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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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How to find the speed to make a curve without sliding using the information of a previous successful curve? [on hold]

If a 1000kg car's coefficient of friction is 0.50, what is the maximum speed the car can make around a curved road with the radius of 45m without sliding? On Another curve on another road with a ...
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General expression for any central orbit [on hold]

(a). show that the particle moving under the central force is in planner motion (b). show that the central force is conservative in nature (c) find the general expression for any central orbit?
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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
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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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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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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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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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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
41 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
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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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What is the direction of velocity at different points in an elliptical orbit? [duplicate]

Consider an elliptical orbit. We know that the direction of velocity is fully tangential at periapsis and apoapsis. But what is the direction of velocity at other points on the elliptical orbit?
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1answer
33 views

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
39 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
880 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
52 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
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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
32 views

Schwarschild Metric from Kepler law

Can we redrive Schwarschild metric from Kepler's law without assuming General Relativity?
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Orbit Trajectory. Anomaly in Topocentric frame

In the same way that there is a relationship between the true anomaly and the eccentric anomaly, could a relationship between the true anomaly and that observed in a topocentric system be defined? in ...
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2answers
46 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
54 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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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
50 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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Trying to calculate the effective gravity of a body under acceleration about a sphere

I am trying to calculate the effective gravity of a body under acceleration about a perfect sphere. This equation I am using is: $$g_{eff} = \frac {\mu}{r^2} + \frac {|\vec r \times \vec v|^2}{r^3}$$ ...
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1answer
43 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
52 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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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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Gravity and shell theorem in strongly curved hyperbolic space

I was reading this post and I was wondering how gravity would work in a strongly curved hyperbolic space (with curvature on the order of ~1km). In particular, would the shell theorem still hold? How ...
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39 views

Orbits in the effective potential $U(r)=k(r^2 -a^2)e^{-br^2}$

Given the effective potential $U(r)=k(r^2 -a^2)e^{-br^2}$, where $r$ is the spherical radial coordinate, could a particle oscillate near $r=0$ even when the particle cannot go to a coordinate with ...
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How does the perihelion advance vanish for a unique circular orbit?

I'm working on a problem set in which I am to find the precession of the perihelion of Mercury given the corrections to the Newtonian potential coming from general relativity. I am stuck on e and f. ...
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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
105 views

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

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
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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
103 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
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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
43 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
109 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
59 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
68 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
51 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
50 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
49 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
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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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26 views

Angular momentum in Rotating Frame for satellites

I am working on satellite orbit propagator, I am propagating the satellite position and velocity in the inertial and rotating frames. To validate my propagator, I am checking the angular momentum and ...
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1answer
72 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
25 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 ...