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
108 views

Anomalous precession of the orbit of Mercury

Can the anomalous precession of the orbit of Mercury be explained just with relativistic length contraction?
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43 views

How did most of the math and physics formulae that govern our lifestyle and help us in space exploration come into being? [closed]

I realise that this isn't a very academic question, but after watching movies like First Man and Interstellar, it got me wondering: How did all these formulas that we use on a regular basis come into ...
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83 views

Difference between Critical and orbital velocity

What is the difference between orbital and critical velocity of satallite ? I have read that critical velocity is constant value and it does not depend upon altitude. It only gives the velocity of ...
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45 views

Orbital velocity of a binary system

My goal is to find a velocity vector for two planets so that they orbit each other. The planets' masses and distances are known, just not their velocities. When googling for an equation, I found a ...
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1answer
76 views

Angular momentum per unit energy in the Schwarzschild spacetime

I am reading Chapter 9 of Hartle's Gravity book, and I'm completely stumped on the following thing. In equation 9.45 he claims that for circular orbits in a Schwarschild geometry: $$\frac{l}{e}=\left(...
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1answer
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Will the Sun's orbit around the Milky Way degrade once it transitions to a white dwarf with half its original mass?

Does the Sun's mass factor in at all when it comes to its orbit around the Milky Way, such that if it lost half its mass, its orbit would change? Or is it a matter of the center of the Milky Way being ...
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1answer
60 views

Violation of Gravity as a Conservative force?

I was trying out a simulation about escape velocity to understand why direction has no impact on it here :http://highered.mheducation.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/...
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Kepler's 3rd law: ratios don't fit data

I have been looking at satellite orbits around the earth, or any object around any planet in fact, and am trying to find the orbital radius, or semi major length of a given satellite. Kepler's third ...
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Why does the Earth not fall towards the Sun? [duplicate]

According to http://wtamu.edu/~cbaird/sq/mobile/2013/07/01/why-doesnt-the-earth-fall-down/ , the earth does not fall down because of the gravitational force of the sun. At the same time , earth's ...
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3answers
85 views

Kinematics and dynamics of a crashing satellite

A satellite in low, circular orbit around the Earth experiences drag (friction) and slowly spirals into Earth's atmosphere. It then enters the Earth's atmosphere, heats up catastrophically and burns ...
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Friction and satellites

There was this question we did in class. There is a satellite orbiting the Earth. It runs into some particles, and due to friction, the satellite loses speed. We were asked to predict what will happen ...
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If a satellite speeds up, does that make move farther away or closer?

If a satellite is in a stable circular orbit and goes about 41% faster (escape velocity) then it leaves its host forever. I get that. However, what if it speeds up by less than 41%? Intuitively, it ...
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About Kepler's laws [closed]

Yesterday I was reviewing some calculations using Kepler's laws and when working the third law that relates orbital periods and distances, it is very normal that, given the parameters of some object ...
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81 views

Force due to motion around Sun [closed]

Think of one person on earth named A . Ignoring Earth for a second, I can imagine him moving around the Sun due to which he should always feel some acceleration towards Sun (Centripetal Force) say F1. ...
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Kepler papers (2-body problem) [closed]

Where can I find papers by Kepler? I am looking for his solution to the two-body problem.
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57 views

How to find Lagrange point $L_2$ of the Earth-Moon system?

I was tasked in my programming lesson to find a value of L1 correct to 5 significant figures, but in my discussion section I began to wonder why there was no second solution to the equation I was ...
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1answer
62 views

How does orbiting work exactly? [duplicate]

First of all I'm not a physicist or anything and I don't know much about physics, so I'm sorry if this doesn't make sense at all :) And if possible please try to explain it with words instead of ...
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Question About Gravity vs. Earth’s Rotation [duplicate]

If a bullet was fired perfectly straight up (assuming a windless environment) such that the peak of its trajectory was just shy of orbit, would it fall back to Earth in the same spot, or would Earth’s ...
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41 views

How to derive orbital velocity without assuming direction

In the usual derivation of orbital velocity at height $r$ we set centripetal acceleration equal to acceleration caused by gravity to get $\frac{v^2 }{r}=\gamma \frac{M}{r^2 }$ and get $v=\sqrt{\frac{\...
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Derivation for magnitude of acceleration of a body in orbit with general relativity coefficient?

I came across an equation that an old professor used in an orbital simulation code and wanted to know how this equation was derived? I also wanted to know where $\alpha$ came from and what it ...
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Rocket Leaving Earth's Gravitational Field

I stumbled across this seemingly simple question that really stumped me on further thought: A rocket is intended to leave the Earth's gravitational field. The fuel in its main engine is a little ...
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1answer
32 views

How is high tide related to tidal bulge?

This is going to be a basic question. But I'm confused at the conceptual level.. The following is a popular diagram explaining the tides: I understand why the bulges appear on the right and left ...
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Free fall ellipse or parabola?

Herbert Spencer somewhere says that the parabola of a ballistic object is actually a portion of an ellipse that is indistinguishable from a parabola--is that true? It would seem plausible since ...
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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 ...
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Would it be possible to do a “slow” translunar injection, lasting an hour or more

Part of my sci-fi novel takes place on a spaceship with centrifugal pseudogravity (initially at ~1g), designed to make passengers comfortable on a week-long voyage to the moon. With that being said, I ...
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1answer
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State of $N$-body system after time $t$ (under gravity and inelastic collision)

Given the centers of gravity of $n$ spherical bodies of unit mass, $p_1$, $p_2$, ...$p_n$, and assuming perfectly inelastic collisions, how does one find the location of the bodies after time $t$? ...
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How to express the Earth's orbital speed as a function of time?

I would like to create a function that tells me the orbital speed of Earth at any given day. The vis-viva equation says that v=√(GM(2/r-1/a) ), expressing speed as a function of distance from the ...
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Why is the angular momentum of blackhole measured by orbital motion of falling objects around it?

When massive star collapsed under it's own weight, it can becomes a blackhole and I have to believe angular momentum is conserved. Since we cannot directly measure the rotation of blackhole, I read ...
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Why do planets revolve around Sun in elliptical orbits? [duplicate]

Let’s consider two planets of mass $m$ and $M$. They both will attract one another with a constant force $F$ according to the law of attraction $F=G m M/r^2$. The force and masses are constant. $G$ is ...
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111 views

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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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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1answer
68 views

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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2answers
63 views

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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1answer
39 views

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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1answer
95 views

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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1answer
61 views

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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2answers
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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'...