All Questions
Tagged with orbital-motion classical-mechanics
172
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Which of Kepler's laws would remain true if the force of gravity were proportional to the product of squares of each masses?
I was asked this question recently on which of the Kepler's Three law would remain if we changed the force of gravitation to be proportional to the product of squares of each masses instead of just ...
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Elevation angle of LEO satellite as a function of time
Let a point on Earth be denoted with (lon,lat,altitude).
Let a LEO satellite be defined by its altitude and inclination.
I would like to compute the angular speed and elevation as a function of time.
...
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Approximation of Nearly Circular Orbit by a Precessing Ellipse
I am self-studying the 3rd edition of Goldstein's Classical Mechanics and have hit a roadblock when working a problem (Chapter 3, Problem 20). The problem asks us to consider a planet of mass $m$ ...
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Physics of paintings created by the orbit of swinging buckets filled with paint
I am intrigued about the physics behind these paintings, which are created by swinging a bucket with a hole filled with paint from a rope (here it is another example).
In principle, it seems to be a ...
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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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On the proof of the Bertrand theorem
I was following the proof of the Bertrand theorem on Wikipedia, which is based on Goldstein "Classical mechanics" (2nd edition).
The explanation was clear upto Eq (3). But then it assumes ...
- 145
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53
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Motion around stable circular orbit
Hello I am to solve whether it is possible for body of mass $m$ to move around stable circular orbit in potentials: ${V_{1} = \large\frac{-|\kappa|}{r^5}}$ and ${V_{2} = \large\frac{-|\kappa|}{r^{\...
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Understanding effective potential gravity
Let's imagine that we have a planet orbiting a star, far away from any other influence. The gravitational potential energy is then given by the following graph, where $E = T + V$:
Since $F = -dV/dr$, ...
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Meaning of a Constant in the Unbound Orbit Equation
The solution to the radial equation for two celestial bodies with eccentricity $\varepsilon$ greater than 1 can be expressed as
$$
\frac{(x-\delta)^2}{\alpha^2} - \frac{y^2}{\beta^2}=1,
$$
where
\...
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HW: particle subject to central force with exponential logarithmic orbit
I've been working on this exercise for some time now and although I've almost got it I can't seem to make it to the end of it. Here is the exercise:
A particle subject to a central force is orbiting ...
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Why is there a *minimum* energy for a particle to be captured in a $r^{-3}$ potential?
I was stuck in a central force problem from David Morin's Book "Introduction to Classical Mechanics".
The problem states that suppose there is a particle of mass $m$ moving under the ...
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Reading on weighing scales at the equator of a moon in a tidally locked two-body system
I'm trying a made-up extension of this problem. Consider the planet Mars and its moon Deimos, which can be approximated as meeting the following simplifying conditions:
Both objects are perfect ...
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Deriving the Equation of a Light Body orbiting a Heavy Body
If a light body orbits a heavy body, the orbit of the light body in classical mechanics is given by:
$$ \frac{d^2}{d \phi^2} \bigg( \frac{1}{r(\phi)} \bigg) + \frac{1}{r( \phi) } = \frac{GM}{h^2} \ ...
- 1,410
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Why is the path parabolic in a central force field if the energy is zero?
In Section 15 of Landau and Lifshitz Classical Mechanics, they discuss the path of a particle under a central field. They show that the path is a conic with a focus at the origin. When the energy of ...
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What happens at the minimal distance in unbound central-force orbits?
The rate of change of the radius of an object subject to a central potential U(r) is given by
$$\dot{r}=\pm \sqrt{E-V_{eff}(r)}$$
where $V_{eff}$ is the effective potential. An unbound orbit is ...
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