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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Two-body central force mechanics problem [closed]

Problem: A particle of mass $m$ is in an attractive central force field given by $f(r)=-km/r^4$, where $k$ is a positive constant and $r$ is the distance from the particle to the centre of force. ...
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Magnetic moment produced by a charge in translatory motion (with no orbital motion)

A moving charge produces a magnetic field, while its magnetic moment is given by $$\mu = -g\frac{q}{2m}\textbf{L}$$ where, $g$ = gyromagnetic ratio, $q$ = charge, $m$ = mass, L = orbital angular ...
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Can the Sun orbit the Earth?

You know how the earth orbits the sun because of gravity?...well if the sun were the right distance from the earth and it had the perfect tangential velocity...could it orbit the earth? In other words....
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Elliptical orbits: Where have I made a mistake? [closed]

Sorry for not using latex, I am new. Assuming conservation of angular momentum and mechanical energy in an elliptical orbit, the sum of velocities at any two arbitrary points in orbit is constant? I ...
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First Law of Motion, Gravitational acceleration and Law of Conservation of Energy [duplicate]

When an object leaves a celestial body (e.g. planet or star) with it's escape velocity, according to first law of motion, it will continue travel away from the body with the same speed (without having ...
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Crystal electric field effects on spin-orbit coupling

Can someone highlight in general the correlation between crystal-electric-field, spin-orbit coupling in case of 3d7 ions under tetrahedral crystal field environment and their mutual effects on ...
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How to transform coordinates from heliocentric to a view from earth?

I'm trying to find and model the apparent motion of the retrograde motion of Mars as viewed on Earth, incorporating Lagrangian or Hamiltonian mechanics. For the lagrangian I have: $L = \frac{1}{2}m_{...
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Classical and QM results both require statistical descriptions

Laskar https://arxiv.org/abs/1209.5996 calculated the position of planets up to 5 billion years. The time period is chosen to cover a time scale before the Sun is thought to expand as a red giant. In ...
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Why is there a third extremum radial coordinate for “rosace-like” trajectories in the Schwarzschild geometry?

I drop a test-particle in the Schwarzschild geometry, at an initial radial coordinate $r_0 > a \equiv 2 G M$ ($a$ is the Schwarzschild "radius"), with initial velocity $v_0 < 1$ ...
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Orbital quadrature and relative velocities

In Robert J. Sawyer's sf novel The Oppenheimer Alternative, a bunch of physicists try to find the composition of the martian atmosphere with spectroscopy. They say that to find water vapour or oxygen, ...
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Does the Earth orbit an ellipse or the barycentre of the Solar system?

I'm taking physics lessons in university and my professor described the Earth's orbit as en ellipse, where one of the focal points is the Sun (1st Kepler's law). However, this doesn't make much sense ...
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Is “the earth moves around the sun” a case of Occam's razor?

This question is a bit more meta and non-straight forward than it might appear on first glance. I recently saw Why The Speed Of Light Is Unmeasurable, which is actually about why the speed of light ...
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How to calculate deceleration of a rocket while descending?

Lets say i have a model rocket that is propelled by Liquid Rocket Engine.(This speculation is according to my knowledge ......that could be wrong ) The engine provides a thrust of 300N and has an ...
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How Does Scalar-Tensor/Jordan-Brans-Dicke Gravity Change Orbits With Different Coupling Constants?

My understanding is that scalar-tensor/Jordan-Brans-Dicke gravity most closely resembles general relativity as the coupling constant omega approaches infinity. I am curious about how its predictions ...
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Kepler's third Law

Kepler's third law states $C=\frac{r^3}{T^2}$, as seen from the orbits of planets around the sun. But as the earth also attracts the sun, the sun must also orbit the earth and so $c=\frac{r^3}{T'^2}$ ...
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Distance between Earth and Sun - Derivation of Equation

While reading a textbook about the solar position of the earth I came across an equation that can't find its derivation. j = d 2 pi / 365.2422 𝜀 ≈ 0.03344 cos(j - 0.049) 𝑟0/𝑟 = √(1 + 𝜀) I think it ...
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Newtonian mechanics in higher dimensions [duplicate]

Once in a book ( I think title was Mathematical Physics, no idea who the author was) saw the proof of instability of planetary orbits in 4 dimensions, cant remember the details of derivations only the ...
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Orbit with crash

Let's assume I shoot an object from a high tower horizontal to the earth's surface. As far as I understand, depending on the velocity I will get different types of orbits. With decreasing velocity I ...
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Solving the Kepler Problem With Cartesian Coordinates? [migrated]

if we look at the Lagrangian for the Kepler problem in cartesian coordinates, we obtain sth like $$\mathcal L\left( \vec X, \vec x, \dot{\vec{X}}, \dot{\vec{x}} \right) = \frac{M}{2} \dot{\vec{X}}^2 + ...
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How to calculate the total energy of a planet at rest?

Let's just say we have the Earth-Moon system isolated in space, with Earth at rest, and the moon orbiting it. How can we calculate the total energy of Earth in such a case (Kinetic energy would be ...
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The possible orbits of a body about the Sun in terms of their total mechanical energy

If we assume that the Sun is at rest in an inertial reference frame, the total mechanical energy ( $E$ ) of the Sun and the orbiting body is constant and equal to the sum of the kinetic energy ( $\...
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Angular momentum conservation - elliptical motion [duplicate]

By equating $F_{\rm gravitation}$ to $F_{\rm centripetal}$, the formula for the velocity of an object traveling along a certain orbital becomes $\sqrt{\frac{GM}{r}}$. The formula for angular momentum ...
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In the rocket equation, does lowering the acceleration due to gravity increase decrease exhaust velocity? [closed]

I'm doing work for an intro space flight class, and I have to calculate the amount of fuel I need to get sizable a space craft, around 200 thousand kg in dry mass, into a transfer orbit from the ...
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Can a radially launched projectile orbit a planet?

Imagine a spherical planet with no atmosphere. A ball is launched radially with a velocity $v$, maintaining $\frac{v_e}{\sqrt2}<v<v_e $ and there is no other objects in the universe (Ideal two ...
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How does a black hole capture an approaching star and force it to start an elliptical orbit?

Let's assume that a standing still black hole attractor can have a star orbiting it in an orbit if the star was somehow a result of the same past proccesses as the black hole.So the star must be on a ...
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Kepler's Second Law: conservation of the energy or of the angular momentum?

Reading from example the old question, Angular Momentum and Kepler's Second Law Considering that now I not remember the proof because starting from the angular moment conservation of $L$ we have ...
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Proof that derives Newton's law of gravity [duplicate]

I was wondering if it is possible to derive Newton's law of universal gravitation, without utilizing Kepler's 3rd law. I have found many proofs that use this type of proof. I read somewhere that ...
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How does physics deal with perpetual motion in orbits?

This is a bit a bit of a weird question. Simply put, if a body orbits something such as a black hole there is no internal issue (that I know of) that would cause it to eventually stop (by internal I ...
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Do you experience no centrifugal force when in orbit?

I think that the answer is no, but in some sense it feels counter intuitive so I just wanted to check here. So if I understand it correctly, the General theory of relativity tells us that any ...
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Why does atmospheric drag speed up satellites?

I've read that old satellites slowly lose altitude when encountering the very thin atmosphere, and strangely enough they speed up. My theory is that the work done by the drag force is insignificant in ...
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Reconciling Wikipedia formulae for time dilation due to gravity and velocity

Wikipedia "Time dilation" shows the formula $\sqrt{ 1-v^2-v_e^2-v_r^2.v_e^2/(1-v_e^2) } $ where v is (perhaps) the 3D speed, $v_e$ is the Newtonian escape speed, $v_r$ is the radial speed. ...
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Dot product between relative velocity and relative position in orbital mechanics

Reading Curtis' book Orbital Mechanics I found this relation that confused me. $$ \underline{r}\cdot\underline{\dot{r}}=r\dot{r} $$ What happens, say, for a circular orbit where $\underline{r}$ and $\...
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What does the orbit of Pluto look like from the perspective of Neptune?

Pluto is locked in 3:2 resonance with Neptune, so that means that it should be possible to generate a simple looping animation that shows what movements Pluto would make given 2 orbits of Neptune. I ...
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Apse divides central orbit into symmetrical portions

I am solving dynamics and unable to digest author's views regarding apse. Help from the community is needed. ...
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Voyager distance

This very nice NASA page continuously updates Voyager 1 & 2 distance away. How is that distance calculated/determined?
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Kepler's third law: the equations $\frac{T^2}{\langle r\rangle^3}=\text{constant}$ and $\frac{T^2}{a^3}=\text{constant}$ are equivalent?

Kepler's third law or periods affirms that: "The squares of the times that the planets use to cover their orbits are proportional to the cube of their average distances from the Sun". font ...
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Really confused about orbital science

Okay let’s start straight away, What is Escape Velocity? Is it the speed required to get into orbit, or is it the speed required to escape the SOI (Sphere of Influence) of Earth completely? If it’s ...
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Deriving the effective potential from the Schwarzschild metric

I am attempting to derive the effective potential for a test particle around a massive object from the Schwarzschild metric; however, an extra term has appeared in my solution compared to Wikipedia's, ...
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Elliptical Orbits

Two astronauts are in the same circular orbit of radius R around the Earth, 180 deg apart. Astronaut A has two cheese sandwiches, while Astronaut B has none. How can A throw a cheese sandwich to B? In ...
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Does Kepler's 3rd law of planetary motion violate the first postulate?

Consider a distant observer traveling at .866 c relative to the solar system along the line that is co-linear with the sun's axis of rotation. According to his/her wristwatch the observer measures the ...
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Force and Velocity directions

When ever the force and velocity are in thesame direction(0°), an object speeds up. When ever the force and velocity are in opposite directions(180°), the object slows down. Also , when ever force ...
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Why is the period of a geostationary satellite not exactly 1440 minutes?

When reading about Astra satellites on Wikipedia (https://en.wikipedia.org/wiki/Astra_1KR), I saw that the period of the Astra 1KR satellite, positioned at 19.2° E, is 1,436.1 minutes (source: NORAD ...
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Derivation of Newton's law of gravitation [duplicate]

How did Newton get $F=\frac{Gm_1m_2}{r^2}$? What is intuition behind it? What kind of experiment or thought experiment can I do to derive this?
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Estimating of the size of the Milky Way from the Sun's motion

I am trying to run a simple first-principles calculation to estimate the diameter of the Milky Way from what we know about the motion of the Sun around its center. In particular, from various online ...
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Combination of electrostatic and magnetic centripetal forces to a moving charged body

If we have a positively charged fixed body at the center of the table and we leave a negatively charged body orbit around it the orbiting body will have a radius of orbit and orbital velocity. If we ...
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In the earth-asteroid two-body problem, is it possible for the asteroid to be captured into an elliptical orbit around earth?

Consider an asteroid of mass $m$ rushing towards the earth. What is the mathematical condition under which the asteroid will be captured into an orbit around the earth (given that the asteroid and the ...
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What about Newton's potential prevents singularities in the two-body problem?

The solutions to the gravitational two-body problem can be described by conic sections. In particular, two abstract point masses don't collapse into each other (that is, do not get arbitrarily close ...
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How does $\frac{mv^2}{r} = \frac{GMm}{r^2}$ work if both planets attract each other?

According to this and this, both posts describe the fact that the earth and the moon are attracting each other due to gravitation. The gravitation force is $\frac{GMm}{r^2}$. However, I am not able to ...
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Kepler problem, How can I prove that the period of elliptic orbit is only dependent on energy?

We are also given the following hint: Equate the energies and sectorial velocities at the apogee and perigee of an elliptic orbit to express the area of the ellipse in terms of E. For some ...
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Does the gravitational distortion of a black hole depend of its rotation?

I would like to know if there is a difference produced by the added spin of a black hole to its gravitational space-time distortion. I am considering the distortion of space-time from a point far ...

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