Questions tagged [celestial-mechanics]

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Kepler's laws for circular orbits

Kepler's first law states that planets revolve around the sun in an ellipse with the sun at one focus of this ellipse. (a special case would be a circular orbit with the sun at the center). The second ...
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Binary stars orbiting around each other are equidistant [closed]

This is a problem that was given to me in my Classical Mechanics course: J.S.Plaskett's star is one of the most massive stars known at present. It is a binary star, that is, it consists of two stars ...
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What are Kepler's laws in equation form? [closed]

So, I know about the worded explanations about them. I also know the equation for Kepler's Third law: $$\left(\frac{P}{\mathrm{yr}}\right)^2=\left(\frac{a}{\mathrm{AU}}\right)^3$$ I have also seen ...
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Replacement of radius with semi-major axis in celestial mechanics

In high school when we first learn about circular orbits we are taught how to derive the period, the energy etc. of orbits with a radius of $r$. When elliptical orbits are introduced, we go through ...
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Prerequisites for getting into Celestial Mechanics?

I have developed an interest in Celestial Mechanics. My math is weak but I'm determined to learn the math and physics required to understand it. I would like to know what maths and physics I would ...
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Why do Solar Systems form in a disc shape? [duplicate]

This has been asked before, but I still don't get some points about all this. From what I've gathered so far, it's something like this: A molecular cloud with some initial spin starts collapsing due ...
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81 views

Why does motion under inverse square law follows elliptical motion? [duplicate]

I have this in mind since quite a time. In book it was given that once kepler asked newton what is relation of distance with gravitational force. Newton said inverse square on which kepler concluded ...
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Will a satellite orbiting the moon have a tidal locked orbit?

Suppose an artificial satellite is launched to orbit the moon. Ignore 3-body problem issues, just assume it follows a roughly titled elliptical orbit relative to the plane cutting through earth's ...
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Why isn't energy conservation equation sufficient to determine the motion?

The star of large mass $M$ is orbited by planets of masses $m_1$ and $m_2$. The energy conservation equation for this system is$$\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}-MG\left(\frac{m_1}{...
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Kepler problem: Time spent by a comet inside the orbit of the Earth [closed]

This is was an exercise on my exam of classical mechanics which I couldn't solve. The question goes as follows: Imagine a comet moving on a parabolic orbit in the plane of the earth. Take the earth's ...
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Calculating orbital path of a planet around a fixed body in a deterministic way given starting conditions

I am making a simulation of the solar system in the unity game engine. A planet is orbiting a stationary star for now using Newton's law of gravitation where $F = Gm_1m_2/r^2$ for the orbit (force is ...
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Keplerian orbits are intersections of planes with the the future light-cone in Minkowski 4-space

Near the end of this essay, Baez comments: In 2011, Guowu Meng pointed out a remarkable fact to me. Orbits of the Kepler problem are precisely the intersections of 2-dimensional planes with this cone ...
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Elliptical orbits of planets

As we know, the velocity of the planet changes as it orbits around the sun, both in its magnitude and direction. The centripetal acceleration causes the change in the direction of velocity but I want ...
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Orbit of Celestial Bodies

To give some insight, I'm creating a simulation, with gravity, planets, forces... And I would like to increase performance, by not doing unnecessary calculations. I could know what calculations, to ...
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1answer
35 views

How would you know if an asteroid could collide with earth, mathematically speaking? [closed]

So, I know the asteroid has an orbit eccentricity of 0.77 and a perihelion of 3.82AU, if the asteroid is on the same orbital plane as earth, should I calculate (if possible) the asteroid's orbit and ...
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How to define “work” on a movement of a celestial body? [closed]

A moving celestial body (such as a planet orbiting the Sun) creates infinite distance. How to relate this to Work formula ($W=F\cdot d$)? I know I must have wrong understanding about this formula when ...
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Going through Kepler's Orbit Derivation.. having a problem

I imagine this was a simple task for many of you during undergrad studies, but I am a lowly engineer attempting to derive Kepler's Law of Orbits. I've tried to do it as cleanly as possible. I've ...
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Analytic solution to Kepler's Problem, exegesis

From 'Solving Kepler's Problem' by Colwell, the first analytic solution to Kepler's Problem used a theorem of Lagrange, and later Burmann, to invert Kepler's equation. When you look on the internet ...
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What is the Kepler problem, position as a function of time, or radius as a function of angle?

From wiki's Kepler Problem the solution is given as $r$ as a function of $\theta $. In R. Fitzpatrick's Kepler Problem we read "In a nutshell, the so-called Kepler problem consists of ...
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How does the orbital motion of reduced mass tell us how the individual planets/stars move?

To give context to my question, here is Kepler's first Law restated in terms of reduced mass. Here, $\vec{r}$ is the position vector of the reduced mass whose origin lies at the centre of mass of the ...
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What are the physical attributes of a system containing a group objects bound together by gravity?

I'm looking to program a simple simulation of a multi-body planetary system. However I don't know where to start in terms of the basic components of such simulation. For example I know that these ...
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How to know when a body completes an orbit?

I'm simulating a solar system, and I would like to know when a body, has completed an orbit around another. Is there any specific formula for it? As shown in the picture, the orbit is elliptical, ...
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4answers
429 views

Can the Sun orbit the Earth?

You know how the earth orbits the sun because of gravity?...well if the sun were the right distance from the earth and it had the perfect tangential velocity...could it orbit the earth? In other words....
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Apsidal precession

There is the formula: $$ \Delta\theta=-2\frac{\partial}{\partial p_{\theta}}\left[\int_{r_{min}}^{r_{max}}\sqrt{2\mu\left(E-V_{eff}\right)}dr\right] $$ That indicates the change in angle for the ...
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First Law of Motion, Gravitational acceleration and Law of Conservation of Energy [duplicate]

When an object leaves a celestial body (e.g. planet or star) with it's escape velocity, according to first law of motion, it will continue travel away from the body with the same speed (without having ...
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How to transform coordinates from heliocentric to a view from earth?

I'm trying to find and model the apparent motion of the retrograde motion of Mars as viewed on Earth, incorporating Lagrangian or Hamiltonian mechanics. For the lagrangian I have: $L = \frac{1}{2}m_{...
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Does the Earth orbit an ellipse or the barycentre of the Solar system?

I'm taking physics lessons in university and my professor described the Earth's orbit as en ellipse, where one of the focal points is the Sun (1st Kepler's law). However, this doesn't make much sense ...
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Distance between Earth and Sun - Derivation of Equation

While reading a textbook about the solar position of the earth I came across an equation that can't find its derivation. j = d 2 pi / 365.2422 πœ€ β‰ˆ 0.03344 cos(j - 0.049) π‘Ÿ0/π‘Ÿ = √(1 + πœ€) I think it ...
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Orbit with crash

Let's assume I shoot an object from a high tower horizontal to the earth's surface. As far as I understand, depending on the velocity I will get different types of orbits. With decreasing velocity I ...
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Tidal locking and heat dissipation

I need to know that how does one measure (approximate) the energy loss of a planet or satellite during the whole tidal locking process? Where do I find this topic to study?
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How to calculate the total energy of a planet at rest?

Let's just say we have the Earth-Moon system isolated in space, with Earth at rest, and the moon orbiting it. How can we calculate the total energy of Earth in such a case (Kinetic energy would be ...
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Calculate Lagrange Points between Sun and Earth [duplicate]

How to calculate the positions of all 5 Lagrange Points between Sun and Earth? (Please give solution for all points especially for L4 and L5)
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What are the sources of error in the formula I derived to estimate sunrise and sunset times, and how can I improve its accuracy? [closed]

I derived the following formula to estimate sunrise and sunset times: $$ t=\pm\cos^{-1}\frac{\sin\theta-\sin L_{loc}\sin L_{sun}}{\cos L_{loc}\cos L_{sun}} $$ $L_{loc}$ is the local latitude $L_{sun}$...
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Deriving Laplace-Runge-Lenz Vector

consider a particle in a central potential, i.e. the potential $V$ only depends on the distance $ r = \| \vec{x} \|$ to the origin. The equation of motion thus reads $$ m\ddot{\vec{x}}=-\frac{\partial}...
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Kepler's Second Law: conservation of the energy or of the angular momentum?

Reading from example the old question, Angular Momentum and Kepler's Second Law Considering that now I not remember the proof because starting from the angular moment conservation of $L$ we have ...
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Proof that derives Newton's law of gravity [duplicate]

I was wondering if it is possible to derive Newton's law of universal gravitation, without utilizing Kepler's 3rd law. I have found many proofs that use this type of proof. I read somewhere that ...
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Does Kepler's 3rd law of planetary motion violate the first postulate?

Consider a distant observer traveling at .866 c relative to the solar system along the line that is co-linear with the sun's axis of rotation. According to his/her wristwatch the observer measures the ...
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Derivation of Newton's law of gravitation [duplicate]

How did Newton get $F=\frac{Gm_1m_2}{r^2}$? What is intuition behind it? What kind of experiment or thought experiment can I do to derive this?
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Does the rotating space skyhook allow for a periodic motion?

Take a look at the relevant wikipedia-page to get accustomed to the concept of the skyhook. My question is whether it is possible to distribute the mass along the tether in such a way and kickstart ...
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Estimating of the size of the Milky Way from the Sun's motion

I am trying to run a simple first-principles calculation to estimate the diameter of the Milky Way from what we know about the motion of the Sun around its center. In particular, from various online ...
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In the earth-asteroid two-body problem, is it possible for the asteroid to be captured into an elliptical orbit around earth?

Consider an asteroid of mass $m$ rushing towards the earth. What is the mathematical condition under which the asteroid will be captured into an orbit around the earth (given that the asteroid and the ...
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What about Newton's potential prevents singularities in the two-body problem?

The solutions to the gravitational two-body problem can be described by conic sections. In particular, two abstract point masses don't collapse into each other (that is, do not get arbitrarily close ...
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How does $\frac{mv^2}{r} = \frac{GMm}{r^2}$ work if both planets attract each other?

According to this and this, both posts describe the fact that the earth and the moon are attracting each other due to gravitation. The gravitation force is $\frac{GMm}{r^2}$. However, I am not able to ...
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Kepler problem, How can I prove that the period of elliptic orbit is only dependent on energy?

We are also given the following hint: Equate the energies and sectorial velocities at the apogee and perigee of an elliptic orbit to express the area of the ellipse in terms of E. For some ...
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Why is the predictability of the solar system in the Lyapunov timescale limited to 5 million years?

Is this due to a mathematical problem that is not solved? Or could this be due to our current amount of information regarding mass and other such factors in our system?
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Orbit around irregularly shaped asteroids

I'm curious how would one calculate the shape of the orbit around irregular objects (let's call them asteroids). How do you tackle this problem? How do you write down basic equations? In classical ...
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Can Binary Stars Escape Each Other?

updated 8/27/2020 While the recession of our Moon from the Earth may slow and even stop, (see When will the Moon reach escape velocity?) binary star systems will (1) never stop experiencing mutual ...
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Escape velocity questions

This topic really screwed with my head in school and my teacher could never answer my questions so I thought I would ask here. I will break it down with mathematics and then logic. Let's assume we ...
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Is a satellite orbit around the Earth Lyapunov stable?

Presume there is a satellite orbiting the Earth in an orbit that follows a closed path around the planet (that is, escape orbits are not permitted here). As I understand it, there are two ...
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90 views

Converting elliptic orbits to circular ones [closed]

My physics teacher has told me that if we have an elliptic orbit under consideration, we can consider it equivalent to a circular orbit of radius equal to that of the semi-major axis of the ellipse. ...

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