# Tagged Questions

The path a body takes while moving through space under the influence of the gravitational forces of other bodies

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### Why is the orbital resonance of the Galilean moons stable?

It is well known that the orbits of Ganymede, Europa and Io are in a 4:2:1 resonance. Most online sources (including but not limited to Wikipedia) say that such an orbital resonance, along with the 3:...
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### Why do they think WT1190F is low density?

A piece of space debris WT1190F is in the news in part because it has been far from earth (farther than lunar distance) in the past but will re-enter earth's atmosphere in a few weeks. See this open ...
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### Calculus used by Gauss to find Ceres' position?

With very little data, the great mathematician Gauss was able to predict the exact location of where to find the asteroid Ceres. If possible I would like a reconstruction of his work, from the data ...
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### Escape velocity for Schwarzschild metric

I can't fill in the gaps in my solution to this and assistance or a reference would be appreciated. The question begins with the straightforward derivation of the EoM for a massive particle orbiting ...
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### Calculation of a Gravity Resonance Keyhole

Can anyone describe the mathematics behind the calculation of a resonance keyhole (for a two-body model)? It seems like the size and position of the keyhole should be a function only of mass and ...
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### Do gravitational vawes deplete energy even if there's nothing they can affect?

I've read multiple times that one of consequences of gravitational waves being a thing is, that they make any orbit unstable. As long as the two or bodies orbit around each other, they create ...
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### From Newton to Kepler without infinitesimals

I've read some interesting calculus-free proofs of at least parts of the derivation of Kepler's Laws from Newton's gravitational force. One is of course Feyman's "Lost Lecture" (which was already ...
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### Different time between equinoxes

I calculated from here that there are 16 104 096 seconds between the vernal and autumnal equinox, if I made no mistake, this is some 650 592 s longer than the other half orbit. I imagine this is due ...
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### When Did Structures Begin to Orbit in the Universe?

In Big Bang Cosmology, I am familiar with the radiation era, and the moment of last scattering, but I am just not familiar with the physics of orbits, or of the “falling outward,“ if you will, that ...
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### Isn't the Jacobi constant just the Lagrangian times 2?

At this wikipedia page the Jacobi constant is expressed as: $$C_J=2\left(\frac{v^2}{2}-U\right)$$ where $U$ is the potential energy and $v$ is velocity. If kinetic energy $T$ is defined (as it ...
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### Is Earth/Luna tidal lock approaching faster?

Wikipedia pegs the mass of Earth at $5.972\cdot 10^{24}\,\text{kg}$ or $5.972\cdot 10^{21}\,\text{metric tons}$. Assuming Earth accumulates approximately $30,000\,\text{metric tons}$ annually. To ...
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### What are the equations of motion that model near light speed orbits of a massive body about incredibly massive bodies?

In Kip Thorne's recently published book, The Science of Interstellar, he describes, by means of an illustration, the complex nature of a spacecraft orbiting a massive black hole with velocities ~ 0....
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### How to calculate launch angle for tangentially launched satellites?

What is the value of theta for a satellite not falling back to the Earth if it is launched from the direction tangent to the surface of the Earth? I have found the escape velocity which is 11.18km/s, ...
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### Would a large, small mass object in orbit experience induced rotation

Imagine a large (multiple earth radii), very small-mass ring orbiting The Sun. Half of the ring would be closer to The Sun than the outer half. Since orbital velocity decreases with distance, two free ...
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### Computing 2d Orbital Parameters

When using formulas that describe a 2d orbit around a planetary body: is it actually OK for the semi-major axis $a$ to be negative? when $a$ is negative, it is impossible to compute mean anomaly ...
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### Where are the L3, L4, and L5 points of a hyperbolic orbit?

Do the L3, L4, L5 points exist in hyperbolic orbits? If yes, then where do they lie?
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### How to travel between tidally locked binary planets

Two planets of roughly the same volume and mass are orbiting each other. What would be the most efficient way to travel from one to the other? Seems unlikely, but could a rocket positioned at the ...
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### For two planets in a 2:1 mean motion resonance , where will their periastron and apastron points be?

I want to animate the changing orbits of planets when they enter a mean motion resonance. Using a 2:1 resonance, I want to show a low-mass inner planet and a low-mass outer planet being tugged by a ...
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### Projectile motion equations @ very (!) high starting velocity

I've already searched Physics StackExchange for some similar question but I didn't find anything about this. Assumptions: Earth is a perfect sphere with it's core (X,Y,Z) -> (0,0,0) as a reference-...
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### How does the Giant Impact Hypothesis resolve impulse for orbital insertion?

The Giant Impact Hypothesis describes that Earth's moon was formed from collision between a proto-Earth and another Mars-sized object. This collision ejected mass from the Earth into orbit, whereupon ...
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### Confused about the solution to a problem in IPhO 2001

The problem statement is thus. "Assume that M >> m0, so that the ordinary star is basically rotating around the neutron star in a circular orbit of radius r0. Assume that the ordinary star ...
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### Orbital period and velocity around a Kerr black hole relative to fixed stars

I've been trying to make progress on some of the smaller pieces of this question about the environment around a Kerr black hole. In order to calculate the effects of special relativistic Doppler shift ...
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### Does Earth eclipse the Sun at the L2 Lagrange point?

Is Earth's diameter large enough to eclipse the sun at the L2 Lagrange point? Or does the sun shine around the edges of the earth? I understand the useful area of the L2 Lagrange point is somewhat ...
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### Orbital period of a satellite in Kerbal Space Program

Let me start off by saying I am really bad at maths and physics, but lately I have been trying to calculate the orbital period of a satellite I have put in orbit around a planet called Kerbin in a ...
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### Laplace's method to determine orbits

I am trying to do the second problem by Laplace's method, it is in spanish but the only thing that matters are the asteroid's observations and the coordinates of Earth https://freeshell.de/~rgh/arch/...
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### Conservation of Angular Momentum…or not?

This is my first post on physics stack exchange, but I thought the question was more appropriate than on that of math.stack. I'm currently designing a crude model of the sun-earth orbit (which I have ...
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### Earth to LEO, gravity drag and potential energy

A lot of references indicate takes about 9.4 km/s of delta-v to reach LEO. https://en.wikipedia.org/wiki/Low_Earth_orbit#Orbital_characteristics The delta-v needed to achieve low Earth orbit ...
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### Bertrand's Theorem: Perturbative Methods Leading to $1/r^3$ Solution

My professor and I have been working on a proof of Bertrand's Theorem using perturbative methods. We have arrived at a solution yielding 1/r^3, which we had presumed to be an incorrect result. While I'...
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### Orbital elevators and the Coriolis effect

Consider an orbital elevator simply modelled as a large mass in geostationary orbit (altitude approx 36,000km) around the Earth, connected to a point on the equator via a strong, light, likely ...
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### What is the particle distribution in Saturn's Ring System?

In watching the scientifically scream-inducing film/movie 'Interstellar', there was a shot of the spacecraft moving through the Rings of Saturn. In this shot, and in every graphical representation of ...
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### Is there any free open source planetary orbit simulator software?

I need a free open source planetary orbit simulator software that should be able to calculate orbit stability for a couple simple planetary systems. Basically, I need to calculate orbit durations for ...
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### Reduced Three-body problem

I know that three-body problem in celestial mechanics can't be solved analytically in general. But suppose that the 3rd body is much smaller than the others, so it does not perturb their orbits. This ...
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### How to calculate orbital eccentricity from the ratio of satellites' velocities?

I have a problem with working out how to calculate the orbital eccentricity from the ratio of two satellites' linear velocities. We know that two satellites encircles the Earth in two elliptical ...
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### Do doomsday arguments influence doomsday hypotheses?

The doomsday argument supposes that in the absence of any other knowledge, if we know the age of something now, we may assume that we are seeing it in the middle of its lifetime and then calculate our ...
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### Terrestrial Space Elevator Construction - Plausability

Framework If there was a cable constructed at the equator about the circumference of the Earth, and if this cable had sufficient strength to remain intact while erect, call this tensile strength T. ...
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### Application of trigonometry to the slingshot effect/gravity assist

I have been trying to understand the formula $$v_f^{2}=v_i^{2}+2V(V(1-\cos\beta)+v_i(\cos(\alpha-\beta)-\cos\alpha))$$ as it relates to Fig. 2 on page 5 of this exposition: http://maths.dur.ac.uk/~...
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### Compute and plot satellite position on 2D Earth map

I would like to create a simple satellite tracking software, that will compute the position of a satellite at any time, and show its location on a 2D map of Earth. Let's assume it is possible to ...
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### Ratio of position error of orbiter to the size of the orbit

This is an assignment question for online AP physics. As if it isn't already tough. This question is killing me. I even asked my physics teacher from last year and my calculus teacher. It stumped them,...
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### What causes an electron to return from a higher orbit to a lower orbit

Ultraviolet light can cause electrons from Hydrogen gas to jump from a lower energy orbit to a higher energy orbit. What causes the electrons to return from the higher energy orbit to the lower energy ...
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### Would ferromagnetic space debris have been magnetized by their orbit in the Earth's magnetosphere?

Given a nail, and a magnet it is possible to magnetize the nail by patiently rubbing the nail until it is magnetized; albeit the field strength may be less than that of the source. With several ...
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### Heliocentric Cartesian position of moons

I have a working Kepler orbit system that is GPU accelerated to allow precision, speed and parallelism and more importantly allow as many factors as possible in calculation. For various reasons I ...
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### What would be the long-term effects of stopping the Sun?

TL;DR: In an orbital simulation, what are the effects of pinning the major body to the origin, and how could these effects, if any, be mitigated? Consider an orbital motion simulator; your basic n-...
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### Keplerian orbits and radial velocities: problem with true anomalies

I am writing a pure Python code to calculate radial velocities of stars with massive objects orbiting them. I am following the formalism from Murray & Correia (2011) (hereafter MC11). In a given ...
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### Tidal heating of body

I am trying to make a plausible, though not necessarily accurate model of tidal heating of a body moving close by a gravitational attractor, not necessarily in orbit and not considering the spin of ...
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### Derivation of Bohr model equations (1) in his original paper

My question is rather straightforward. In his original paper ("On the Constitution of Atoms and Molecules") Bohr provides equations (1) for the frequency and major axis orbit: \begin{align} \omega &...
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### Deriving Stumpff functions for parabolic and hyperbolic orbits

I would like to know how I can derive Stumpff functions analytically for hyperbolic and parabolic orbits? It would be nice if you could tell me where I can read about it. Thanks, KS