Questions tagged [celestial-mechanics]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
2answers
53 views

Central force problem

Two masses, $m$ and $2m$, orbit around their CM (center of mass). If the orbits are circular, they don’t intersect. But if they are very elliptical, they do. What is the smallest value of the ...
0
votes
0answers
38 views

How to solve a general planet orbit differential equation? [on hold]

According to Newton's gravitation law, the following differential equation can be made $$\frac{d^{2}}{d t^{2}} \mathbf{x}{\left(t \right)} = - \frac{G M }{\left|{\mathbf{x}{\left(t \right)}}\right|^{...
0
votes
1answer
51 views

Do all the planets in our solar system orbit the sun in the same direction and in the same plane?

Do all the planets in our solar system orbit the sun in the same direction and in the same plane? (as in a flat orbit if you are looking from "above")
1
vote
1answer
121 views

Kepler's 3rd law/law of periods

Kepler's 3rd law of planetary motion is The square of the time period of a planet orbiting a sun is proportional to the cube of the semi major axis of the elliptical orbit. $$(T_1)^2   =   (A_1)^...
0
votes
1answer
40 views

Ever looming shadow

If I'm not mistaken the reason the moon eclipses the sun is because the ratio of distance to size, in regards to the moon and sun, is 1:1. And is it not also true that the reason we only ever see one ...
2
votes
5answers
137 views

What is the reason for Moon and satellite in free fall condition?

I am a high school student. I read in my book that moon and satellite are in free fall condition with Earth. I asked my teachers about this, but I'm not able to understand. Can anyone explain to me ...
2
votes
1answer
43 views

Particle moving on ellpse with foci as origin

I'm reading the book "An introduction to Celestial Mechanics" by Forest Ray Moulton. In the first chapter, I got stuck on the following problem: A particle moves in the ellipse whose parameter and ...
0
votes
0answers
10 views

How to calculate orthogonal component of trajectory after pass through orbital plane of 2-body system

For an encounter between a stable 2-body system and a 3rd body which has sufficient velocity to escape after a pass through the orbital plane between these two objects, I am setting up the frame of ...
3
votes
1answer
961 views

Determing Velocity of Moons

I have a question that I believe is relatively easy to answer, I am working on an $N$-body simulation of a fictional star system and am having trouble finding the velocity of moons so that they will ...
0
votes
1answer
33 views

Ptolemaic system parameters

I recently learned about the Ptolemaic system, which seems pretty accurate. There is even a simulator on the Internet: https://astro.unl.edu/naap/ssm/animations/ptolemaic.html You can see that there ...
0
votes
1answer
35 views

What is the relation between Earth's orbit and orbit of another planet around Sun? [closed]

Lately, I come across the following problem, "The maximum and minimum speeds of a comet that orbits the Sun are 80 and 10 km/s respectively. The ratio of the aphelion distance of the comet to the ...
1
vote
1answer
127 views

Velocity in different time frames

A satellite orbiting the earth experiences time faster than a person on earth as its in a weaker gravitational field (which has a greater effect than the slowing down of time caused by its motion) ...
6
votes
4answers
8k views

How is it possible for orbits to maintain stability?

According to $a = v^2/R$, the circular velocity and radial distance between two attracting objects (such as planets), must remain in perfect proportion in order for orbital motion to take place. How ...
0
votes
2answers
65 views

Which orbit planet will take with 2 stars?

Is there a law or an equation that shows which star gravity will win and suck a a planet that has 2 stars Assume planet P has 2 stars A & B A is smaller than B Planet P is closer to A more than ...
1
vote
2answers
89 views

On Planets orbiting binary stars

Several years ago a discovery was made of planet orbiting a star of a binary system (two stars orbiting each other). Since binary star systems are plentiful in our galaxy, I presume we will be ...
3
votes
2answers
230 views

Orbital period and nodal precession & apsidal precession

In classical orbital mechanics as per Newton/Kepler, the time taken to complete one orbit around a body of mass $M_e$ is: $$ T = 2 \pi \cdot \sqrt { \frac {a^3} {G \cdot M_e} } $$ But also, for ...
2
votes
1answer
38 views

Mars longitude reference?

Platforms like NASA's JPL HORIZONS web-interface for solar system dynamics often have obtainable parameters like sub-solar or sub-terrestrial longitude for a given time and celestial object. (example: ...
3
votes
1answer
163 views

Gravity assist, Coordinate system transformation

I am currently learning about the physics and the mathmatics behind gravity assist. I have a question regarding the coordinate transformation between the planet frame and the sun frame. I want to ...
34
votes
3answers
6k views

Is there a maximum distance from a planet that a moon can orbit?

Given a planet that orbits a star, and a moon that orbits that planet, is it possible to define a maximum orbital radius of that moon, beyond which the moon would no longer orbit the planet, but the ...
7
votes
3answers
339 views

Do SR account for one sixth or one third of the anomalous perihelion shift?

In answers to two other questions on this site: Mercury's Orbital Precession in Special Relativity and Do 2-body elliptic orbits precess in special relativity? it is stated that special ...
1
vote
1answer
263 views

Geocentric Ecliptic to Perifocal Coordinate Transformation

I'm self-studying elementary orbital mechanics and am experimenting with transforming satellite position and velocity vectors between different coordinate systems. I know there are coordinate ...
1
vote
0answers
42 views

Why are so few inclined circumbinary planets known?

For a research project I'm studying the orbits of circumbinary planets, most of these planets orbits are coplanar. However I was wondering if orbits with a high inclination could be stable. I made a ...
1
vote
3answers
2k 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 ...
2
votes
2answers
256 views

The Earth revolves around the Sun or the Sun revolves around the Earth

Well, in today's world we know that the earth resolves around the sun. But that is seen from frame of reference of sun or an observer stationary wrt sun. From frame of reference of the earth, sun ...
7
votes
2answers
1k views

What are the forces behind the orbit of the Earth around the Sun?

Does the gravity of the sun alone affect the orbit of the earth around the sun? Look at the image below,(Image is not to scale), Is it that when earth is going from position 1 to position 2, it ...
4
votes
6answers
18k 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 ...
3
votes
3answers
217 views

Since the Earth orbits the Galaxy, why doesn't it “fly away” from astronauts?

It is known that the Sun (and thereby all the planets in our Solar System) orbit the center of our galaxy at roughly 1 million miles per hour. From our point of view on Earth, everything looks ...
0
votes
2answers
75 views

Revolution of Earth around the Sun

We study the orbit of many planets around the sun modelling it as a uniform circular motion. Is this due to the fact that empirically we measured that the magnitude of the earth's velocity (for ...
16
votes
7answers
5k views

Why does the Earth follow an elliptical trajectory rather than a parabolic one?

I was taught that when the acceleration experienced by a body is constant, that body follows a parabolic curve. This seems logical because constant acceleration means velocity that is linear and ...
1
vote
1answer
741 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
43 views

How did most of the math and physics formulae that govern our lifestyle and help us in space exploration come into being? [closed]

I realise that this isn't a very academic question, but after watching movies like First Man and Interstellar, it got me wondering: How did all these formulas that we use on a regular basis come into ...
8
votes
4answers
878 views

What is the origin of spin of celestial objects?

In an older question from June 2011, Why does each celestial object spin on its own axis?, apparently revived by the system, a user is asking about the origin of the rotation of celestial bodies. The ...
0
votes
1answer
382 views

How do I use Kepler's Laws to propagate an orbit for a Two-Line Element (TLE) Set?

I need to propagate a large number of orbits (get a satellite's position at a certain time) from TLEs (two-line element sets) using Kepler's laws. Ordinarily I'd use a real propagator like SGP4/SDP4, ...
7
votes
5answers
1k views

Kepler's 3rd law: ratios don't fit data

I have been looking at satellite orbits around the earth, or any object around any planet in fact, and am trying to find the orbital radius, or semi major length of a given satellite. Kepler's third ...
-1
votes
1answer
36 views

About Kepler's laws [closed]

Yesterday I was reviewing some calculations using Kepler's laws and when working the third law that relates orbital periods and distances, it is very normal that, given the parameters of some object ...
0
votes
2answers
53 views

How to find Lagrange point $L_2$ of the Earth-Moon system?

I was tasked in my programming lesson to find a value of L1 correct to 5 significant figures, but in my discussion section I began to wonder why there was no second solution to the equation I was ...
40
votes
8answers
8k views

“Falling upward” - how far you have to be from Earth to start falling to the Moon?

Talking about gravity with my 9 y/o she asked when do we start "falling upward" to the Moon. What is the distance at which the Moon's gravitational attraction is higher than that of the Earth and thus ...
1
vote
1answer
75 views

Two bodies orbiting around common barycenter

Assume $2$ bodies of mass $M_1$ and $M_2$ orbiting in a plane around their common barycenter $G$. It means the axis $(M_1M_2)$ is rotating in the plane around a vertical axis through $G$. [Please ...
11
votes
3answers
2k 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 ...
-1
votes
2answers
53 views

Why do planets revolve around Sun in elliptical orbits? [duplicate]

Let’s consider two planets of mass $m$ and $M$. They both will attract one another with a constant force $F$ according to the law of attraction $F=G m M/r^2$. The force and masses are constant. $G$ is ...
0
votes
1answer
66 views

Two-body problem - point of closest approach

I am reading through an exercise : One of the hints to solve this problem is that at the point of closest approach the comet's velocity must be tangential only, why is this the case ?
1
vote
3answers
327 views

Calculating speed of satellite in vacuum?

Satellite speed is $35\ \mathrm{km/s}$ after burn for $500\ \mathrm{ sec}$ and after some days or months this speed is reduced automatically $34$, $33$, $32$ respectively. Questions: How the ...
1
vote
0answers
63 views

Mass distributions within two bodies such that the orbit is no longer Keplerian?

The trajectories of two point masses or spherically symmetric masses with respect to their center of mass are conic sections or Kepler orbits. Consider that the bodies have finite size with respect ...
-1
votes
3answers
80 views

Radius of the Sun

Is it possible to calculate the radius of the sun with minimal amount of physics? I couldn’t find resources on the internet that gives me an answer using a theoretical formula. You are given values ...
0
votes
1answer
52 views

Is there any model explaining why would a particle revolve around another one in an elliptical orbit? [duplicate]

The reason for asking this question is to understand the elliptical orbits of planets and why aren't they circular, we know that if a particle moves with an initial velocity perpendicular to the ...
0
votes
1answer
46 views

How was the equation for a gravitational assist derived?

Im currently writing a paper about a hypothetical probe meant to escape our solar system and I want to analyse how gravitational assists would be beneficial for its mission. I found a website with an ...
0
votes
2answers
62 views

What's the nicest proof that two isolates masses orbit their center of mass? [duplicate]

Although it seems intuitive, I haven't found proof of this fact in my textbooks from a purely mathematical standpoint. I was wondering if anybody knows of a particularly elegant proof of this fact, ...
-1
votes
1answer
89 views

Why doesn't the Earth slowly collapse into the Sun? [duplicate]

I understand that the sun exerts a force on the earth and that if that was the only force exerted on the earth then the earth would have already crashed into the sun a long time ago. The reason the ...
2
votes
2answers
62 views

How come planets with different masses can orbit at the same velocity at the same altitudes?

Angular momentum is equal to r × p and angular momentum is also what gives planets with lower orbits a higher speed (because angular momentum is conserved). So as r decreases either m or v (p=mv) has ...
2
votes
2answers
38 views

How can I determine a planet's mass based only off of information about its orbit and its parent star?

I'm coding a video game with procedurally generated planetary systems and I want some and I want to make sure I'm at least somewhat scientifically correct. I've reached the part in my code where I ...