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

learn more… | top users | synonyms (1)

6
votes
0answers
59 views

Lyapunov stability of circular orbits

I'm studying Classical mechanics on Arnold's "Mathematical Methods of Classical Mechanics". In a problem i'm asked to find for which $\alpha$ the circular orbits in the central field problem are ...
6
votes
0answers
430 views

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:...
5
votes
0answers
118 views

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 ...
4
votes
0answers
98 views

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 ...
3
votes
0answers
45 views

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 ...
3
votes
0answers
115 views

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 ...
3
votes
0answers
39 views

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 ...
3
votes
0answers
75 views

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 note ...
3
votes
0answers
62 views

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 ...
3
votes
0answers
246 views

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 ...
3
votes
0answers
141 views

Travel time in elliptical orbit around the sun

Hi I'm calculating a problem, and I think it ought to be correct - but the result I get isn't. The problem is described as follow: A spacecraft is traveling from Earth to Venus in an elliptical, ...
3
votes
0answers
121 views

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 ...
3
votes
0answers
218 views

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 ...
2
votes
0answers
160 views

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....
2
votes
0answers
248 views

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, ...
2
votes
0answers
45 views

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 ...
2
votes
0answers
101 views

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 ...
2
votes
0answers
63 views

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?
2
votes
0answers
93 views

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 ...
2
votes
0answers
536 views

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 ...
2
votes
0answers
326 views

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-...
1
vote
0answers
54 views

On the Stability of Circular Orbits

Bertrand's Theorem characterizes the force laws that govern stable circular orbits. It states that the only force laws permissible are the Hooke's Potential and Inverse Square Law. The proof of the ...
1
vote
0answers
64 views

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 ...
1
vote
0answers
48 views

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 ...
1
vote
0answers
51 views

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 ...
1
vote
0answers
28 views

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 ...
1
vote
0answers
25 views

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/...
1
vote
0answers
71 views

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 ...
1
vote
0answers
42 views

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 ...
1
vote
0answers
26 views

Eccentricity of planetary orbits: What information is contained?

I'm having a little trouble understanding what makes a planetary orbit explicitly elliptical. Is it simply that the initial velocity was different from the circular orbit case for a given starting ...
1
vote
0answers
42 views

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'...
1
vote
0answers
33 views

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 ...
1
vote
0answers
255 views

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 ...
1
vote
0answers
139 views

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 ...
1
vote
0answers
197 views

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 ...
1
vote
0answers
365 views

How to show circular orbit as a precessing ellipse

A uniform distribution of dust in the solar system adds to the gravitational attraction of the sun on the planet an additional force linear in $r$ where m is the mass of the planet, k is a constant (...
1
vote
0answers
98 views

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 ...
1
vote
0answers
67 views

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. ...
1
vote
0answers
229 views

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/~...
1
vote
0answers
292 views

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 ...
1
vote
0answers
30 views

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,...
1
vote
0answers
189 views

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 ...
1
vote
0answers
69 views

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 ...
0
votes
0answers
28 views

Average of the velocity vector along a Keplerian orbit

I would like to show that the average of the velocity vector $\mathbf{v}$ along one Keplerian orbit vanishes, i.e. $$ \frac{1}{2 \pi}\int_{0}^{2 \pi} \!\!\!\! \mathrm{d} M \, \mathbf{v} = \frac{1}{T}\...
0
votes
0answers
59 views

Why does a velocity that gives gravity's centripetal acceleration make you stay in orbit?

Explanations of basic orbital mechanics that I can find all go, $$\frac{v_{satellite}^2}{r} = a_c = \frac{F_{gravity}}{M_{planet}} = \frac{(\frac{G M_a M_s}{r^2})}{M_{planet}}$$ , and so you get a ...
0
votes
0answers
30 views

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 ...
0
votes
0answers
42 views

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-...
0
votes
0answers
27 views

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 ...
0
votes
0answers
16 views

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 ...
0
votes
0answers
40 views

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 &...