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

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390 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 ...
4
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86 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 ...
4
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103 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 ...
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98 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
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34 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
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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 ...
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188 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
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131 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
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120 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 ...
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215 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
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67 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 ...
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142 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 ~ ...
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201 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, ...
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43 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 ...
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99 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 ...
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60 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?
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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 ...
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0answers
480 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 ...
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315 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 ...
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22 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 ...
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65 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 ...
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36 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 ...
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23 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 ...
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40 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 ...
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31 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 ...
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180 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 ...
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116 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 ...
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151 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 ...
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318 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 ...
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97 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 ...
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65 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. ...
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207 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: ...
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245 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 ...
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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 ...
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172 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 ...
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62 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 ...
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28 views

Finding the distance a spaceship would travel given a time of departure and velocity

Let's say a spaceship leaves Earth at a day t and with velocity v. Is there a way to know how many kilometers it will cover to arrive on Mars? This would be a trivial question were it not by the fact ...
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32 views

Could a satelite be pulled away by gravity while the object it was orbiting keeps unaffected in its own orbit?

I'm asking this, since I try to educate my self a bit in the field of astrophysics. From my point of knowledge the by title given scenario could occur. But I haven't yet read anything that sounded ...
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16 views

What orbital elements would show earth orbiting in the opposite direction?

Would earth rotate in the opposite direction if inclination and argument of periapsis were 180 degrees? Looking at this diagram: https://en.wikipedia.org/wiki/Argument_of_periapsis Thanks!
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11 views

Initial guess for calculating the Universal Variable Formulation of the two-body Kepler problem

I am trying to simulate orbits using the Universal Variable Formulation of Keplers two-body problem, using the algorithm provided by Howard curtis in Orbital Mecanichs for Engineering Students as per ...
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37 views

Orbit of a planet

Can a planet move around a star in an exact circle? Does Kepler's laws prevent this from happening. Answers with mathematical base will be accepted.
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22 views

Einstein-Infeld-Hoffman Equations generalized coordinates

There are three (heavy,fast) bodies in a Cartesian coordinate system with position vectors $\{\mathbf{r_1},\mathbf{r_2},\mathbf{r_3}\}$, velocities ...
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49 views

Does a planet's orbital angular momentum affect its rotational angular momentum?

For example: If the moon was closer to the earth, assuming the orbital momentum was conserved and not worrying about earth's rotation, would the moon's rotation rate be effected?
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24 views

Is it possible to determine perigee distance from distance recordings from a spacecraft to Earth?

If you are on a spacecraft orbiting earth in an elliptical orbit and were able to take measurements of the distance between the spacecraft and earth as well as the time intervals between those ...
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32 views

Lunar orbit homework question

So what I did was find the potential energy of the lander at the 50km orbit and the 300km orbit, then I took the difference between the 2 potential energies and I though that would be the work done ...
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63 views

Graduate level orbital mechanics book

I recently finished an undergraduate course in classical mechanics and really enjoyed the subject, particularly the sections regarding the mechanics of orbits. I am considering pursuing a graduate ...
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0answers
43 views

Finding position with respect to time along a trajectory across a sphere (orbital mechanics)

When trying to find an object's position with respect to time on a ballistic trajectory along a curved surface, what equation should I use? I know that when adding force to an object to achieve ...
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35 views

Efficient orbit transfer

Well simple orbital (in plane) manoeuvres are quite easy and straight forward. Currently I found however an orbit I have a hard time calculating/reasoning the ideal path to get to. - Just as a note, ...
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23 views

Time of an elliptical orbit

We know that T, the time of a revolution in an elliptical orbit is equal to the time of a circular orbit, can you tell what is the formula that relates time elapsed and space travelled (on the major ...
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32 views

How far inside a white dwarf Roche limit does the Earth have to be to start losing large chunks of rocks?

I have calculated that for a one solar mass white dwarf orbited by the Earth, the Roche limit is about 600,000 kilometers. I understand that any loose mass on the surface of the Earth would start ...