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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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Approximating the orbit of an object tied to another by a rope which is shortening

Working off my previous question, I think I've finally managed to describe what I'm wondering about in a quite clear, non-vague way. Suppose we have an object $B$ tied to an object $A$ by a rope, ...
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Change of orbit with tangential impulse

I see a similar question: Change of orbit with a radial impulse. The answer to that question seems fine to me. In the answer, mention is made of this similar question, but it is not fully treated. ...
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Movement of an object tied to another

Suppose we have two objects $A$ and $B$, where $B$ is tied by a rope to $A$ with the slack pulled out, the initial tangential speed $c'(0)=(0,1)$ is perpendicular to $c(0)$ and $c(0) = (1,0)$, and ...
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Some questions concerning orbits of objects

I've been playing around with some physics problems and trying to figure out things by myself, mostly just for fun. I would appreciate if someone corrected my thoughts and gave me some feedback. I'm ...
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Velocity of an object orbiting on a string

First, I'm sorry if this question is dumb, incoherent or vague - I never really studied any physics and this might be out of my grasp, but I tried to apply some of the math I know and figure these ...
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51 views

What is the energy source for Earth movements? [on hold]

What is the source of energy responsible for Earth movements (rotation, translation, etc.)?
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52 views

Precession - Great year [on hold]

Is this true? Why not? Because of precession after 12900 years there will be summer where where there one was winter and spring where there used to be fall, and vice versa. Does precession change the ...
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1answer
18 views

Time period of a body moving under central force in a circle [on hold]

It is given that a body of mass m with non zero angular momentum L under influence of gravitational force . if area of particle's bound orbit is A then find out time period of revolution My approach ...
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Radial component of velocity at extreme distances

Suppose I am given that a planet's position with respect to some star is of the form $\textbf{r} = r\textbf{e}_{r}$. Then of course $\textbf{v} = \dot{r}\textbf{e}_{r} + r\dot{\theta}\textbf{e}_{\...
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If a body is moving under central force in a circle then how its path will be changed if it is subjected to a impulse [on hold]

A particle of mass m moves under an attractive central force of $Kr^4$ with an angular momentum L Find the frequency of the radial oscillations if the particle is given a small radial impulse and ...
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2answers
109 views

Trajectory of a satellite whose velocity is less than circular orbital velocity? [closed]

If the velocity of the satellite orbiting around a planet is reduced somehow...then what would it's trajectory looks like spiral(1) or elliptical(2) Or Does it depends on the  velocity it has(less ...
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The Earth revolves around the Sun or the Sun revolves around the Earth

Well, in today's world we know that the earth resolves around the sun. But that is seen from frame of reference of sun or an observer stationary wrt sun. From frame of reference of the earth, sun ...
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52 views

Help with Gravity Assist [closed]

In our scenario, a spaceship of mass 70,000 kg and velocity $v_o$ is planning on slingshotting around Earth and we're supposed to find what the exit velocity will be. The Earth is the origin in our ...
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1answer
52 views

Does the density of an object play a role for it's gravitational effects?

My thought experiment: We repalce our sun with an object of identical mass, rotation, shape, etc. but not the same density, i.e. the object would have a radius of 100km. The "replacement-time" would ...
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6answers
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Why aren't satellites disintegrated even though they orbit earth within earth's Roche Limits?

I was wondering about the Roche limit and its effects on satellites. Why aren't artificial satellites ripped apart by gravitational tidal forces of the earth? I think it's due to the satellites being ...
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What are the forces behind the orbit of the Earth around the Sun?

Does the gravity of the sun alone affect the orbit of the earth around the sun? Look at the image below,(Image is not to scale), Is it that when earth is going from position 1 to position 2, it ...
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1answer
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Can satellites stay in orbit when the Earth is being accelerated?

In a TV show I'm watching, the people of Earth have decided to leave the solar system, and take Earth with them, so they've built a large number of powerful rocket engines on one side of the Earth (as ...
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Why is the orbit of the Earth around the Sun very intricate?

The movement of the earth around the sun is very Goldilocky. Did it happen over the years as the orbit of earth averaged out into how it is now? Is there any chance of it (orbit) changing by itself in ...
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69 views

Revolution of Earth around the Sun

We study the orbit of many planets around the sun modelling it as a uniform circular motion. Is this due to the fact that empirically we measured that the magnitude of the earth's velocity (for ...
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1answer
151 views

Is there a general relativistic mass in general relativity?

In general relativity the energy of a test-body moving in a spherically symmetric gravitational field can be written as: $$E=mc^2\left(\frac{\sqrt{1-\frac{2GM}{rc^2}}}{\sqrt{1-\frac{v^2}{c^2\left((1-\...
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7answers
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Why does the Earth follow an elliptical trajectory rather than a parabolic one?

I was taught that when the acceleration experienced by a body is constant, that body follows a parabolic curve. This seems logical because constant acceleration means velocity that is linear and ...
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4answers
104 views

Is the angular momentum in uniform circular motion zero?

In uniform circular motion the direction of linear velocity changes (although magnitude is constant), so linear velocity is not constant and we know that the formula of angular momentum contains ...
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3answers
55 views

Kinds of orbits in two-body problem

I have a numerical simulation for two bodies moving under gravitational interaction, and some of the outputs are not cohering with my understanding of the theory. My understanding of the theory: In ...
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0answers
45 views

What do orbits around a black hole look like doing the calculations in isotropic coordinates?

JPL and others calculating ephemerides in the solar system are using a method based on taking the Schwarzschild solution, not as expressed in the most common Schwarzschild coordinates but in the ...
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1answer
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Why are orbits $1.5r_{s} < r < 3r_{s}$ unstable around a Schwarzschild black hole?

The "Orbital motion" section of the Wikipedia entry corresponding to Schwarzschild metric reads: A particle orbiting in the Schwarzschild metric can have a stable circular orbit with $r > 3r_s$. ...
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2answers
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What if we set the exact equality $u^2=\frac{2GM}{R}$? Escape or not?

Let an object of mass $m$ is thrown up with an initial velocity $u$ from a spherical gravitating body $A$ of mass $M$ and radius $R$. Let us assume that when it reaches a height $h$ its velocity ...
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1answer
81 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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42 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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31 views

Time derivative of Kepler's equation

How to compute time derivative of Kepler's equation $E = e- \sin E = M$? where $M$ is the mean anomaly, $E$ is the eccentric anomaly, and $e$ is the eccentricity. $r = a (1-e \cos E)$ I mean $\...
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0answers
61 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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0answers
24 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
66 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
28 views

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
45 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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5answers
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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
66 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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2answers
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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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1answer
33 views

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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3answers
74 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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1answer
28 views

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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2answers
42 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
56 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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2answers
72 views

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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1answer
30 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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46 views

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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4answers
111 views

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
26 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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2answers
3k views

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 ...