Questions tagged [orbital-motion]
The path a body takes while moving through space under the influence of the gravitational forces of other bodies
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Why doesn't the Moon fall onto the Earth?
Why doesn't the Moon fall onto the Earth? For that matter, why doesn't anything rotating a larger body ever fall onto the larger body?
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Why do we say that the Earth moves around the Sun?
In history we are taught that the Catholic Church was wrong, because the Sun does not move around the Earth, instead the Earth moves around the Sun.
But then in physics we learn that movement is ...
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Why are our planets in the solar system all on the same disc/plane/layer? [duplicate]
I always see pictures of the solar system where our sun is in the middle and the planets surround the sun. All these planets move on orbits on the same layer. Why?
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Why do all the planets of the solar system orbit in roughly the same 2D plane?
Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that the ...
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Why don't planets have Circular orbits?
This might be a completely wrong question, but this is bothering me since many days ago. Given the mass (Sun) curves the space around it, gravitation is the result of such curved space (Correct me if ...
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Are tidal power plants slowing down Earth's rotation?
Are tidal power plants slowing down Earth's rotation to the speed of the orbiting moon? (1 rotation per 28 cca days)
Are they vice versa increasing the speed of moon orbiting by generating some ...
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Kepler problem in time: how do two gravitationally attracted particles move? [duplicate]
Two particles with initial positions and velocities $r_1,v_1$ and $r_2,v_2$ are interacting by the inverse square law (with G=1), so that
$$ {d^2r_1\over dt^2} = - { m_2(r_1-r_2)\over |r_1-r_2|^3} $$
...
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Where does the extra kinetic energy come from in a gravitational slingshot?
I read in this answer in this site that the KE a free-falling ball acquires is not originated by the attracting body but that energy was actually stored in the ball when it had been lifted to the ...
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Radial fall in a Newtonian gravitational field [duplicate]
Suppose an object of mass $m$ starts at rest at a radial distance $ r_0$ from a perfectly spherical mass $M$ (where $m << M$), $r_0 > R =$ radius of $M$.
Can we analytically determine when ...
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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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Derivation of Kepler's laws
How can analytically be derived the Kepler's laws?
I found some extremely synthetic equations which from the Newton's laws (in particular $\mathbf{F} = m \mathbf{a}$) tried to obtain the Kepler's ...
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How does Newtonian mechanics explain why orbiting objects do not fall to the object they are orbiting?
The force of gravity is constantly being applied to an orbiting object. And therefore the object is constantly accelerating. Why doesn't gravity eventually "win" over the object's momentum, like a ...
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Why does the Moon drift away from Earth?
I once saw on TV that the Moon is slowly drifting away from the Earth, something like an inch a year. In relation to that the day on Earth what also increase in time.
I wonder why is that?
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What did general relativity clarify about Mercury?
I frequently hear that Kepler, using his equations of orbital motion, could predict the orbits of all the planets to a high degree of accuracy -- except Mercury. I've heard that mercury's motion ...
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Significance of the second focus in elliptical orbits
1.In classical mechanics, using Newton's laws, the ellipticity of orbits is derived. It is also said that the center of mass is at one of the foci.
2.Each body will orbit the center of the mass of ...
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What are common methods for calculating the time dependency of elliptical orbit?
After playing a game called "Kerbal Space Program" I got interested in orbital mechanics and started messing with simplified calculations to determine $\Delta v$ requirements. In which I compared two ...
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Where does tidal energy come from?
Kind of an odd, random question that popped into my head. Tidal energy - earth's ocean movement, volcanism on some of Jupiter's moons, etc. - obviously comes from the gravitational interaction between ...
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Why are orbits elliptical? [duplicate]
Almost all of the orbits of planets and other celestial bodies are elliptical, not circular.
Is this due to gravitational pull by other nearby massive bodies?
If this was the case a two body system ...
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What causes matter to initially rotate/spin/orbit?
What causes matter to initially rotate/spin/orbit? All I can find is the statement that in space particles of dust/gas/matter contract into a spinning disk due to gravity (to form stars, solar systems,...
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Why doesn't dark matter affect planetary motion?
If the universe is made up of ~95% dark matter, and it interacts only gravitationally then why didn't Newton and Kepler discover it before ? Why does it show itself only in the radial velocity profile ...
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How to calculate eccentricity of a planet via energy?
The relative distance of a planet moving around the sun is found to be:
$$r(\varphi) = \dfrac{\kappa}{1+\varepsilon\,\cos(\varphi)} \quad \text{where} \quad \kappa = \dfrac{L^2}{G\,{m_p}^2\,m_s} \quad ...
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Are planets actually moving in elliptical orbits around the Sun or do they move in circular orbits around their center of mass?
In every derivation of Kepler's Laws that I have seen, we assume that the sun is stationary. However, in other places I have read that celestial bodies move about their barycentre (center of mass).
So ...
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Elliptical Trajectory, or Parabolic?
Discuss whether this statement is correct: “In the absence
of air resistance, the trajectory of a projectile thrown near the
earth’s surface is an ellipse, not a parabola.”
Is the above statement ...
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What is the simplest way to prove that Earth orbits the Sun?
Assume you're talking to someone ignorant of the basic facts of astronomy.
How would you prove to them that Earth orbits the Sun? Similarly, how would you prove to them that the Moon orbits Earth?
tQuarella
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Using 2D position, velocity, and mass to determine the parametric position equations for an orbiting body
I have a gravity-related question. I am programming an orbit simulator. I have everything up and running, but I would like to render the smaller body's orbital path (the larger body is fixed). To do ...
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Is Earth's orbit altered by recoil from take-off/launch/recovery of aero/space vehicles?
Just what the title states.
Pretty much all movement on Earth is by pushing against the much greater mass of Earth. Given there are easily thousands of aircraft taking flight/landing, and a lesser ...
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How do you calculate the anomalous precession of Mercury?
One of the three classic tests of general relativity is the calculation of the precession of the perihelion of Mercury's orbit.
This precession rate had been precisely measured using data collected ...
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Gravity in other than 3 spatial dimensions and stable orbits
I have heard from here that stable orbits (ones that require a large amount of force to push it significantly out of it's elliptical path) can only exist in a three spatial dimensions because gravity ...
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How will the super massive black hole affect our galaxy?
I've recently learned that the general consensus is that several (if not, most) galaxies have super massive black holes in their center, in particular the Milky Way. This, at least to me, makes ...
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Why does reduced mass help when talking about two body problems?
I hear people say that reduced mass, $\mu$, is used for two body problems, but what sort of problems? Is it so that the two body system can be treated as one body or is it to simplify calculations ...
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Might a planet perform figure-8 orbits around two stars?
Might a planet perform figure-8 orbits around two stars?
I'm thinking that if the two stars were equal mass (and not orbiting each other) then a planet that were to go right between them would ...
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How is the equation of motion on an ellipse derived?
I would like to show that a particle orbiting another will follow the trajectory
\begin{equation}
r = \frac{a(1-e^2)}{1 + e \cos(\theta)}.
\end{equation}
I would like to do this with minimal ...
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Why is the center-of-mass of 2 bodies at the focus of their elliptical orbits?
Why is the center-of-mass of 2 bodies (which interact only via Newtonian gravity) located at a focus of each of the elliptical orbits?
I know that when there are no external forces, the center of ...
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Why is Larry Niven's Ringworld Unstable?
In his 1970 science fiction novel Ringworld, author Larry Niven describes the eponymous Ringworld, a gigantic structure shaped as a ring with a radius of around 1 AU, rotating around a star in the ...
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Proving Kepler's 1st Law without differential equations
Is there a way to show that the motion of Earth around the Sun is elliptical (Kepler's 1st law) from Newton's laws without resorting to the use of differential equations of motion?
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Are there actually any photons in orbit in the photon sphere of a black hole?
My intuition says 'no'. I know from my knowledge of spaceflight that every orbit includes the point at which delta-v was last spent; you can't use only a cannon on the ground to put something into a ...
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Proof for elliptical orbits
Its mentioned in several books that a satellite launched with a velocity less than the escape velocity and other than the critical velocity will follow an elliptical orbit. However I can't find a ...
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How strong of a gravitational field do you need for a projectile to make a full loop?
How strong of a gravitational field do you need for a projectile to make a full loop? By full loop I mean it curves once around the by dot, and then it ends up on the same trajectory as it was one ...
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Uniform Circular Motion
Why does the object not go inward, into the circle if the acceleration is inward? I think its because the velocity to outward? So they sort of cancel each other out? But if the speed is kept constant ...
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What is the resulting orbit of objects launched from the ISS?
Two identical masses are launched from ISS at 10 meters per second, one towards the earth and one away. Since their orbital velocity vector has changed by the same magnitude would they have the same ...
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Projectile/orbital motion over very long distance
We know the optimum angle for greatest horizontal displacement when launching an object with projectile motion is 45 degrees.
How to solve the angle when it is real long distance around the earth ...
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What's is the origin of Orbital Angular Momentum of electrons in atoms?
Consider the Hydrogen 1s electron. We know that, in the quantum picture, the electron isn't orbiting or rotating at all, rather we simply state that the electron is spread over the entire space with ...
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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 \...
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What happens to orbits at small radii in general relativity?
I know that (most) elliptic orbits precess due to the math of general relativity, like this:
source: http://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity
I also know that something is ...
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Which mass distributions guarantee two bodies have non-Keplerian orbits? Which non-spherical distributions still allow noncircular Keplerian orbits?
The trajectories of two point masses or spherically symmetric masses with respect to their center of mass are conic sections or Kepler orbits.
Consider that the bodies have finite size with respect to ...
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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 ...
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Why are the Lagrangian points $L_1$, $L_2$ & $L_3$ unstable?
Why are the Lagrangian points $L_1$, $L_2$ & $L_3$ unstable? I am doing a physics presentation in front of my class and I am just confirming this is correct, and if it isn't, could somebody ...
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Gravity on the International Space Station - General Relativity perspective
My question is an extension to this one: Gravity on the International Space Station.
If all the outside views of the ISS was sealed, then the crew inside would not be able to tell whether they were ...
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What's the reason for the seasons?
In the diagram, it shows that the fundamental reason for different seasons is when the northern hemisphere is titled towards the sun there's summer in northern hemisphere and winter in southern ...
user102321
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Table of matrix elements of powers of $r$ for radial functions in $H$ atom
Im looking for some references here. I hope it is the right place to ask.
I need to find a table of (or a formula from which to extrapolate) the matrix elements of the radial functions of the hydrogen ...