All Questions
2,678 questions
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Gravitation satellite orbiting earth
In circular orbit as angular momentum is conserved so we can write $v$ is inversely proportional to $r$ but by equating gravitational force and centripetal force we get that v is inversely ...
2
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0
answers
73
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Condition on conserved quantities to escape Kerr black hole
For a classical two-body gravitational system, we can easily check whether the trajectory is bounded by calculating the energy. If the energy is larger than a threshold $E > E_0$ (and if they are ...
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3
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81
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What is the difference between Innermost Bound Circular Orbit (IBCO), Innermost Bound Spherical Orbit (IBSO), and Sphere Radius?
⚠ My question is related to Schwartzchild and Kerr Blackholes.
In a few words:
Innermost Bound Circular Orbit (IBCO):
It is the constant radius at which this circular orbit occurs at 1.5 Schwarzchild ...
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0
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29
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Does the trajectory of a body in a central-force field leave the force undetermined if I don't specify the number of bodies interacting?
Suppose I have a body orbiting in a (unstable, as shown by the effective potential of the system) circular orbit around another one in accordance to a inverse law of the form $$-kmm_1\frac{1}{r^4}$$
...
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1
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What is the base of defining eccentricity like this?
In an Introduction to Modern Astrophysics, the author first derived the Laplace-Runge-Lenz vector, and then used the vector to derive the equation of orbit ($\mu$ is reduced mass, $\mu = \frac{m_1m_2}{...
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2
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117
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Why does not the Moon get faster? [duplicate]
I've learned that an object has an equivalent acceleration motion due to gravity in a vertical direction in parabolic motion. And the moon is also an example of parabolic motion, right? As Isaac ...
- 19
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2
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How does larger change in KE lead to Oberth effect (or is it something else)?
(I know, there are similar questions here already, but not identical, and I haven't found a satisfying answer on any of them yet. If you do find one, let me know)
In short, I still don't get how the ...
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Finding the complete Keplerian orbit from position and velocity
Question's aim summary: finding 5 points on any Keplerian orbit so I can use the "Five points define a conic" method to get the complete conic. I already solved this for the case of an ...
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1
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How much force is needed to keep a 1000kg satellite at LEO in a geostationary position? [closed]
There are many advantages to keeping communication satellites at LEO, but in order to maintain communications 24/7, you either need a swarm of satellites or multiple ground stations.
Assuming it is ...
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Does the Earth’s Geoelectric field affect its orbit around the Sun?
https://en.wikipedia.org/wiki/Atmospheric_electricity
https://www.sciencedirect.com/topics/earth-and-planetary-sciences/geoelectric-field
Is the interaction between the electric field of the Sun and ...
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What is the $ \theta' $ means in Kepler problem in Goldstein's Classical Mechanics?
In Goldstein's Classical Mechanics, 3 edition, equation 3.50 is
\begin{align*}
\theta=\theta^{\prime}-\int\frac{du}{\sqrt{\frac{2mE}{l^2}+\frac{2mku}{l^2}-u^2}}\tag{3.50}
\end{align*}
I think $ \...
- 79
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1
answer
47
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Relation between speed of satellite and radius/orbit
I don't understand how increasing the velocity will lead to increase in the radius at which a satellite orbits. Shouldn't radius decrease i.e satelite should orbit closer to the earth as the velocity ...
-5
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1
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108
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Is the perihelion precession formula of general relativity dimensionless? \[ \dot{\omega} =\frac{6 \pi G M}{c^2 a (1 - e^2)} \] [closed]
WHere:
G is the gravitational constant
M is the solar mass
c is the speed of light in vacuum
a the Mercury's semi-major axis
e the eccentricity of Mercury's orbit
I have tried several times but from ...
3
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3
answers
325
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Total energy of a planet in orbit
Consider a planet in orbit. It has some kinetic energy and some gravitational potential energy. Now my question is, how much energy must we supply to move this planet's orbit to infinity? So by ...
2
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1
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223
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Does the orbital plane that contains the trajectories of 2 bodies pass through the center of mass of each of the bodies?
Two bodies that attract each other gravitationally will move in a conic trajectory with respect to the center of mass of both. A conic is the meeting of a cone and a plane thus it is always a plane ...
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1
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I'm trying to replicate Rømer's experiment but can't seem to get even close to the correct value for the speed of light
I am trying to replicate Rømer's experiment where he determined the speed of light by observing and measuring the eclipse timings of Io by Jupiter. I'm using Stellarium for this experiment and no ...
- 191
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2
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126
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Understanding Gregory's argument for the closed orbit condition in the one-body problem
Gregory (Classical Mechanics, 2006) gives the argument below for the condition for a closed orbit in the relatively general case of a spherically-symmetric central force on a particle, $f(r)$ (the &...
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22
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Central force motion happens in 2d instead of 3d (Lagrangian Formalism argument) [duplicate]
What is the argument purely from Lagrangian formalism (without using forces), that the Lagrangian of a mass in a central force would exhibit motion in 2 dimensions as opposed to 3 dimensions?
Details:
...
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How do you find how long an object will take to travel to a specific point in a planets sphere of influence?
So I haven't been able to find a solution to this:
Let's say there is an asteroid the will travel through Earth's SOI. We know the object's periapsis in Earth's SOI and its speed relative to Earth ...
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0
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43
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Lunar capture simulation
So I'm trying to simulate the Apollo 11 mission and I'm kinda stuck. I've set the origin of my coordinate system to be in Earth's center of mass and was able to complete a gravity turn to get into ...
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3
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Does General Relativity predict Mercury's orbital precession without other planets?
From Newtonian mechanics, the precession of Mercury can be calculated by taking into account the gravitational pull of other planets. From that, I assume that in the absence of external planets, ...
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A thought experiment regarding elliptical orbits
Say I'm in a circular orbit around the Earth. I give my motor a burn in the tangental direction. My understanding is that my trajectory now becomes an ellipse, and if I want to enter a new, higher ...
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3
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115
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What is the reason that the unstable Lagrange point $L_2$ is used for the JWST instead of the stable $L_4$ or $L_5$ points?
I understand how the Lagrange points work in the two-body problem. I can do that math. I understand that for L1, L2, or L3, if the object is perturbed to deviate away from that point, the ...
- 1,733
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38
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Does mass of comet change its orbit? [closed]
Consider a comet that is losing mass as it begins to orbit a planet. Does the mass of the comet affect its path? I have seen answers that say that the path will be affected. However, the change in ...
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1
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78
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Stability of extended rigid bodies around Lagrange-points $L_1$, $L_2$ and $L_3$
$L_1$, $L_2$ and $L_3$ are known unstable for point-like bodies, cf. e.g. this Phys.SE post. They assume for point-like objects, which might not cover all practical scenarios. For example, there are ...
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523
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Advanced Composite Solar Sail (ACS3) Orbit
According to NASA the ACS3 has an altitude roughly twice that of the ISS. But according to NASAs ACS3 tracker it is visible about every 1.5 hours, same as ISS. How can it have twice the altitude but ...
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2
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1
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339
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Issue with the roots of the Equation of Time
Regarding the famous derivation of the Equation of Time available here that i'm trying to rewrite a modern version with much more detailed steps:
http://info.ifpan.edu.pl/firststep/aw-works/fsII/mul/...
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2
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109
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Derivation of the Classical Lifetime of Hydrogen
In derivations of the classical lifetime of a hydrogen atom, the key assumption seems to be that the orbit is circular, allowing us to write
\begin{equation*}
\frac{mv^{2}}{r} = \frac{q^{2}}{4\pi \...
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2
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75
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Does the tangential velocity of an object, traveling in an elliptical path, always decrease while approaching the perihelion?
I know that the (magnitude of) the tangential velocity of a planet in an elliptical orbit decreases while approaching the aphelion and increases while approaching the perihelion because the ...
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50
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Validity of Bertrand's theorem for a self-interacting system
We know that in classical mechanics, a particle of mass $m$ orbiting in a given central-force potential $V$ will satisfy the following eom:
$$\frac{d(m\dot{r})}{dt}-mr\dot{\theta}^2+\frac{\partial V}{\...
- 1,992
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Showing Kepler's first law using the Triangulation method
Historically, Kepler came up with his first law using the triangulation method on Mars's orbit (here is a video of Terence Tao referencing the same: https://www.youtube.com/watch?v=7ne0GArfeMs&t=...
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5
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307
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It seems the statement "an object in orbit is in a permanent free fall around Earth" is wrong. Is my understanding correct?
Here is an excerpt from an Wikipedia article on low Earth orbit
However, an object in orbit is in a permanent free fall around Earth, because in orbit the gravitational force and the centrifugal ...
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2
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Does retarded Newtonian gravity predict apsidal precession and gravitational radiation?
This is a question that have troubled me for a while, beginning with the historical fact that the apsidal precession of Mercury as noted by Urbain Le Verrier was one of the motivating issues behind ...
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3
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Do all the planets orbiting a star lie in one plane? [duplicate]
If you look at our solar system and our galaxy, the stars and planets are generally all in one plane. So, are all galaxies in one plane? And why are they in one plane?
user424518
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2
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Can light become a satellite of a black hole?
In general, stars can have satellites orbiting around them.
Then, can a photon become a satellite of a black hole?
Once a photon enters the Schwarzschild radius, it cannot escape the black hole.
...
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33
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Kepler's measurements in solar system
I am interested in knowing that does Kepler measured distances in solar system or only relative distances to a astronomical unit which he doesn't know how long is it in our meters.
- 1,419
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Is there any way in which orbits emitting gravitational waves could avoid coalescence?
In the very far future, all orbits will eventually coalesce as they lose orbital energy through gravitational waves emission.
However, can there be 3-body or N-body interactions in which the members ...
- 2,878
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64
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GR: angular velocity in circular orbits
Starting with the Schwarzschild metric:
$$
A = 1-\frac{2m}{r}
$$
$$
\mathrm{d}\tau^2 = A\mathrm{d}t^2 - \mathrm{d}r^2/A -r^2\mathrm{d}\theta^2 - r^2\sin^2{\theta}\mathrm{d}\phi^2
$$
I want to ...
- 861
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46
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How to find velocity at apogee in Hohmann transfer?
How can you determine the velocity at the apogee in a Hohmann transfer, given the radii of the initial circular orbit $r_p$, and the velocity change $\Delta v$ for the transfer? If I'm not mistaken, ...
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3
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The Circular Orbital Velocity Relative to a Stationary Observer in Schwarzschild Geometry [closed]
Relative to a stationary observer (constantly accelerating to maintain a fixed radius) what would be the velocity measured of an object in circular orbit. I've tried using J B Hartle (9.47) and (9.48) ...
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1
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247
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How to calculate jerk in uniform circular motion?
We can calculate the centripetal acceleration in circular motion by the equation v^2/r. But how do we calculate the jerk (which is acceleration over time)?
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3
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Which type of trajectory would an object take in the below stated case?
What type of trajectory would an object take if it is suddenly stopped by some external force while revolving in a circular orbit around the sun?(Neglect the radius of the sun i.e radius of the ...
3
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1
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52
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Is any planets angular speed roughly constant?
The duration of a sidereal day stays pretty much constant on Earth as far as I know. But I was wondering if that is typical or even always the case. For example, can moons influence it? Or can ...
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Tilting due to Earth's rotation at a distance
I just stumbled upon a video on spacetime and a weird fact caught my attention.
In the video, it explained that a free falling body dropped onto the Earth would change its orientation and would be ...
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33
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Where does an eccentric 1:1 tidal-locked planet reach its maximum longitudinal libration?
I have been studying longitudinal libration for several days now, but have a question about where libration occurs in a planet's orbit.
For example, let us say that planet Alice has an eccentricity of ...
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2
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64
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When does electrostatic effect failed and needs quantum mechanics?
This is a question from 2022 AP physics 2 FRQ, I am not here to ask how to solve the question, but I am curious about the assumption made by this question. It says that electrostatic force is the ...
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Why particle is certain to escape the conservative field when the mechanical energy is positive?
It is generally said that the particle is bound into the conservative field when the mechanical energy is negative and zero is the limiting case and the particle will escape the field when the ...
- 608
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Can perfectly stable orbits exist in GR?
Defining "stable orbit" between two bodies as one where, in the absence of other bodies or non-gravitational forces, the distance stays between some value pair $r_{min}>0$ and $r_{max}$. ...
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544
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How accurate does the ISS's velocity and altitude need to be to maintain orbit?
We know the the ISS is not drifting weightless in space, but rather is constantly falling as it circles the Earth. To do this it must be at a specific altitude and moving with a specific velocity. ...
- 4,861
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2
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92
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What would happen to the moon's orbit if we reduce (instantaneously) its mass? [closed]
In my opinion the moon's orbit shouldn't change, because an orbiting body is a free falling object and the trajectory of a free falling object is not affected by its mass (because the inertial mass ...
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