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3
votes
2answers
75 views

What is the “associated scalar equation” of equations of motion?

In an essay I am reading on celestial mechanics the equations of motion for a 2 body problem is given as: $$\mathbf{r}''=\nabla(\frac{\mu}{r})=-\frac{\mu \mathbf{r}}{r^3}$$ Fine. Then it says the ...
0
votes
1answer
36 views

What does an $n$-body system with constant $T$ and $U$ look like?

Can someone give an example of a system where the kinetic $T$ and potential $U$ energy are constant (but not zero)? Here's what I have in mind: Say you have $n-1$ satellites of negligible mass ...
2
votes
1answer
41 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
45 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
0answers
127 views

Story about a mathematician, a dinner party, and the three-body problem

I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story ...
1
vote
1answer
75 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 ...
0
votes
0answers
43 views

How can I describe an equation for multiple objects over time?

Lets say i have $n$ different objects that effects each other only by the classic gravity force. I have their initial locations, masses and velocity's: $$ x_1(0),\cdots,x_n(0) $$ $$ m_1,\cdots,m_n ...
8
votes
1answer
68 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
149 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
32 views

Initial conditions at Lagrange Points

I'm simulating the restricted three body problem. But I don't know how to found the initial conditions of the object located at the Lagrange points analytically or computationally. I mean my problem ...
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 ...
0
votes
1answer
58 views

Square Cube Law?

I've heard about something called the square cube law. What is it? All I know of it is that it has something to do with mass of large objects and their gravitational influence.
2
votes
1answer
46 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 ...
1
vote
0answers
24 views

The equation of the location of L1

On http://en.wikipedia.org/wiki/Lagrangian_point#L1 it says that the location of L1 can be determined as $\frac{M_1}{(R-r)^2}=\frac{M_2}{r^2}+\left(\frac{M_1}{M_1+M_2}R-r\right)\frac{M_1+M_2}{R^3}$, ...
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
195 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
171 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
1answer
45 views

Convert constant of gravitation to days and AUs

I'm working on a problem with celestial bodies and for my purpose days and AUs are more appropriate units than seconds and meters. So I tried to convert the constant of gravitation, $G$, like this: ...
1
vote
0answers
44 views

Radial and tangential velocities of a star

(source) Early in this piece it states that the radial and tangential velocities are: $$V_r = V_c \cos(\alpha) -V_{c,0} \sin (l)$$ $$V_t = V_c \sin(\alpha) -V_{c,0} \cos (l)$$ but I am struggling ...
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
83 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
146 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
202 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
120 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
111 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
197 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
123 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
57 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 ...
2
votes
3answers
813 views

Converting between Galactic and Ecliptic coordinates

I was hoping someone would be able to tell me the formula to convert between ecliptic and galactic coordinates. I've been able to convert values using ...
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
234 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 ...
0
votes
0answers
62 views

Orbital motion (Mechanics) [duplicate]

I am a student in Mechanical department and I took today a lesson with a title of Orbital motion. I need a good mechanics reference that discusses this topic.
5
votes
2answers
173 views

Celestial Time-Keeping and Navigation

Say, for sake of argument, someone was randomly transported in time and space. Would it be possible for them to determine their location on Earth and the current time using just observations of the ...
2
votes
0answers
230 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 ...
0
votes
0answers
76 views

Relation between the period of rotation and the period of revolution of a satellite

I read somewhere that the tidal forces between the earth and the moon causes the equality between the 2 periods of the moon and that every planet-satellite system will evolve to this condition (like ...
8
votes
3answers
266 views

Parallax, obliquity, precession, and Orion?

Today, the obliquity of the earth is about 23.4°. 6500 years ago, it was about 24.1° Imagine the blue square is the constellation of Orion, and the yellow star is the sun. Viewpoint B is you, on ...
0
votes
1answer
170 views

Does the possibility of large scale entanglement mean 2-Body Problems are also unsolvable?

Experiments are showing that larger and larger objects can be entangled whereby proving that this quantum feature has no upper limit. Assuming this is true, does entangled celestial bodies mean even ...
0
votes
1answer
102 views

Relation between satellites' potential energy and quantum mechanical confinement energy?

The energy of a single planet in a gravitational potential is $$E=\frac{m\dot{r}^2}{2}+\frac{L^2}{2mr^2}-\frac{GMm}{r}$$ And the effective potential energy is defined as the last two terms. Note this ...
1
vote
3answers
741 views

Speed of the Moon

Why the motion of the Moon looks very slow in the sky? Doesn't it need the high speed in order to escape the earth's gravity?
7
votes
3answers
254 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
280 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 ...
5
votes
1answer
214 views

Potential Energy tends to infinity on the N-Body Problem

I need help to solve this problem related with the N-Body problem, i dont understand quite well what I need to define or to express in order to solve it. We assume a particular solution to the N-Body ...
6
votes
2answers
163 views

Is there any dynamical reason for the winter solstice to happen close to the perihelion?

When the winter solstice arrives, the angular momentum of the Earth, its orbital angular momentum and its radius vector with the orbital focus in the Sun are in the same plane. This happens quite ...
4
votes
1answer
1k views

What would it be like if we had a planet very close to us?

My desktop background rotates through a bunch of space and nature scenes, and this one came up. What would be the effect on people walking around down here, if another earth was looming overhead ...