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 ...
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3
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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 ...
- 213k
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0
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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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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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5
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Regarding the objects in free fall in the ISS
There are lots of information about this topic, but I'm still greatly confused about something:
Astronauts in the ISS are in free fall all the time because they have only gravity acting on them, but ...
- 998
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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 ...
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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 ...
- 109k
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Energy in central force orbit
Given a mass $m$ moving under the central force
$$F(r) = -\frac{k}{r^n}$$
and a circular orbit passing through the force center, I want to show $n$ must equal $5$. I ultimately arrive at the ...
CommunityBot
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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 ...
- 446
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Expression for components of gravitational force in spherical polar coordinates
How do one find the gravitational force components of the earth of a satellite moving around the planet in spherical polar coordinates. Since gravitational always towards the centre does it meant that ...
- 12.9k
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3
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Since the Earth orbits the Galaxy, why doesn't it "fly away" from astronauts?
It is known that the Sun (and thereby all the planets in our Solar System) orbit the center of our galaxy at roughly 1 million miles per hour. From our point of view on Earth, everything looks ...
CommunityBot
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4
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1
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Book recommendation for classical Newtonian gravity
I’m looking for a good textbook that covers Newtonian Gravity in detail (preferably advanced undergrad/grad level). One that covers important things like
Calculating trajectories of satellites around ...
CommunityBot
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1
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Calculating specific orbital energy, semi-major axis, and orbital period of an orbiting body
Is it possible to calculate the specific orbital energy $ϵ$, the semi-major axis $a$, and the orbital period $T$ (or $P$) without any of them being available to you? The values I do have available to ...
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Potential Energy for Non-conservative Forces
I was studying for the GRE and came across the problem below.
A small puck of mass $M$ is attached to a massless string that drops through a hole in a platform, as shown in the diagram above. The ...
CommunityBot
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1
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Where did Paul Gerber go wrong in arriving at the same equation as Einstein in explaining the Mercury anomaly?
We know that Einstein admitted that Paul Gerber's 1898 formula explaining the anomaly of Mercury's perihelion was the same as his own. Reportedly Gerber had made a mistake somewhere, so - even though ...
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3
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What causes our Sun to oscillate around its mean Galactic orbit?
According to this answer on Astronomy.SE,
The Sun executes oscillations around its mean orbit in the Galaxy, periodically crossing the Galactic plane. I borrowed this illustration (not to scale!) ...
- 13k
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453
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How can I obtain the position of the Earth on the orbit for given date?
I would like to be able calculate (or at least download some time-series data of) the position of the Earth on it's orbit at given date. For my purposes, it would be sufficient to account for the ...
CommunityBot
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1
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317
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Derivation of the equation of a hyperbolic orbit from the conic section expression derived via the orbit equation
So I'm looking to derive the equation of a hyperbolic orbit from the general expression for a conic section $$r=\frac{l}{e\cos\theta+1}$$ that you get out of solving the orbit equation for an inverse-...
CommunityBot
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2
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178
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Does Newton's Theory with Retarded potentials give rise to the motion of perihelion of Planets
If we take into account the retarded potentials and the motion of the Sun(due to the planet), does Newton's Gravitational theory give rise to the motion of Perihelion of planets (qualitatively, not ...
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2
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186
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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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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 ...
- 213k
3
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1
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268
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Geodesic equations and Carter constant: how can I derive the right equations?
Introduction
Suppose the Hamilton-Jacobi equation:
$$\frac{\partial S}{\partial \lambda} + \frac{1}{2}g^{\mu\nu}\frac{\partial S}{\partial x^{\mu}}\frac{\partial S}{\partial x^{\nu}}= 0. \tag{1}$$
Now,...
CommunityBot
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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 ...
- 213k
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0
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41
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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 $ \...
- 213k
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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 ...
- 3,680
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959
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How do I use Kepler's Laws to propagate an orbit for a Two-Line Element (TLE) Set?
I need to propagate a large number of orbits (get a satellite's position at a certain time) from TLEs (two-line element sets) using Kepler's laws. Ordinarily I'd use a real propagator like SGP4/SDP4, ...
CommunityBot
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Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?
In the book of Classical Mechanics by Goldstein, at page 88, it is given that:
$$
\frac{d^{2} u}{d t^{2}}+u=-\frac{m}{l^{2}} \frac{d}{d u} V\left(\frac{1}{u}\right) .
$$
The preceding equation is such ...
CommunityBot
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1
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Deviations from purely circular orbit for an object in a Yukawa potential
I am struggling with the logic for completing the following problem.
The problem is part b of 3.19 in Goldstein's Classical Mechanics book.
A particle moves in a force field described by the Yukowa ...
CommunityBot
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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 ...
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2
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850
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Good sources to get velocity/position vectors for all planets and moons in the Solar System for building an orbital simulator?
I’m building an $N$-body simulator, and I have everything ready to begin simulating. But my issue is is that I have no idea how to get all the starting positions and velocities for the celestial ...
CommunityBot
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When a body completes one revolution around a circular path will its acceleration be 0?
When a body is moving in a circular motion the acceleration keeps changing, will it be zero when it comes back to the same point it started from(will the average acceleration be 0?)
CommunityBot
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Circular velocity vector on the surface of spherical potential (gravity)
So, I would like to integrate paths of particles on circular velocity on the surface of a sphere (due to some potential, i.e. gravity).
The problem is to fix the two angular velocities $\dot \theta $ ...
CommunityBot
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3
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No stable closed orbits for a Newtonian gravitational field in $d\neq 3$ spatial dimensions
We are supposed to show that orbits in 4D are not closed.
Therefore I derived a Lagrangian in hyperspherical coordinates
$$L=\frac{m}{2}(\dot{r}^2+\sin^2(\gamma)(\sin^2(\theta)r^2 \dot{\phi}^2+r^2 \...
- 213k
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3
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Is this definition of "escape velocity" correct? [duplicate]
According to Wikipedia:
In physics, escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body.
But, say, I have a spaceship in low ...
- 24.7k
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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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3
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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 ...
- 1,723
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6
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What symmetry causes the Runge-Lenz vector to be conserved?
Noether's theorem relates symmetries to conserved quantities. For a central potential $V \propto \frac{1}{r}$, the Laplace-Runge-Lenz vector is conserved. What is the symmetry associated with the ...
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How does the Earth's orbit change as the Sun decreases in mass?
When the sun transitions into it's red giant phase it's mass is said to decrease (An article I read quoted it to go down to 67% of its mass however the number is not important). Since the orbital ...
- 1,723
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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 ...
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7
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Understanding geosynchronous orbits in an otherwise empty universe
Suppose the universe was completely empty except for a rotating planet with a moon in geosynchronous orbit. How would it be possible to understand why the moon did not fall since there is nothing to ...
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2
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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 ...
- 213k
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3
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Motion of body in central field lies in a plane -- Lagrangian Formalism
Say we have a body in 3D space inside a central field $ V(r) $. We want to show, using Lagrangian mechanics and spherical coordinates, that the body will move in a plane, which is defined by the ...
- 437
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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:
...
- 213k
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4
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Are stable orbits within the event horizon of a black hole possible?
This paper https://arxiv.org/abs/1103.6140 theorizes that orbits inside the event horizon of a rotating or charged black hole are not only possible but actually stable enough to potentially support ...
- 12.9k
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6
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5k
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Would it be possible to reenter the atmosphere without a heat shield using a glider design? [closed]
Say my vehicle currently in orbit had large wings that would provide the necessary lift, would it be possible to bleed off the energy so slowly and gradually lose altitude that no heat shield would be ...
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3
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2k
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Relation between velocity and position vector in a central force
I am aware that the dot product of the position and velocity vector, $(\vec{r}\cdot\vec{v})$, in circular motion under a central force, $F(r)=-\frac{k}{r^2}$, is equal to zero as the two vectors are ...
- 12.9k
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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 ...
- 60.5k
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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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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 ...
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