2
votes
1answer
38 views

Unexpected eccentricity in moon orbit simulation

I've used Mathematica's NDSolve function to calculate the orbit of the Moon around the Earth. I used the following initial positions (perigee): ...
1
vote
1answer
39 views

Getting first and second time derivative of mean motion of spacecraft - without TLE?

The Celestrak website provides information on reading the TLE ( Two-Line Element Set ) format. In Line 1, Column 34-43 & 45-52 give information about ...
1
vote
1answer
73 views

My orbiting body is orbiting about the wrong focus of it's elliptical orbit… why?

I am coding in c++ and am computing the position of an orbiting body as a function of time. Everything is almost working. I have a nice elliptical orbit. Except, my orbiting body speeds up as it ...
8
votes
1answer
67 views

What could cause an asymmetric orbit in a symmetric potential?

My question can be summarized as: Given a potential with a symmetry (e.g. $z\rightarrow-z$), should I expect orbits in that potential to exhibit the same symmetry? Below is the full motivation for ...
4
votes
2answers
145 views

Gravitational slingshot maximum

I have recently read an article about gravitation slingshot assist used by Voyagers 1-2, and was thinking on why this hasn't been used for travel between solar and other systems. I mean sligshot can ...
0
votes
0answers
37 views

Effect of small variable transverse force on satellite orbital precession

Consider a small satellite which moves in a 2D elliptical orbit around a much larger body (e.g. the Sun) under the influence of Newtonian gravitational acceleration $$Ar = G.M/d^2 $$ Next imagine ...
0
votes
1answer
76 views

Which planet in the solar system is it?

It is known that the period of revolution of the earth about the sun is $365.3$ days and that the semimajor axis of the earth's orbit is $1.495 \times 10^{11}$ m. An astronomer notes that the ...
2
votes
1answer
45 views

Synchronized rotation of the moon

Does the moon rotates? Yes. The rotation matches exactly the orbit of the Earth. Which means in 28 days the moon makes one rotation. Shouldn't this be also happening with the Earth rotation around the ...
7
votes
3answers
1k views

Kepler's third law doesn't give earth's orbital period! Why? [closed]

I tried to calculate earth's orbital period using Kepler's third law, but I found 365.2075 days for the orbital period instead of 365.256363004 which is the correct value. I checked everything, and I ...
1
vote
1answer
79 views

What are Lagrange points in gravitation fields? [closed]

What are Lagrange points in gravitation fields? Additionally, what are their properties? For example, if a satellite or asteroid rested at a Lagrange-point.
2
votes
2answers
191 views

Why do the planets orbit the Sun? [duplicate]

Why do the planets orbit the Sun? If it's because the gravity of Sun then why don't they just fall in and burn up?
5
votes
1answer
168 views

How to derive Kepler's equation?

The Internet lacks, so far as I know, a derivation of Kepler's equation $$ M = E - e\text{sin}(E) $$ where $M$ is the mean anomaly, $E$ the eccentric anomaly and $e$ the eccentricity. Since there ...
1
vote
2answers
61 views

Finding sphere of influence in multibody system

I would like to draw a boundary illustrating the sphere of influence of each body in a 3 body system. What is the best way to find such a boundary? My understanding is at the edge an SoI is the ...
3
votes
0answers
81 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
1answer
145 views

Can a very small portion of an ellipse be a parabola?

We consider that when a body is projected from any height from the earth surface with a speed lesser than the orbital speed ( tangentially to the earth surface at that point.) it follows an elliptical ...
4
votes
2answers
201 views

Is tripleaxis planet possible?

Imagine. Our solar system. Our sun. Then earth and moon orbiting it. And you have "powers" to create any planet you want, any size, any density, any weight and any velocity. Would it be possible for ...
0
votes
2answers
41 views

Why turning velocity of star towards point “A” makes it's satelites, change their apoapsis to side opposite of velocity vector?

Why turning velocity of star towards point "A" makes it's satelites, change their apoapsis to side opposite of velocity vector? Sentence above turned a bit crazy or not understandable (possible ...
1
vote
1answer
118 views

Determine orbital position after change in velocity

I am working on a satellite simulator for a project/game and I am stuck on this one bit of physics. So far I have a satellite that revolves around earth on a 2D plane following Keplerian motion using ...
4
votes
0answers
106 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 ...
2
votes
3answers
196 views

How to find a hyperbolic escape orbit with a starting point and a desired velocity after sphere exit

How would you find an escape orbit which includes a given starting point (not assuming a circular starting orbit) and escapes the sphere of influence of the current body with a given remaining ...
1
vote
1answer
121 views

Do convection currents under the crust affect Earths motion in the solar system?

Whilst browsing through this website I began to wonder whether all of that molten rock underneath the Earth's crust would have a notable effect on how the Earth moves in it's orbit of the Sun. ...
0
votes
0answers
56 views

How to derive “Anti-Lagrangian” $L_4$ and $L_5$ points

In this paper on co-orbital dynamics the authors discover, numerically, "Anti-Lagrangian" solutions to the restricted 3 body problem. These Anti-Lagrange $L_4$ and $L_5$ points are 120 degrees ahead ...
0
votes
0answers
33 views

Will the moon really escape the Earth? [duplicate]

I heard that the moon is moving away from the Earth gradually. Will it escape at some point?
1
vote
2answers
232 views

Why do orbital speeds decrease further away from the focus?

Why do orbital speeds decrease further away from the focus? A simple question, but I want to make sure I am understanding this correctly: Is it ONLY a function of the gravity well? As in, the ...
1
vote
1answer
119 views

The circumference of the Moon's orbit around the sun?

I know that it orbits the sun in what looks like a 12 sided polygon with rounded corners. But I can't seem to find the radius/circumference anywhere.
2
votes
5answers
2k views

Why the center of our galaxy doesn't absorb us?

Depending on the theories, the center of our galaxy is a super massive black hole, this is easy to accept as a truth, but what I couldn't simply devour is how the solar system is orbiting around it ...
1
vote
0answers
65 views

Interpretation of a quantity from the reduced three body problem [closed]

Consider two bodies $S$ and $J$ that gravitate about their center of mass $O$, under the influence of mutual attraction. A third massless body $P$ is moving in the same plane. What is the ...
2
votes
0answers
227 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 ...
7
votes
3answers
253 views

Falling through the rotating Earth

Suppose you were standing on the rotating Earth (not necessarily Equator or the poles) and suddenly your body lost the ability to avoid effortlessly passing through solid rock. Because the earth's ...
9
votes
3answers
277 views

Can an orbit be calculated using two points and transit time?

Working in only two dimensions and assuming that the central body is at the origin of the coordinate system, given two points in space and knowing the transit time between those points, as well as the ...
9
votes
6answers
20k views

Gravity on the International Space Station

We created a table in my physics class which contained the strength of gravity on different planet and objects in space. At altitude 0(earth), the gravitational strength is 100%. On the moon at ...
16
votes
4answers
5k views

What did general relativity clarify about Mercury?

I frequently hear that Kepler, using his equations of orbital motion, could predict the orbits of all the planets to a high degree of accuracy -- except Mercury. I've heard that mercury's motion ...
3
votes
0answers
177 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 ...
3
votes
4answers
2k views

Historically, how do we know that Earth moves around Sun? And it does so in an elliptical orbit?

I know the basics of solar system like how Earth moves around Sun, and that we have so many planets, elliptical orbit of earth, and how far is sun from earth etc etc. I want to take a step back and ...
6
votes
3answers
313 views

How accurately is the moment of perihelion of Earth known, and how is it measured?

Earth's perihelion passed about nine hours ago. How accurately do we know the moment of closest approach of the Earth to the center of the sun? How do we make this measurement?
18
votes
6answers
3k views

Why are the orbits of planets in the Solar System nearly circular?

Except for Mercury, the planets in the Solar System have very small eccentricities. Is this property special to the Solar System? Wikipedia states: Most exoplanets with orbital periods of 20 ...
5
votes
2answers
449 views

How about an exact solution for the position of a planet as a function of time?

Recently I was surprised to discover that no exact solution for the position of a planet as a function of time exists. I am referring to the two-body problem in a gravitational field where Newtons law ...