3
votes
2answers
77 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 ...
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 ...
1
vote
1answer
80 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?
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
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 ...
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 ...
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 ...
1
vote
2answers
235 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
120 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.
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.
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 ...
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 ...
1
vote
1answer
303 views

What is the typical orbital life of an artificial satellite?

The orbit of satellites around Earth eventually decays, or so I read. This is typically caused either by atmospheric drag, or by tides. I would assume most satellites have a limited service life in ...
5
votes
2answers
451 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 ...