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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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Could a trajectory around a large mass ever deflect by more than 180 degrees due to general relativistic effects?

Possible mechanisms that could be an answer to the question What natural mechanisms could lead to the unlikely case of the same rogue asteroid or planet passing through our solar system twice? include ...
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Two-body problem - point of closest approach

I am reading through an exercise : One of the hints to solve this problem is that at the point of closest approach the comet's velocity must be tangential only, why is this the case ?
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Energy in central force orbit

Given a mass $m$ moving under the central force $$F(r) = -k/r^n$$ and a circular orbit passing through the force center, I want to show $n$ must equal 5. I ultimately arrive at the expression $$E = \...
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Find the orbital period of a satellite in a circular orbit 600 km above the surface of the earth? [closed]

Question: Find the orbital period of a satellite in a circular orbit 600 km above the surface of the earth? What I tried to do: By applying Kepler's third law to the combination of centripetal and ...
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Do orbiting bodies consume energy? [duplicate]

Since orbiting bodies are under constant acceleration, this means they are experiencing force. Considering work = force X distance and work is energy, where does ...
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When a body completes one revolution around a circular path will its acceleration be 0?

When a body is moving in a circular motion the acceleration keeps changing, will it be zero when it comes back to the same point it started from(will the average acceleration be 0?)
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Is there any model explaining why would a particle revolve around another one in an elliptical orbit? [duplicate]

The reason for asking this question is to understand the elliptical orbits of planets and why aren't they circular, we know that if a particle moves with an initial velocity perpendicular to the ...
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Orbits of satellites

For a satellite orbiting the earth, if there is only gravitational force acting on the satellite, does it mean it can only orbit the earth around the equator or through north and south poles? (only in ...
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Calculating Inital Velocity required to stablize an orbit of a moon

I am currently attempting to create a little solar system simulation and I was curious if there's a decent way to calculate what a moon or planet's initial velocity would need to be to remain in orbit ...
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Do orbiting planets have infinite energy?

I know that planets can't have infinite energy, due to the law of conservation of energy. However, I'm confused because I see a contradiction and it would be great if someone could explain it. ...
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Duration of Satellite orbit in the shadow of the Earth (elliptical orbit)

This question here calculated the time a satellite was in the shadow of the earth for a circular orbit. I was wondering if there was a way to do the same thing for an elliptical orbit.
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How was the equation for a gravitational assist derived?

Im currently writing a paper about a hypothetical probe meant to escape our solar system and I want to analyse how gravitational assists would be beneficial for its mission. I found a website with an ...
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What's the nicest proof that two isolates masses orbit their center of mass? [duplicate]

Although it seems intuitive, I haven't found proof of this fact in my textbooks from a purely mathematical standpoint. I was wondering if anybody knows of a particularly elegant proof of this fact, ...
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What orbit does a planet have to have to be a planet? [closed]

Other questions have dealt with where you could find a planet-like object, and what a planet has to consist of to count as a planet. But this question is directed as what orbit or path an object would ...
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How is it possible to see a full moon at midday? [closed]

I’m currently doing an observational study of the moon that’s been a passion of mine for the last few years. I’ve found I can see the moon all the way to almost full at about midday). Added I can see ...
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Declination as a function of orbital position

Reading this Wikipedia article and following the derivations (https://en.wikipedia.org/wiki/Solar_irradiance#Milankovitch_cycles), I have found an equation I can't see where it comes from. Perhaps it'...
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Orbit such that distance from Earth is always the same as distance from Mars

Would it be possible to place a satellite into an orbit such that its distance from Earth and Mars always remained the same? That is the distance between the satellite and Earth and the satellite and ...
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Why doesn't the Earth slowly collapse into the Sun? [duplicate]

I understand that the sun exerts a force on the earth and that if that was the only force exerted on the earth then the earth would have already crashed into the sun a long time ago. The reason the ...
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Can a spacecraft use the planet's gravitational gradient to boost it's orbit without rockets?

A spacecraft orbits a planet. It extends a mass about a horizontal direction on a long tether. At this point there is not much gravitational gradient between the craft and the ejected mass so there is ...
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How come planets with different masses can orbit at the same velocity at the same altitudes?

Angular momentum is equal to r × p and angular momentum is also what gives planets with lower orbits a higher speed (because angular momentum is conserved). So as r decreases either m or v (p=mv) has ...
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How can I determine a planet's mass based only off of information about its orbit and its parent star?

I'm coding a video game with procedurally generated planetary systems and I want some and I want to make sure I'm at least somewhat scientifically correct. I've reached the part in my code where I ...
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Large mass body on Lagrange point L4/5

Lagrange points L4 and L5 are stable for a test particle. But what happens if instead the body at L4/5 (let's call it C) has a mass significant enough that its gravitational pull on the other two (let'...
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I don't understand why escape velocity is necessary [duplicate]

I have read multiple explanations of escape velocity, including that on Wikipedia, and I don't understand it. If I launch a rocket from the surface of the Earth towards the sun with just enough force ...
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Kepler's third law is unintuitive

Kepler's third law states that the ratio between the period of a planet in orbit round a star squared over the average distance to that star cubed, is constant. And in the case of an elliptical orbit, ...
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Proving that gravitational potential is work done by the object against gravity while KE increases and PE reduces

There's a person in my class who thinks that the formula for gravitational potential (-GM/r) represents the work done by gravity to move an object from infinity to any point in the gravitational field....
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gravitation (kinetic energy and angular momentum)

When a satellite in a circular orbit around the earth enters the atmospheric region it encounters small air resistance to its motion. then (1) kinetic energy increases (2) angular momentum decreases ...
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On what timescale does gravitational wave emission circularise an orbit?

Gravitational waves remove both energy and angular momentum from a binary orbit. Both rates are enhanced in non-circular (eccentric) orbits and I presume that (like tidal friction) the net effect will ...
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Central Forces: Newtonian/Coulomb force vs. Hooke's law

We know that a body under the action of a Newtonian/Coulomb potential $1/r$ can describe an elliptic orbit. On the other hand, we also know that a body under the action of two perpendicular Simple ...
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Does gravity sometimes get transmitted faster than the speed of light?

Consider Earth moving around the Sun. Is the force of gravity exerted by Earth onto the Sun directed towards the point where Earth is "right now", or towards the point where Earth was 8 minutes ago (...
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Experimental considerations for measuring the gravitational constant/effects, with two large (1000kg) masses orbiting each other? [closed]

So @uhoh, wanting to get some experimental data to verify Limits on non-Newtonian gravity at length scales larger than 1 meter?, proposed an experiment: Place two large (1000kg) spherical masses in ...
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In Schwarzchild solution what happens between $r=2M$ and $r=3M$?

Numerical Relativity by Tomas Baumagrte and Stuart Shapiro page 10. By adapting $h=c=1$, so in schwarzchild solution the areal radius $r=2M$ is the event horizon, and $r=3M$ is the photon orbit. But ...
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Velocity of an orbiting body

The velocity of an orbiting body is given by: $$v = \sqrt{\frac{Gm}{r}}$$ I was trying to derive this formula earlier but I was struggling with incorporating $G$ into my derivation. I tried looking ...
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How many orbits to catch up to ISS and Hubble?

To dock with orbiting satellites like the ISS or Hubble, how many orbits of earth do rockets and spacecraft clock up while they close in on their target satellite? Is the number highly variable ...
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Satellite Motion centripetal force

Once I read in a book that the centripetal force that keeps the satellite in its circular orbit around the Earth is approximately equal to its weight. My question is why the word "approximately" was ...
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A confusion between geocentric and heliocentric model [duplicate]

As per Ptolemy, he proposed firstly geocentric model and that model if one see with aspects of relativity he would find true. Here is an example how Suppose you are in a train which is moving and you ...
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Horseshoe orbit cycle times

I asked on Worldbuilding originally, but was directed here instead I've been working on a habitable moon system for a story, and I'm now trying to populate the other moons around the parent planet. ...
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Stability of circular orbit in attractive inverse cube central force field

Considering a motion of a body under an attractive inverse cube central force, $\textbf{F}(\textbf{r}) = -\frac{k}{r^3} \hspace{1mm}\hat{\textbf{r}}$ with $k>0$. Is it possible for a body to move ...
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Is a stable orbit possible inside the ergosphere of a Kerr (spinning) black hole?

I have heard that it's "impossible to hover" inside of an ergosphere, but everywhere I read this seemed to be speaking in the context of "relative to a stationary observer outside of the ergosphere". ...
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Why does angular momentum being constant prove Kepler's first law?

So I was watching this video and this video on Kepler's first law in order to understand the proof of Kepler's first law. He started off by saying that for an ellipse, the distance from a focus point ...
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Thought experiment. Earth orbital motion if we stopped Earth spinning

This is a thought experiment that puzzles me. Imagine we could magically stop Earth’s rotation around its own axis (and locally verify it by disappearance of inertial forces generated by the spin ...
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How fast would an object at cruising altitude (around 10,600 m) need to travel to stay on the opposite side of the Earth to the Moon? [closed]

I am trying to figure out how fast an object will have to travel (at a height around 10,600 m) to never be in the presence of the moon. Meaning the object will always be on the opposite side of the ...
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I have a question about the gravity probe B geodectic precession formula and why it seems to be twice the planetary precession formula

Specifically, I can work out the planetary precession formula to give radians per orbit as 6*pi*GM/c^2r (and I find that on the web at places like http://farside.ph.utexas.edu/teaching/336k/...
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What determines the direction of an object that has undergone the effect of a gravitational slingshot?

I just started researching this topic and therefore I do not know much about it. Nonetheless, I am still curious about what determines the direction an object takes after passing by a planet. I think ...
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Mass distributions within two bodies such that the orbit is no longer Keplerian?

The trajectories of two point masses or spherically symmetric masses with respect to their center of mass are conic sections or Kepler orbits. Consider that the bodies have finite size with respect ...
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On Planets orbiting binary stars

Several years ago a discovery was made of planet orbiting a star of a binary system (two stars orbiting each other). Since binary star systems are plentiful in our galaxy, I presume we will be ...
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If gravitation force varied with $r^{-3}$ instead of $r^{-2}$ what would happen to Kepler's laws [duplicate]

2nd law wouldn't change as it is LCAM. 3rd Law would change. But I'm confused about first law. Does any body under influence of any central force move in an ellipse?Can anyone give a simple proof/...
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How does the Earth's radial acceleration affect it's velocity during orbit around Sun? [closed]

When the earth moves along its ellipse at $67,000mph $ it accelerates at $0.006m/s^2$ would it be correct to say it's speed at some points relatively increases by $0.006m/s$ every second
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Which force described the “absolute” speed change of the moon in Newtonian mechanics?

In the world of "absolute" speed values in the Newtonian mechanics, the moon must move faster (i.e., must have a higher speed) if he travels with the earth (i.e., has the same velocity direction) than ...
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What's the Earth's linear acceleration component around the Sun?

The earth's centripetal acceleration around the Sun is $0.006m/s^2$ does this mean one can say the earth's acceleration when it travels(revolves) at $670,000mph$ is simply equal to its centripetal ...
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Shouldn't ball has to move in the circle even after cutting the rope by which it was attached? [closed]

Since the tension force is a central acting force, the torque on an orbiting ball about that center is zero. But if the rope is cut down during motion the torque would still remain zero. This would ...