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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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2answers
102 views

Why aren't shape of galaxies depicted as a funnel?

Let's say if a galaxy is moving, shouldn't it be shaped like a funnel? I am saying this because it would take considerable time for the outermost star to know that the center of gravity has shifted. ...
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1answer
34 views

How is Geo Stationary Rocket placed exactly above the Location after Launch

My Question is bit deeper on the Satellite been put into orbit of GEO . Recently ISRO Launch GSLV Mark 3 to put into GSO . After the Rocket is launched and reached the Perigee ( 190 km ) the ...
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1answer
50 views

A dreidel on a spinning table

In the spirit of the holidays. Let's assume that a dreidel is spinning counter-clockwise at frequency $f$ on a table. From external point of view, what will I see if I rotate the table clockwise at ...
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1answer
42 views

Will space junk handle itself to an extent?

So suppose that two satellites traveling in opposite directions collide and some bolts are hurdled at higher speeds than either of the bodies were traveling before. Since the junk is traveling at a ...
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1answer
36 views

The shape characteristics of gravitational wells given different masses and spread of objects

I am curious as to research that calculates the shape of gravitational wells, and their limits, and affect on time, for different masses and spread of mass. The actual question is st the end. For ...
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5answers
139 views

How would the path of a satellite be affected by the gravitational constant decreasing? [closed]

An artificial satellite is moving around the surface of earth. If the magnitude of the gravitational constant starts decreasing at a constant rate, then what would the effect on the path of the ...
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2answers
77 views

How are Quantum Mechanical energy levels related to atom shells?

I'm currently taking Quantum Mechanics in school and I came across a table displaying the following in the given order: $E_n (\text{energy levels}), g_n (\text{eigen functions})$ $n \ l, [m]$ $E_1, ...
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1answer
69 views

What's the eccentricity of our sun's orbit around the center of the galaxy? [duplicate]

Just thinking about "galactic habitability zones." Is this even a valid question?
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0answers
45 views

A question about almost stationary orbits

For an orbit around the earth with period equal to a sidereal day with eccentricity $e=0$ and inclination $i=0$, the path on earth would be a single point on the equator. I have done some simulations ...
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3answers
217 views

Equation of motion for Central Force problem with repulsive inverse square law

This seems to be a very simple question, but it has been bugging me for days. I have found many material related to this, including the great Goldstein book, but none get quite were I want. I'm ...
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0answers
60 views

Is angular momentum independent of axis (if axis is parallel)?

I have been told this is true for the moon on this question: Angular momentum of orbiting + rotating body but I don't understand why it should work. Surely the axis must be chosen such that the ...
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0answers
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The event horizon of a black hole supposes an absolute zero in some field?

Based on the Schwarzschild black hole theory, if the gravitational pull of the singularity were to equalize the energy that a photon has by approaching the event horizon from a special angle, would it ...
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1answer
51 views

Gravity, planetary orbits [closed]

If a planet was slowed down, what effect would it have on it’s orbit around a star. Or adversely if it were speeded up what effect would that have ?
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4answers
201 views

Why does not the central force $-1/r^4$ violate Bertrand's theorem?

An orbit $r(\theta)$ is said to be bounded if $0<r_{min}\leq r(\theta)\leq r_{max}<\infty$. Otherwise it is called unbounded. Goldstein defines closed orbits as orbits in which the particle ...
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2answers
51 views

The radius of a body in circular motion

If the kinetic energy of an object in circular motion due to a gravitational force is given by: $$E_{kinetic} = \frac{GM_{object}M_{planet}}{2X_{radius}},$$ then why does radius decrease when ...
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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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1answer
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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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3answers
94 views

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
63 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
38 views

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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2answers
435 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
59 views

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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0answers
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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
93 views

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
107 views

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
86 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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2answers
93 views

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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0answers
54 views

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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0answers
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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
386 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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0answers
43 views

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
156 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
116 views

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
84 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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3answers
124 views

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
74 views

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
98 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
89 views

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
54 views

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
79 views

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
195 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
89 views

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 ...