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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1answer
1k views

Isn't the velocity in an orbit always tangential, not radial and tangential?

In this video the person resolves the momentum vector into two components, tangential and radial. But isn't the velocity at every point on the orbit tangential?
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Rotational mechanics $u$-substitution

In classical physics, when we try to get the force as a function of $r$; Why do we substitue $$r=\frac{1}{u}?$$ I don't get it, what is the point of it? Is the substitution arbitrary? I am looking ...
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What is the distance from the Earth where the centripetal force would equal the gravitational force?

I've been trying to find the length of an unbendable and unbreakable tether of zero mass extending off the surface of the Earth with a mass at its end, where the centripetal force would equal the ...
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1answer
65 views

Where does the energy from tidal power plants come from? [duplicate]

Tidal power plants taps into the energy in the motion of the oceans due to the gravitational interaction between the earth and the moon, so much is clear to me. This question is about where would this ...
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1answer
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How does the shape of a planetary body affect the orbit of its moon?

More specifically, would the distortion from a sphere of the planetary body lead to shifts in angular momentum for the moon.
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4answers
1k views

Reason for inertia of motion of Earth orbiting the Sun [duplicate]

We all know the following universal truth since childhood. Earth (and other planets) orbits around the Sun. And, while I was reading this post, I found that the reason behind Earth revolution is ...
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1answer
59 views

Orbits within orbits

Do galaxy clusters have structured orbits (e.g. ellipticals)? If not, why not? Moons orbit planets, planets orbit stars, and stars orbit galactic centres. Is there something different about the ...
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1answer
37 views

Can we ever calculate the exact period and semi-major axis for an orbit with strong perihelion precession?

To calculate the period of an orbit with strong perihelion precession we could just pick an arbitrary point in the sky, and time how long it takes for it to pass it again. But wouldn't we get ...
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1answer
43 views

Schwarschild Metric from Kepler law

Can we redrive Schwarschild metric from Kepler's law without assuming General Relativity?
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544 views

Work done to change circular orbit and orbital speed

If a satellite of mass $m$ is orbiting a planet of mass $M$ with radius $r_1$ and orbital speed $v_1$ and is brought to orbit at $r_2$ with speed $v_2$, its kinetic energy changes by a quantity $$ \...
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3answers
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What prevents galaxies from collapsing towards the galactic center? [duplicate]

Galaxies have supermassive black holes at their cores exerting huge gravitational field. What is the reason that galaxies don't contract towards the center? What prevents this from happening.
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Goldstein central force problem [closed]

I was reading Goldstein chapter 3 central force motion. I tried to do the exercise 21 on p. 130 of 3rd ed. but cant think of any way how to do it. any clue would be very helpful. Show that the ...
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1answer
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How did the Moon get into orbit?

It's the accepted theory that Moon was formed when an object collided with Earth, throwing off a lump of matter which became the Moon. But also, an object cannot be launched into orbit from a planet ...
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2answers
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How do astronomers explain trajectories of planets?

I'm wondering how astronomers can explain the trajectories of planets because: planets spin, so have angular kinetic energy. Thanks to the mass-energy relationship this means space-time curvature. ...
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2answers
88 views

How can the Hohmann transfer work?

When you want to move from a lower circular orbit to a higher one, one may decide to boost their velocity, which causes the satellite to require more centripetal force than gravity can provide and ...
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1answer
49 views

Confirmation / interpretation of unphysical(?) Kepler orbits

The following two pictures show the Kepler orbit of two masses $m_1, m_2$, where $m_1/m_2=7/3$, as I calculated them using $$ r(\varphi)=\frac{a(1-\varepsilon^2)}{1+\varepsilon\cos\varphi},\quad\...
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Centripetal Acceleration to find Orbital Velocity

When presented with a problem asking for the orbital velocity of an object $1,000 km$ above the Earth's surface, the formula I know you can use is $$v=\sqrt{\frac{G*m}{r}}$$ However, I was thinking ...
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Proof that, for any force law in Newtonian Mechanics, if a planet gets closer and then further from its star repeatedly, the orbit is bounded

I have run simulations of planetary motion using various force laws that are functions of distance $f(r)$, including but not limited to $$f(r)=\frac{1}{r^2}$$ $$f(r)=\sin(r)$$ $$f(r)=r!$$ $$f(r)=\...
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Why Euler-Lagrange Theorem gives the optimal control law? [closed]

Can anyone explain me in simple language why applying Euler-Lagrange Theorem on Hamiltonian equations gives the optimal control law? I am specifically talking about trajectory optimization problems ...
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1answer
391 views

How would the rotational and orbital mechanics differ on a torus-shaped planet as compared to a spherical planet?

I am making the attempt to develop some computational models of Star systems and I was wondering how the a torus shaped planet would compare to a traditional spherical planet in the context of ...
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Star orbit and dark matter [closed]

In a college entrance examination of my country, there was the following question: Suppose that, in a galaxy, the dark matter, which is evenly distributed, can be removed. Suppose also that in the ...
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4answers
162 views

How to find angle something turns as it orbits in orbital mechanics? [closed]

Short version: Take a look at this animation really quick. https://commons.wikimedia.org/wiki/File:Orbital_motion.gif The direction in which the arrows for $\alpha$ and $\nu$ is adjusted as the ...
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1answer
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Kepler's Second Law: Why do we calculate the area of a triangle rather than the area of a sector?

Kepler's Second Law states that equal areas are swept in equal times. When calculating this area, why do we use the formula for the area of a triangle rather than the area of a sector?
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1answer
86 views

Is a complex Keplerian eccentricity $e=\sqrt{1+\frac{2\varepsilon h^2}{\mu^2}}$ possible?

Wikipedia provides the following formula for the Keplerian orbital eccentricity: $$e=\sqrt{1+\frac{2\varepsilon h^2}{\mu^2}}$$ Considering that a bound object means negative energy, if the magnitude ...
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1answer
45 views

Speed of a body in orbital motion [closed]

I assume I'm making a silly error somewhere but I can't see how. The question is concerning two objects $M$ and $m$ orbiting each other at a distance of $r$ apart. The first part was simply finding ...
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Is there a chance for moon to collide with earth?

I have learned that attraction between the bodies increases when it's mass increases ,if the population increases day by day and hence it can increase the mass of earth which causes attraction ...
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1answer
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What would be the shape of a space elevator?

I have never seen a discussion of the shape of a space elevator (as viewed from above the North Pole, let us say). Would it be straight or curved? I have included a diagram of several potential ...
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1answer
103 views

Equation of motion from potential energy [closed]

Given that the potential energy of a particle in 2D space is $$V(x, y) = \frac{1}{2}k(x^2 + y^2),$$ find the equations of motion and show they are circular orbits. Substituting $r^2 = x^2 + y^2$, I ...
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1answer
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Sidereal time calculation from orbital elements and mean anomaly

I'm following the instructions given here for calculating the apparent position of the planets in the sky and I've come to calculating the sidereal time in section 1.8. The formula for calculating ...
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2answers
63 views

Can Kepler's laws apply for circular motions?

Can Kepler's laws apply for circular motions? (First law states planets take an elliptical orbit)
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3answers
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Energy of a planet moving around the Sun

In chapter 13 of volume 1 of The Feynman Lectures, Feynman is discussing how the work done in going around any path in a gravitational field is zero. Here's the link: http://www.feynmanlectures....
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2answers
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Parker Solar Probe top speed

All the news articles say it'll orbit the sun at 430,000 mph. How do they get that? It seems too low. Isn't orbital velocity proportional to $1/\sqrt{r}$? Parker will be 4 million miles above the "...
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1answer
199 views

Geodesic of a massive particle in Schwarzschild metric

what happens to particle in unstable circular orbit in schwarzschild metic when it is pushed outwards? Does its geodesic change into an ellipse with around stable radius corresponding to its angular ...
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1answer
33 views

Would a Lunar space elevator only be stable if it passes through Earth-Moon L1 or L2?

I understand that space elevators are extremely hypothetical (bordering on pure fiction), but they are supposed to be theoretically possible. My questions is about what longidtudes a lunar space ...
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2answers
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Day/Year Length Of Larger, but same mass, Earth? [closed]

I’m wondering how the length of a day and year would change on Earth if it was twice as big, but the same mass (less density)? Also, would such a difference cause it to orbit closer or further from ...
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1answer
366 views

How can I find the areal velocity of a body, moving under a central force, in Cartesian coordinates?

My textbook tells me that the areal velocity of a body under central force is expressed by $\vec A$ = $r^2$$\dot\theta$$\hat k$. How can I express this in Cartesian coordinates, since the above ...
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1answer
50 views

Question about angular speed

Lets assume that the motions of the Moon around the Earth and of the Earth around the Sun are uniform circular. If $\omega_L, \omega_T$ are the respective angular speeds find $\omega_L/\omega_t$. ...
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1answer
97 views

Was Feynman right about the chalk in the spaceship?

I have heard this problem many times before from various sources, but I am quoting Feynman's words from his Lectures On Physics (Vol : 1) , just in case you want it to be authentic. Therefore, ...
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1answer
53 views

Orbit of detached mass

I was wondering what precisely would happen to parts detached by objects in orbit. To specify: Let a large object of mass $m$ is in a stable orbit around a planet with mass $M$ at a distance $r$ ...
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2answers
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What is the orbit of SDO (solar dynamics observatory)? How does it takes images of Sun non-stop?

There is a orbital diagram given in sdo website https://sdo.gsfc.nasa.gov/ It takes images of sun 24hr.
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3answers
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Is the path that a planet takes orbiting the sun a centripetal one or one that follows a geodesic path?

Is the path that a planet takes orbiting the sun a centripetal one or one that follows a geodesic path? My point is that if the planet follows a centripetal path all objects on the planet will ...
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1answer
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Gravitation question

I’d like to ask the following doubt that came to me after some exercises: Is it possibile to exactly establish,given a satellite orbiting Earth with a certain $\vec v_{0}$ and distance $\vec R_{1}$ ...
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3answers
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Since astronomers are adding 'leap seconds' to our years nowadays, does that mean Earth's orbital period is getting longer?

How long was an Earth year several billion years ago? (I'm assuming constant days, even though I know days were much shorter back then).
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1answer
107 views

Is spacetime in an ellipse around a massive object, or does it just slope down towards the massive object?

In some discussions, people seem to imply that spacetime is in an actual ellipse around a massive object so that, for example, the planet orbiting a star is actually traveling in a straight line in ...
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1answer
118 views

Can a single electron have an orbital angular momentum in the direction of propagation in free space?

I trying to understand the article about quantized orbital angular momentum in electron vortex beams. The article is not important per se, as there are many others. But I'm reading it as if an ...
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1answer
57 views

What would happen to the Moon if the Earth stopped providing it with a centripetal force owing to its force of gravity?

Would the Moon really only travel in a straight line then? What about the other planets and their forces of gravity? Wouldn't they prevent this rectilinear and undisturbed motion of the Moon?
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1answer
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How do astronauts and spacecrafts float away into space if they're always under the influence of the Earth's gravity? [duplicate]

I understand that as the distance between the planet and the body increases, the gravity decreases, but how can they still just 'float away'?
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1answer
467 views

How to prove Kepler's 3rd law? [duplicate]

How to prove Kepler's 3rd law? How did Kepler proved it? Is it possible to prove the third law without applying Newton's universal law of gravitation?
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Goldstein on Bertrand's theorem

Bertrand's theorem (Wikipedia) Regarding central force motion, Bertrand's theorem states that only inverse-square and linear force law produce stable closed, if bounded, orbits. Wikipedia's proof of ...
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1answer
162 views

Can anything orbit a black hole with dipping under the event horizon?

The event horizon is the boundary, from where light cannot escape. But can anything else? Something with real mass will gather inertia while falling into the black hole. First it will mainly increase ...