# 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?
16k views

### 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 ...
4k views

### 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 ...
87k views

### 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 ...
8k views

### 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 ...
2k views

### 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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### 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 $${d^2r_1\over dt^2} = - { m_2(r_1-r_2)\over |r_1-r_2|^3}$$ ...
12k views

### 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 ...
78k views

### 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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### 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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### 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 ...
11k views

### 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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### 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 ...
7k views

### 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 ...
26k views

### 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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### 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 ...
24k views

### 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?
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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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### 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 ...
12k views

### 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 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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### 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 ...
8k views

### 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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### 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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### 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 ...
16k views

### 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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### 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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### 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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### 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 ...
170 views

### 3PN and higher order post-Newtonian Schwarzschild approximation

This expression can be found in documentation from the JPL determining the relativistic acceleration under Schwarzschild conditions in the euclidean approximation they use to calculate the orbits of ...
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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 ...
800 views

### 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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### Proving Kepler's 1st Law without differential equations

Is there a way to show that 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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### What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum. I was wondering, though: why did he quantise angular momentum instead of some other quantity?
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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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### Why are the orbits of planets in the Solar System nearly circular?

Except for Mercury, the planets in the Solar System have very small eccentricities. Is this property special to the Solar System? Wikipedia states: Most exoplanets with orbital periods of 20 days ...
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### Does everything orbit around some universal “center of mass”?

I have read many questions about the center of the Universe. I even have some favorite ones. I understand the fact that every point in the universe experiences expansion of space the same way. Also ...
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### Could there be a star orbiting around a planet?

I wonder if there ever could be a star (really small) which may orbit around a planet (really big)?
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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 $$r = \frac{a(1-e^2)}{1 + e \cos(\theta)}.$$ I would like to do this with minimal ...
22k views

### Why are some galaxies flat?

What is the explanation for the flatness of some galaxies? (If it's due to their rotation then why they are rotating, why some other galaxies are not flat etc., I would like to hear a nice and ...
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### Conservative central force and stable orbits

I saw a question a few days ago which referred to Bertrand's theorem. So, I now know that stable, closed orbits only occur when the potential function is $\frac{-k}{r}$ or $\tfrac{1}{2}kr^2$. If ...
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### How to calculate a ballistic trajectory for a suborbital flight?

I'm trying to calculate the initial launch angles and velocity of a projectile (atmosphere's effects can be neglected), assuming that I know the lat/lon coordinates of both the launch and the ...
4k views

### Semi-major axis and ellipticity of a binary system?

In the image below (source at bottom), it seems to be suggesting that $$a = a_{1} + a_{2}, \hspace{8cm}(1)$$ where $a_{1}$ and $a_{2}$ are the semi-major axis of the ...
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### Work in circular motions

Suppose that a satellite circles around a planet that exerts $2000N$ of gravitational force on the satellite. I understand the fact that since the circular motion and the centripetal force are ...
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### Velocity of an satellite in an elliptical orbit

Consider some some satellite of mass $m$ around earth, traveling in an elliptical orbit about a focus (earth). Let's suppose at one point $A$ the satellite is a distance $a$ units away the focus at ...
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### What is the relationship between mass, speed and distance of a planet orbiting the sun?

After reading this fascinating story about a new exoplanet, I was wondering about how mass, speed and distance determine a circular orbit of a planet around a star. Given the mass of the sun and star,...
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### Why don't we feel the subtle speed change of Earth's elliptical orbit?

Earth's orbit is a slight ellipse, so to conserve momentum its speed increases when it is closest to the Sun. If the speed changes there is an acceleration. If there is an acceleration there is a ...