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 can these two definitions of the eccentric anomaly give the same answer?

The eccentric anomaly,$E$, is defined via the equation, $$ r = a(1-e \cos E) \tag{1} $$ for radius $r$, semi-major axis $a$ and eccentricity $e$. It is ALSO defined in terms of the Kepler Equation ...
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Is this a valid way to estimate the solar system's orbital velocity around the galactic center?

I know there are better ways to derive this, such as finding orbital velocities of other stars at approximately the same radius from the GC as ourselves and finding our own velocity $v_0$ as within ...
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Is spin-orbit coupling mass dependent?

When comparing spin-orbit coupling in the case of electrons and in the case of nucleons, do nuclear states exhibit a stronger level splitting compared to atomic states because the nucleons are more ...
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Between Mercury and Venus, which planet produces a longer transit? Assuming both planets describe same path on the solar disk

Is it even possible to give a definite answer to this question? There are a lot of factors involved in this like Earth's position and motion relative to the planets and of course their own motion and ...
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Units in orbital modeling

I'm trying to make a simulation of simple planetary orbits in Python (with only Earth and Jupiter) and was wondering if there are any convenient units one could use? I currently have the gravitational ...
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Eccentricity of two bodies in an unbound orbit

There seems to be two definitions of an eccentricity of orbiting bodies, one for when it’s not bound and the other for when it is bound (Keplerian binary). When the binary is bound there is a simple ...
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Equations of motion and phase portrait

I have a force $$f(x)=x^3+x^4\tag{1},$$ and a point particle of mass $m=1$ that moves along $x$ axis. How do I find the equations of motion and phase portrait? I think I have to start with finding ...
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Vis viva equation - finding how change in velocity changes the semi-major axis distances - math trick [closed]

I'm reading about how to deorbit. I stumped upon a trick here. In the question, we wish to find how a chance in orbital speed changes the semi-major axis distances. So in the answer we start with the ...
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Lagrange equations of the second kind of a flat pendulum [closed]

Find the Lagrange equations of the second kind of a flat pendulum with a mass hooked on an inextensible string of length $l$ to a trolley of mass that can move along a vertical line. I'm a total noob ...
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Find the gravity and the speed of the point that moves in a circle in polar coordinates [closed]

A point particle of mass $m$ moves in a circle of radius $a$, being gravitated by some point $A$ of this circle. Find the gravity and the speed of the point depending on the distance to point $A$. (...
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Analytical proof for Kepler's first law using cartesian co-ordinates

Many detailed proofs are available for Kepler's first law, like this one. But all of them use polar co-ordinates. There is one which doesn't even use differential equations. I'm looking for a proof ...
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Do planets orbiting stars emit gravitational waves?

I have heard it said that charged planets could not orbit a massless (low mass) oppositely-charged star based on electromagnetic attraction the same way they can with gravitational attraction, because ...
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Orbital Mechanics: Initial velocity of a Parabolic trajectory

If I want to calculate the initial velocity, say for a planet orbiting a massive body, can I use the vis-viva equation in terms of eccentricity, and plug $e = 1$, to obtain the initial velocity that ...
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Relation between velocity and position vector in a central force

I am aware that the dot product of the position and velocity vector, $(\vec{r}\cdot\vec{v})$, in circular motion under a central force, $F(r)=-\frac{k}{r^2}$, is equal to zero as the two vectors are ...
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Derive hamiltonian from equations of motion

Is there a method for deriving the hamiltonian given that you know the equations of motion? For example given the equation (equation 5 in paper linked) they simply the derive the Hamiltonian in ...
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Lorenz System in reference to Astrophysics / Planetary orbits

From my research I have found that there are a system of ordinary differential equations for atmospheric convection. What I am seeking are any Lorenz equations that apply to any areas of Astrophysics ...
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Transform from Cartesian coordinates to Delaunay elements

Place a central mass $M = 1/G$ at the origin $(0,0,0)$. We know that for a test particle moving in the $xy$-plane, we can transform $(x,y,p_x,p_y)$ to the Delaunay elements $(\theta_\lambda, \theta_\...
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Does it take 41 Hiroshima “Little Boy” bombs worth of energy to send ISS in orbit? [closed]

I calculated the amount of energy needed to send ISS to orbit. It seems crazy expensive. I'm approximating my calculation with the following equation: $$\begin{align} E_\text{tot} &= E_\text{kin} ...
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Why do we have eclipses if the Earth's orbit around the Sun and the Moon's orbit around the Earth aren't in the same plane?

We know that eclipse is when the Sun, the Earth and the Moon align in a straight line. How do they do this align if their orbit planes aren't in the same angle?
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How does thermal expansion actually happen on the quantum level? [duplicate]

Classical physics states that when an object is heated, its particles gain kinetic energy, which causes them push away from each other. But on an even smaller level, what is actually happening? I read ...
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How to calculate the initial velocity needed for three or more masses to orbit each other?

Lets say I have one planet of mass $m_A$ and another of mass $m_B$. Lets say the distance between each of them is $r$. How would I calculate the initial velocity needed for each in order to make ...
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Predicting orbital trajectory of an object

I'm new here, I'm not a physics student, I'm a programmer and a soon to be computer science student (I come in peace). I'm developing a space simulation thing and I need your help. I know the ...
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How wide is the $L_4$ and $L_5$ Moon-Earth Lagrangian point?

How far would an object need to be displaced from the $L_4$ and $L_5$ Lagrangian points so that it can escape returning to those points?
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How does the Earth's orbit change as the Sun decreases in mass?

When the sun transitions into it's red giant phase it's mass is said to decrease (An article I read quoted it to go down to 67% of its mass however the number is not important). Since the orbital ...
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Why can atmospheric re-entry heat up the air into plasma?

The adiabatic processes of re-entering earth from a spaceship, creates intense heat. Heat in the range of 1700-2000 degrees Celsius. I've read the the temperature in the air molecules generate a ...
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How much at least should the Earth be smaller so that we notice these three phenomenons?

The Earth is moving with a speed of about $1670$ $km/h$ around its axis. This speed is more than the sound speed. So the Earth is always breaking the speed of the sound. How much at least should the ...
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What is the reason for assuming angular momentum is conserved for a moon-planet system where the moon is in an elliptical orbit around the planet?

I came across a question in the Princeton Review book for AP Physics 1 and then found the same question in the Collegeboard AP Physics course guide. Both have different answers. (See the questions ...
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About Simple Harmonic Motion [duplicate]

the earth is revolving around the sun in a fixed orbit does this motion execute Simple harmonic motion
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Path of an object in gravitational field [duplicate]

How do you prove that path of a satellite or a planet is a second degree curve? In other words, how do you prove Kepler's law which states that planets move in elliptical paths?
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Should the centripetal force of Earth's orbit around the Sun affect a pendulum on Earth?

Lets use approximate earth angular velocity around the sun with $\omega\approx2*10^{-7}\frac{r}{s}$ and earth translation orbit radius with $r\approx1.5*10^{11}m$ we can approximate centripetal ...
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Two-body problem: equal mass keplerian orbit? [duplicate]

Sorry to post a question on this again but I am still struggling putting two equal mass objects in a keplerian orbit. To summarise: 1) I have placed two bodies of masses 0.5 at +- 10 units on the x-...
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Two-body problem: reduced mass velocity to individual velocity

I asked a question on finding the initial velocity of two objects of equal mass in order to follow a keplerian orbit with a given eccentricity but I am still having some trouble. I have seen the ...
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Will deceleration in a geostationary orbit kick me into a higher orbit? [duplicate]

Lets say I am in a spaceship, and I throw a piece of space trash out the back of the spacecraft in the opposite direction from my direction of motion. The mass of the trash is small enough that it ...
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Solving Keplerian two-body problem numerically?

I'm trying to solve the two-body problem numerically, setting up G, m1 and m2 =1.0. The masses are placed at the positions -10 and 10 respectively along the x-axis and gave them both 0 on the y-axis. ...
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Validity of the two-body system approximation in astrophysics

I'm taking an intro course in astrophysics and studying Kepler's Laws of planetary motion - all of which are built over the assumption that we can approximate our system to one where there's only two ...
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Earth's orbit: chaotic but stable

The eccentricity of Earths orbit follows a bounded random walk-like pattern, see this chart. I presume most other planets are similar. One could think of eccentricity and argument of periapsis as "...
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Gravitational Oscillation and Kepler's Third Law [duplicate]

I want to figure out the motion of a comet that can somehow pass freely through the sun (mass much, much greater than the comet's so that its movement is negligible) if it starts out stationary ...
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If I use the Earth as my point of reference on a model, would it be valid if I said that the Sun orbits the Earth? (in my model)

What the title says. If I create a model, and I use the Earth as my point of reference, is it valid to say that the Sun orbits the Earth inside my model? Or is claiming that invalid?
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Platonic solids and Kepler’s theory of planetary orbits

In the preface to the second edition of Classical Mathematical Physics: Classical Dynamical Systems (1988), Walter Thirring includes this tantalizing comment: Even Kepler’s [orbital ratio] laws, ...
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What is the interplay between the “spinning tennis racket” effect on a planet with three principle axis of rotation and its moon?

Suppose I have a tennis racket spinning on its second axis of rotation such that it is subject to periodically flipping over on its spinning axis, as per the Dzhanibekov effect (explained in ...
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Why it takes more energy to pull satellite towards Earth than pushing it away?

Newton's law of motion states that satellite in orbit stays in orbit unless external force is applied, so we shall apply the force through it's thruster to deorbit. Strangely, it takes more energy to ...
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Minimum Velocity for a projectile to leave the Earth

Let's say we have a cannonball that can shoot at various angles. How would we find the minimum velocity for this projectile to leave the Earth when the cannonball is shot at an angle $\theta$. I think ...
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Finding parameters of a Gravitational Assist

I am trying to answer a simple question: If a rocket performs a gravitational slingshot around a body of mass m, altitude h, and angle $\theta $ and initial velocity ${ v }_{ sun }$, what will be the ...
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Extra energy in rotating frame of reference

Consider a particle at rest in frame of reference $S$. Its energy is $$E_S=0$$ (ignoring things like rest mass energy etc). Now suppose I move to a frame $S'$ which moves at speed $v$ in $S$. The ...
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What is the fastest moving macroscopic object people have made? [closed]

The Parker Solar Probe will move at 690,000 km/h (430,000 mph), or 0.064% the speed of light, at its closest approaches to the sun. Parker Solar Probe top speed Will that be the highest speed yet ...
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Is net force on a geostationary satellite, (when observer is standing just below it on earth) equal to '0'?

Since a geo stationary satellite appears to be at rest form earth, should not the net force acting on the satellite equal to $0$. Now since earth is a non-inertial frame we will have to apply a ...
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Is this a viable way to calculate the mass of the sun?

By measuring the Earth’s distance from the Sun, and knowing its orbital period, Newton’s Law of Universal Gravitation and Newton’s 2nd Law can I calculate the mass of the sun?
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Oberth effect with regard to relativistic velocity

So the Oberth effect is a little application of kinetic energy in classical mechanics. Essentially, since KE is proportional to $v^2$, at higher velocities a change in kinetic energy produces a ...
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Mistake in proof of virial theorem for gravity

I'm having trouble proving the virial theorem for gravity. I get an extraneous term, but I think my work is correct. Starting with the Lagrangian: $$\frac{1}{2}m\dot{r}^2+\frac{1}{2}mr^2\dot{\theta}^...
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Neutral buoyancy and free fall

Is an object that is neutral buoyant the equivalent of the same object in the microgravity (free fall) of the International Space Station? If a pingpong ball floating on top of still water in a basin ...

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