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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69
votes
9answers
179k views

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?
52
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15answers
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 ...
49
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2answers
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?
19
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4answers
3k views

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 ...
36
votes
6answers
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 ...
23
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3answers
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 ...
6
votes
1answer
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 ...
7
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1answer
2k views

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 $$ {d^2r_1\over dt^2} = - { m_2(r_1-r_2)\over |r_1-r_2|^3} $$ ...
78
votes
4answers
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 ...
45
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4answers
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 ...
11
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3answers
5k views

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 ...
16
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1answer
1k views

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 ...
44
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6answers
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 ...
21
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3answers
4k views

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 ...
12
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3answers
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 ...
24
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9answers
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 ...
31
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5answers
5k views

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 ...
16
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7answers
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?
6
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4answers
3k views

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,...
29
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4answers
8k views

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 ...
14
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4answers
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 ...
11
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2answers
964 views

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 ...
4
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1answer
2k views

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 ...
2
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3answers
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 ...
6
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3answers
1k views

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 ...
4
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2answers
3k views

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 ...
33
votes
3answers
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 ...
7
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3answers
5k views

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 ...
4
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4answers
2k views

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 ...
19
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3answers
7k views

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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2answers
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 ...
4
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2answers
1k views

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 ...
2
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4answers
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 ...
11
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1answer
6k views

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?
14
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4answers
16k views

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?
14
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4answers
8k views

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 ...
25
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6answers
11k views

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 ...
19
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2answers
11k views

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 ...
35
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6answers
13k views

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)?
6
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1answer
5k views

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 ...
18
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4answers
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 ...
12
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2answers
2k views

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 ...
6
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2answers
4k views

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 ...
2
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2answers
4k views

Semi-major axis and ellipticity of a binary system?

In the image below (source at bottom), it seems to be suggesting that \begin{equation} a = a_{1} + a_{2}, \hspace{8cm}(1) \end{equation} where $a_{1}$ and $a_{2}$ are the semi-major axis of the ...
6
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7answers
27k views

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 ...
5
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2answers
8k views

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 ...
1
vote
1answer
8k views

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,...
37
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7answers
9k views

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 ...
45
votes
5answers
26k views

Is it possible to have a geostationary satellite over the poles?

My understanding of orbital mechanics is very limited, but as I understand geostationary satellite, they stay in place by having an orbital speed corresponding to the spot they're orbiting over. So ...
22
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3answers
9k views

Why are Saturn's rings so thin?

Take a look at this picture (from APOD https://apod.nasa.gov/apod/ap110308.html): I presume that rocks within rings smash each other. Below the picture there is a note which says that Saturn's rings ...

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