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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Can someone please explain this paragraph on work from the Feynman lectures?

This is a portion from Feynman Lectures: ...............We have proved previously that the answer is zero for any path composed of a series of notches like those of Fig. 13–3, and also that we do the ...
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291 views

Circular motion problem - is this solution correct?

Recently in my physics class, my instructor introduced this problem, yet I have some doubts about how to answer the question, as I believe it is missing some information. I have thought about the ...
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What additional velocity must be imparted to an orbiting satellite so that it leaves the earth's gravitational pull?

Consider this problem from my physics workbook: A spaceship is launched into a circular orbit close to the earth's surface. What additional velocity must now be imparted to the spaceship to overcome ...
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108 views

Where does this formula come from? [closed]

I am doing revision for my module stellar & galactic astrophysics and have come upon this formula which I cannot seem to derive. Could someone please explain where it comes from? "For an ...
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85 views

Why isn't energy conservation equation sufficient to determine the motion?

The star of large mass $M$ is orbited by planets of masses $m_1$ and $m_2$. The energy conservation equation for this system is$$\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}-MG\left(\frac{m_1}{...
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25 views

Conservation of energy for a planet [duplicate]

I was reading Lectures by Feynman (which are soo good at any qualification!) and he talks about how energy of a particular planet in our solar system is constant at all times $ i.e, KE+PE= constant.$ ...
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How are the locations of solar system planets expressed in their orbits?

and where can I find the data about the locations of the solar system planets during their entire year? I would like to find the data on the orbits of solar system plantes. Also I would like to know ...
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Kepler problem: Time spent by a comet inside the orbit of the Earth [closed]

This is was an exercise on my exam of classical mechanics which I couldn't solve. The question goes as follows: Imagine a comet moving on a parabolic orbit in the plane of the earth. Take the earth's ...
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Cause of seasons

NB: I live in the northern hemisphere so when I say summer and winter I'm referring to ~July and ~January respectively. I've been reading online about the cause of the Earth's seasons and I'm still ...
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How to find position vector in Kepler orbit?

As the title says, I am trying to determine the position vector $r$, knowing true anomaly, semi-major axis, angular momentum and eccentricity vector. There is an equation describe the distance to the ...
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65 views

Gravitational collapse of a gas/dust cloud into a disk and subsequent evolution (minimizing energy?)

Assuming a relatively isolated cloud of dust and gas with a well-defined total mass and well-defined net angular momentum. Perhaps also assume that the size (or density) of the initial cloud is ...
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I don't understand why my graph of the variance of the Sun's true noon is so bumpy

I understand that the true noon, defined as the sun reaching its highest point in the sky, varies from the noon we have on our clocks. I understand the impact that the eliptic orbit has on the speed ...
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58 views

Calculating orbital path of a planet around a fixed body in a deterministic way given starting conditions

I am making a simulation of the solar system in the unity game engine. A planet is orbiting a stationary star for now using Newton's law of gravitation where $F = Gm_1m_2/r^2$ for the orbit (force is ...
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782 views

What are Lagrange points?

We were taught that Lagrange points are where the resultant gravitational intensity is zero. Does that mean the resultant gravitational attraction of an object kept there is zero? If that's the case ...
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Is a deforming force tension acting on the Moon while orbiting Earth?

As the Moon shows only one face to the Earth can this statement be correct:As a point mass closest to Earth should orbit Earth faster than the most distant point regarding Earth according to the Law ...
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176 views

What causes tangential velocity of a planet to change in an elliptical orbit?

I am confused about this concept of central force motion. We have read that object undergoing a change in velocity must possess acceleration. However, in elliptical orbit motion gravitational force is ...
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Precession of a closed orbit under a central force other than the inverse square force

Consider the motion of a closed orbit in a central force field ${\bf F}({\bf r})$ other than the inverse square force i.e., $${\bf F}({\bf r})\neq -\frac{k}{r^2}\hat{\bf r}.$$ However, since ${\bf F}({...
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Keplerian orbits are intersections of planes with the the future light-cone in Minkowski 4-space

Near the end of this essay, Baez comments: In 2011, Guowu Meng pointed out a remarkable fact to me. Orbits of the Kepler problem are precisely the intersections of 2-dimensional planes with this cone ...
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What happens with trash that is left after a satellite expires?

I was reading an article that Japan is experimenting with wooden chassis for satellites so that they can keep the trash minimal. I was wondering if it was possible to design the satellites in a way ...
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132 views

Elliptical orbits of planets

As we know, the velocity of the planet changes as it orbits around the sun, both in its magnitude and direction. The centripetal acceleration causes the change in the direction of velocity but I want ...
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1answer
42 views

Electron density in low orbit space

Assume a spacecraft orbiting earth in about 400km. Now you want to measure the free charge carriers there per volume unit, how would this be done? I have an idea, please comment on my reasoning: The ...
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Are orbiting masses in a uniform disc affected by masses outside its orbit?

For a sphere of uniform density, we know an orbiting mass experiences a net attraction only by the mass inside its orbit, and that the mass outside its orbit exerts a net zero force (using Newton's ...
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How to not change the shape of the orbit of a planet while increasing or decreasing the size(perimeter) of the orbit?

I want to know if I can fast forward planetary movement by putting a planet closer to its star so that the planet can move faster but the shape of its orbit remains the same?
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Does a non-rotating satellite always show the same side towards the main body?

If an initially non-rotating (zero angular momentum) satellite starts moving around a main body, such as the earth, will then the satellite continue to have zero rotation or will it show the same ...
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How does one calculate apsidial rotation after a spacecraft's radial burn?

I am researching orbital mechanics (for fun and knowledge) and I've come across a problem: How do I calculate the new orientation of the Apsis line (the major axis), periapsis, and apoapsis after a ...
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Is Sergei Krikalev living slightly in the future, or is his body just younger than it otherwise would have been? [closed]

Due to cosmonaut Sergei Krikalev's time on board space station Mir in Earth orbit, the combined effects of velocity and gravity have caused him to experience an accumulated 20 milliseconds of time ...
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Time period for Mercury

General Relativity predicts the orbit of Mercury to be not closed. Does time period of orbit lose it's meaning in general relativity? Does Mercury have a variable time period?
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Kepler's second law in General Relativity

Kepler's second law, that planets in orbits sweep equal area in equal time, is a consequence of orbital angular momentum conservation. In the case of Schwarzschild spacetime, the angular orbital ...
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Orbit of Celestial Bodies

To give some insight, I'm creating a simulation, with gravity, planets, forces... And I would like to increase performance, by not doing unnecessary calculations. I could know what calculations, to ...
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Going through Kepler's Orbit Derivation.. having a problem

I imagine this was a simple task for many of you during undergrad studies, but I am a lowly engineer attempting to derive Kepler's Law of Orbits. I've tried to do it as cleanly as possible. I've ...
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Relative speed of satellites in different orbits [closed]

The question is "The Hubble Space Telescope is in orbit around the Earth at a height of 560km above the Earth’s surface. Take the radius and mass of the Earth to be 6.4×10^ 6m and 6.0×10^24 kg, ...
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Bounded orbits in non-Keplerian central force laws

Bertrand's theorem famously states that for a central potential $V(r) = r^k$, all bounded orbits are closed if and only if $k = 2$ (harmonic oscillator) or $k = -1$ (Kepler problem). I am curious ...
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How does a satellite maintain circular orbit?

Given a crewed satellite placed at a distance $r$ from the center of the Earth, with an initial velocity perpendicular to its position vector, the magnitude of the initial velocity that would allow it ...
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Satellite potential energy zero? [closed]

Satellite is at a numerical distance to the earth so by $$-GMm/R$$ it must have a non-zero potential energy then how can it have zero potential energy?
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Does an angular acceleration applied to a large body affect any bodies orbiting it?

Imagine the Earth (large body) and a single satellite, let's exclude all other bodies for this example. The satellite is orbiting the Earth parallel to the equator and is maintaining a constant ...
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Solving for the mass of the larger star in a binary star system. (Larger star is much larger, so orbit is essentially circular)

I'm a teaching assistant for a class on Newtonian mechanics, and was confronted with a way of solving for the larger mass in this two-star system that gets the right symbolic solution, but seems to ...
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Power in uniform circular motion

Say you have a rocket ship in a vacuum away from all gravitational fields firing its engines to maintain uniform circular motion. Since the engines are burning fuel, it seems to make sense to ...
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What is the Kepler problem, position as a function of time, or radius as a function of angle?

From wiki's Kepler Problem the solution is given as $r$ as a function of $\theta $. In R. Fitzpatrick's Kepler Problem we read "In a nutshell, the so-called Kepler problem consists of ...
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$N$-Body Solar System Simulator - Why are there inaccuracies in the $x$ plane but not the others? [closed]

I have written a basic $N$-Body simulator that simulates the motion of the planets in the solar system. The system reads the positions and velocities of the planets at a given time, measures the time ...
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How does the orbital motion of reduced mass tell us how the individual planets/stars move?

To give context to my question, here is Kepler's first Law restated in terms of reduced mass. Here, $\vec{r}$ is the position vector of the reduced mass whose origin lies at the centre of mass of the ...
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What are the physical attributes of a system containing a group objects bound together by gravity?

I'm looking to program a simple simulation of a multi-body planetary system. However I don't know where to start in terms of the basic components of such simulation. For example I know that these ...
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169 views

How to know when a body completes an orbit?

I'm simulating a solar system, and I would like to know when a body, has completed an orbit around another. Is there any specific formula for it? As shown in the picture, the orbit is elliptical, ...
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Possible moon orbits about a torus world (donut or ringworld)

Thinking about the "objects falling in a mineshaft through the earth" scenario, this doesn't work in general terms as coriolis effects would require a figure 8 orbit , (else the objects ...
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Kinetic energy at perihelion [closed]

How do you find the kinetic energy of an object (in orbit around the sun) at perihelion given it's eccentricity, the mass of the object and it's period?
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Magnetic moment produced by a charge in translatory motion (with no orbital motion)

A moving charge produces a magnetic field, while its magnetic moment is given by $$\mu = -g\frac{q}{2m}\textbf{L}$$ where, $g$ = gyromagnetic ratio, $q$ = charge, $m$ = mass, L = orbital angular ...
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443 views

Can the Sun orbit the Earth?

You know how the earth orbits the sun because of gravity?...well if the sun were the right distance from the earth and it had the perfect tangential velocity...could it orbit the earth? In other words....
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Elliptical orbits: Where have I made a mistake? [closed]

Sorry for not using latex, I am new. Assuming conservation of angular momentum and mechanical energy in an elliptical orbit, the sum of velocities at any two arbitrary points in orbit is constant? I ...
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First Law of Motion, Gravitational acceleration and Law of Conservation of Energy [duplicate]

When an object leaves a celestial body (e.g. planet or star) with it's escape velocity, according to first law of motion, it will continue travel away from the body with the same speed (without having ...
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Crystal electric field effects on spin-orbit coupling

Can someone highlight in general the correlation between crystal-electric-field, spin-orbit coupling in case of 3d7 ions under tetrahedral crystal field environment and their mutual effects on ...
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57 views

How to transform coordinates from heliocentric to a view from earth?

I'm trying to find and model the apparent motion of the retrograde motion of Mars as viewed on Earth, incorporating Lagrangian or Hamiltonian mechanics. For the lagrangian I have: $L = \frac{1}{2}m_{...

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