# What is Celestial mechanics: Definition and 39 Discussions

Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data.

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1. ### What are the latest developments in discrete Quantum Field Theories?

I have been interested in physics for a very long time. Initially in high school celestial mechanics and soon afterwards quantum mechanics. During my chemistry studies I specialized in quantum chemistry at the end of my bachelor and continued to do a Bachelor and Master in pure Mathematics, with...
2. ### I I need some support, please, for a gravity assist analysis

I am having a discussion with a couple of very obtuse individuals on another forum who think they know celestial mechanics, but do not. These two have long promoted themselves to be something they are not, and since I am rather new on the forum they are unwilling to even listen (or heaven...
3. ### Solving a Celestial Mechanics Task with Velocity Vector Scattering

Hi, the task is as follows Unfortunately, I am not getting anywhere at all with task c. I have now proceeded as follows: I assume that the calculation takes place in the reference system of the sun. In the task the following is valid, $$\vec{v}_{si}=-s\vec{v}_p$$ I have now simply assumed...
4. ### Maximum duration of Solar eclipses

The result I get is 2 hours and 10 minutes. My reasoning is down here. But! Checking the map for the 2024 Solar eclipse, https://www.timeanddate.com/eclipse/map/2024-april-8, in many locations you can see a partial eclipse of over 2 hours 40 minutes. What is the main source of error here? Here...
5. ### B Celestial mechanics: Why is my planet orbiting faster and faster?

I've tried to make a "naive" implementation of a planet orbiting a gravitational point source, in Processing (basically Java). Gravity is a constant, and adds to the planet's velocity inversely proportional to the square of distance. I start the planet off with a tangential velocity. I get an...
6. ### Classical Textbooks of celestial mechanics

Hi I'm reading classical mechanics by Taylor and there is a section about Kepler orbits that i find very interesting so i'd like to see more of classical mechanics with space applications. I appreciate rigouros mathematical books, thanks
7. ### Averaging the cube of semimajor axis to position ratio wrt to time

Summary:: Averaging (a power of) semimajor axis to position ratio wrt to time - celestial mechanics I evaluated it this far, but i don't know how to change the dt to d theta ... the final solution is supposedly (1-e^2)^-(3/2) . Any help will be appreciated. [Image re-inserted with correct...
8. ### B How long it takes the Earth to fall halfway to the Sun--ellipse method

There's a classic physics problem that is: If Earth is orbiting the Sun at 1 au from and is suddenly stopped. How long does it take to fall into the Sun (neglecting the size of the Sun/Earth)? I know that a clever way to solve this problem is by using degenerate ellipses and an object...
9. ### On the convergence of the three body disturbing function

For the three-body-disturbing function expanded in multipolar orders with respect to the ratio of the semi major axes, the function converges for small ratios, how to check the convergence for a certain set of parameters? I'm using the work of the Laskar in his paper "Explicit expansion of the...
10. ### Extract anomalies from two-line element set (TLE) on ISS

Homework Statement I am faced to a problem of interpretation illustrated on figure below : I must precise that I talk about **mean anomaly**. Homework Equations for the 2 questions, I am asked to find : 1) at which anomaly is the ISS at the two lines epoch ? 2) at wchich anomaly is the...
11. ### Deriving Ball Movement on Northern Hemisphere with Rotating Reference Frame

I have a ball of mass m that is situated on horizontal plane on the northern Hampshire. I am asked to show that the ball is moving, clockwise, in a manner of r = v / ( 2Ω*sin(λ) ) where v is the ball's velocity, Ω is Earth's angular velocity, and λ is the terrestrial latitude So here's what...
12. ### I Circular orbit + small radial oscillation about circular orbit

The potential energy of a particle of mass $m$ is $U(r)= k/r + c/3r^3$ where $k<0$ and $c$ is very small. Find the angular velocity $\omega$ in a circular orbit about this orbit and the angular frequency $\omega'$ of small radial oscillation about this circular orbit. Hence show that a nearly...
13. ### Solution to the Two-Body Problem: Cross-Product and Dot-Product Integration

Homework Statement Two-body problem given as $$\ddot{\textbf{r}}+\frac{GM}{r^2}\frac{\textbf{r}}{r}=0$$ $$\textbf{h}=\textbf{r}\times\dot{\textbf{r}}$$ where the moment of the momentum vector mh Homework Equations The vector solution to the above equation may be obtained by first taking the...
14. ### A How Do External Satellites Influence Planetary Ring Dynamics?

I'm working through a paper "Dynamics of Planetary Rings" by Goldreich and Tremaine (http://www.annualreviews.org/doi/pdf/10.1146/annurev.aa.20.090182.001341). I'm working through p.22 about expanding the potential of an external satellite as a double Fourier series. The external satellite is in...
15. ### Shell theorem: Gravity of a hollow planet

Homework Statement There is a planet (spherical) with a hollow that is concentric with the planet.if the inner radius is r and outer radius is R and mass of the planet is M what would the gravity be outside of the planet at distance x from the center ? Homework Equations Shell theorem...
16. ### Classical Lagrangian and Hamiltonian Celestial Mechanics

Hi folks, I am looking to learn the Lagrangian and Hamiltonian approach to celestial mechanics - I have previous experience in Newtonian numerical solutions for orbital motion but am looking to achieve similar things but through the use of Hamiltonian formulations. After having a poke around...
17. ### Help with contour plots of effective potential in R3BP.

Hello everyone! I'm currently trying to plot the effective potential for Sun-Jupiter system, to show the lagrangian points in this system. I've converted to a system of units where G=1, m_sun+m_jupiter=1 and R=1, whereby I get the following equation describing the effective potential of a third...
18. ### Classical Looking for "New methods of celestial mechanics"

Hello everyone, I am looking for Vol. I of "New methods of celestial mechanics" by H. Poincare and D. Goroff. Do you know where to find it as an actual pdf or djvu file? (disregarding fake free-ebook websites that ask you for your credit card before showing if they actually have the book). I...
19. ### Celestial mechanics, particularly as it relates to spacecraft navigation

I'm trying to teach myself celestial mechanics, particularly as it relates to spacecraft navigation. Essentially I'm interested in how spacecraft can get from A to B with the lowest delta-V (or whatever the criteria are), and how mission planners figure this out. Can anyone recommend a...
20. ### MHB Taylor's question at Yahoo Answers regarding celestial mechanics

Here is the question: I have posted a link there to this topic so the OP can see my work.
21. ### Celestial mechanics with symplectic integrators

Homework Statement The problem is that I just don't understand how the algorithm described here in section 2 hangs together... I have to present this on Thursday morning and that sensation of 'I'll never understand this soon enough' is growing ominously. Homework Equations Equations 2,6,7...
22. ### How to learn celestial mechanics?

I'm a PhD student in math and am really excited about celestial mechanics. I was wondering if anyone could give me a roadmap for learning this subject. The amount of information about it on the internet is overwhelming, and I honestly don't know where I should start. Any help would be...
23. ### Celestial mechanics & Stanford

Hi, I'm interested in celestial mechanics and would like to do an internship about it in Stanford, kind of computational one. I visited many projects webpages on Stanford's website but I didn't find anything about researchs including celestial mechanic ... What keywords should I use on Google...
24. ### Celestial Mechanics: Solving Differential Equations for N-Body Systems

I am getting stuck trying to solve a differential equation describing the gravitational relationship between two celestial bodies. What I have so far is this: a1 = G m2 (r2 - r1) / ||r2 - r1||^3 a2 = G m1 (r1 - r2) / ||r1 - r2||^3 where: boldface denotes vectors in 3 dimensional...
25. ### Why Don't Cowell's and Gauss' Methods Match for Osculating Orbital Elements?

Homework Statement The orbital elements (a,e,i,w,Omega,f) are to be integrated forward in time using two methods: 1) Cowell's method, which is direct interation, and 2) Gauss' Variational diffeential equations. The full assignment description, initial conditions, and my code are given in the...
26. ### Mass of Star Using Celestial Mechanics

Homework Statement A planet of mass 8.01 MJ (MJ = Jupiter's mass is known) has been discovered orbiting the star HD 168443 . HD 168443 is an G6 IV star of L = 2.09 Lsun and T = 5300 K about 37.9 pc from the Earth in the constellation Serpens Cauda. The planet, so far known only as HD 168443b...
27. ### How to learn celestial mechanics

Good morning, (I'm not sure if this is the right place for this question.) I want to learn about the Physics of orbits and how to calculate planets' position, velocity, etc. Basically, the only source I have is Internet, but the majority of the sites give incomplete and fragmented information...
28. ### Celestial Mechanics: Calc Mass & Velocity of Proton

Homework Statement a) Calculate the mas of a proton ( ms = 1.67 * 10^-27 kg) whose kenetic energy is half its toral energy. (ANS. 3.34 * 10^ -27 kg) b) How fast is it travelling? ( ANS. 0.87c) c- speed of light Homework Equations E(kenetic) = Gm(1)m(2) all over R^2 E(total) =...
29. ### Celestial Mechanics: Earth Orbit Time & Why 80 Minutes is Impossible

The greater the altitude of an Earth satellite, the longer it takes to complete one orbit. Why is it impossible for any vehivle to go aroung Earth in less than 80 minutes?
30. ### Macsyma package for celestial mechanics

Hello, I would like to make my hobby time somewhat easier. I would be interrested in a Macsyma package for celestial mechanics. I am first interrested by secular pertubation theory and using the Lagrange/Poisson bracket algebra. I have too little time and patience to develop such...
31. ### Does Reducing a Satellite's Speed Guarantee Its Descent to Earth?

Suppose we have a satellite orbiting in circular motion around the Earth (steady velocity) in a radius R.Everything is ok now. If suddenly we reduce the speed of the satellite is it bound to fall to the Earth ? Or it can continue moving in circular orbit with smaller R ? If i want it to fall ...
32. ### Dynamical systems: celestial mechanics, Poincare, Laplace, butterfly effect

There is a work in history of astronomy I've been preparing for the most of the time in living memory. I can't say is it late, or due, or long, but counting from the 3 books I've seen, the one in focus of some private interest is Michael Hoskin "Cambridge Illustrated History of Astronomy"...
33. ### Software for celestial mechanics

Hello, I would like a in-depth approach to some questions, like the Mercury's perihelion question. Precise definitions, precise result, access to full information. I think that computer programs and related input data are probably the most precise answer to my need. What is calculated is...
34. ### Understanding Gravitational Potential Energy of Artificial Satellites

I've bumped into a little problem while solving some tests for my physics course, so I'd appreciate some help :) : Consider an artificial satellite circling around the Earth; how much times is the absolute value of it's gravitational potential energy greater than it's kinetic energy?
35. ### Textbook on Numerical Celestial Mechanics

Forum, I'm seeking for a good textbook on numerical celestial mechanics. My current level of proficiency is: 1- understanding of classical mechanics is at the level of Goldstein's textbook 2- understanding of numerical analysis is at the level that I can easily pick up an algorithm from the...
36. ### Where can I find comprehensive formulas for Celestial Mechanics?

I was just wondering if anyone here , knows a good site (or a book) for general Formulas for Celestial Mechanics ? I have looked a little, But I only find one or two equations per site, and most of them are the same, So if you do know one that would be great
37. ### Geosynchronous Orbit | Min Speed for Satellite | Celestial Mechanics

How do I find out the minimum speed required for a satellite to place it in a geosynchronous orbit(24 h per orbit)?
38. ### Recommendation about Celestial Mechanics

can someone please recommend to me a free text (preferabely in pdf or ps format) about Celestial Mechanics?

what is it?