixed
Consider the following problem:
A frictionless tube lies in the vertical plane and is in the shape of a function that has its endpoints at the same height but is otherwise arbitrary. A chain with ...
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3
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140
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Perpetual motion: Conditions for rolling a wheel sliding on a bar [closed]
This is a basic question about energy conservation and classical mechanics:
Question: Under what situations can this motion be perpetual?
Without gravity and without frictions.
Without gravity and ...
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Is there an equation for the gravity of Earth that accounts for a comprehensive set of variables?
(e.g., longitude/latitude, elevation, and Earth’s mass and rotational speed)
I know a couple of approximations for the gravity due to Earth’s mass. The usual one I’ve been given is $g \approx 9.8 \, \...
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Why Copernicus frame can be considered to be inertial for planetary motion?
In the standard courses of classical mechanics inertial reference frame is defined as a frame with respect to which every free material point, i.e. not interacting with other bodies or fields, moves ...
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The potential energy of universal gravitation with dynamic mass
Everyone knows that the potential energy is generally represented by -GMm/r.
Now, consider the M will decrease or increase depending on time or the m's position (we can think m moves in v). What will ...
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Angular momentum and star system in space with four spatial dimensions
I came across a YouTube Video by minutephysics, a YouTuber with a Ph.D. degree in physics. In this video, he explains that the solar system is approximately flat because of two reasons:
1) ...
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Path of an object in gravitational field [duplicate]
How do you prove that path of a satellite or a planet is a second degree curve? In other words, how do you prove Kepler's law which states that planets move in elliptical paths?
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240
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Toppling over of a body
Why does a body topple over only when the perpendicular from its centre of gravity does not pass through its base?
I had read a paragraph on it from a book by Y. Perelman. I did find a half-...
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65
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Does the Laplacian of any scalar gravitational field vanish outside the source?
Besides the common spherical symmetric gravitational field, there are 2 classical examples: infinite plane and infinite wire.
For spherical symmetrical and infinite plane, the Laplacian of the field ...
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68
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Confusing about orbital speed [closed]
The Earth's distance from the Sun varies from $\ R_p=\ $ 1.471x$\ 10^8\ $km to $\ R_a=\ $ 1.521x$\ 10^8\ $km during the year. Determine the difference in the Earth-Sun system kinetic energy.
I have ...
- 3
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85
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Are the models describing the classical gravitational and electric fields mathematically equivalent?
In other words if I have a static point mass and a static point charge, we model them as having a scalar potential field surrounding them: $$V(r)\propto\frac{1}{r}$$ and their vector fields are ...
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2k
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Why does Friction act Parallel to the Surface (Microscopic Level)?
If we assume an object (blue layer) sliding towards the right across a surface (black layer). According to Newton's 3rd Law, the frictional force would act to the left (resisting the object's relative ...
user226894
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1k
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Why is it that forces like gravity and electricity (approximately) basically act between pairs of bodies only?
In classical mechanics, with the limit of little movement (so no relativity, waves, and/or "magnetic" effects), we can see that gravitation and electricity can both be described as "two-body" forces, ...
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90
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Reference Frame conceptual confusion
I am getting confused as to why a ball still feels gravity when inside a moving car. The point of a reference frame is to reinterpret all the forces acting on a particle in one frame only. Hence all ...
