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Questions tagged [celestial-mechanics]

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3answers
530 views

Why is the pull from the Sun a central force if it is not at the centre of an elliptical orbit?

Closed Kepler orbits are ellipses with the Sun at one focus. The force felt by the planet points in the direction of the Sun. As such, it is not a central force, since the focus is not the center. I ...
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4answers
133 views

What is the stable range for orbit of the Earth?

Suppose a force pushes/pulls Earth straightly toward Sun and make earth x kilometers closer/farther from Sun. For what x the Earth remains in a stable orbit, rather than spirally fall to the Sun or ...
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2answers
330 views

Third law of Kepler [closed]

I can not find any solution to this exercise on the internet. Calculate the mean radius of the orbit of a fictitious planet X, expressed in kilometers and UA, so that its orbital period is 1.9x10 ...
2
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0answers
244 views

Is there an elegant way to integrate Lagrange's equations for an inverse-square central force? [closed]

This question pertains to problem 3.10 in Lagrangian Dynamics by D.H. Wells (Schaum's Outlines). The mass $m$ [figure omitted] is attracted to a stationary mass $M$ by the gravitational force $F=-...
3
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2answers
210 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 ...
1
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1answer
152 views

Elliptic Orbit Solution based on initial conditions

$$\ddot{\bf{r}}=-\frac{\bf{r}}{|r|}\frac{k}{|r|^2}$$ $k$ here is a constant dependent on the gravitational constant, and the masses of the two objects. If I transform it into cartesian coordinates: $...
2
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4answers
764 views

Spiral trajectory under gravity?

I know that the general equation of motion for a two body problem under gravity is usually an ellipse. $$r(\theta) = \frac{R}{1-e\cos(\theta-\theta_0)}$$ where $R$ and $e$ depend on initial ...
-2
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1answer
86 views

Why orbital ellipse? [closed]

Of what exactly depends the eccentricity? I suppose that the smaller orbit its eccentricity will be greater, reason why it is closer to forming a circumference, but because the comment halley has ...
-2
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2answers
272 views

How did people get ellipses of Newton's equations of motion and gravitation? [duplicate]

It has become somewhat general knowledge that from Newton's laws of motion and his law of universal gravitation it is possible to verify that the trajectories of the planets are ellipses, i remember ...
4
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1answer
103 views

Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?

I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
2
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4answers
2k views

Satellite in Elliptical orbit

When finding the period of a satellite orbiting the earth we equate the centripetal force to the gravitational force $$\frac{mv^2}{r} = \frac{-GMm}{r^2}$$ If I understood well the $r$ cancels into ...
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1answer
355 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, ...
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1answer
214 views

Impact of Moon's gravitational pull on Earth [closed]

What speed does the Moon's gravitational pull impart to Earth?
2
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3answers
244 views

Is it possible to have stable orbits around Lagrange point $L_1$?

Is it possible to have stable orbits around Lagrange point $L_1$? If yes, is there an upper limit to the mass of a body on such an orbit?
1
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1answer
70 views

What are the gravitational implications of a planet orbiting a star perpendicular to the star's axis of rotation?

I just read about the planet KELT-9b, and one thing which stuck out to me was the fact that this planet orbits this star parallel to the star's axis of rotation (the article says "perpendicular", but ...
1
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1answer
112 views

Why does our Solar system not feel the effects of dark matter the way our galaxy does? [duplicate]

It is said that stars rotate around the nucleus of our galaxy at too high a speed than should be possible based on the amount of visible matter. An explanation given for this is dark matter. However, ...
3
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5answers
756 views

How did planets have an elliptical orbit in the first place? [duplicate]

I know that planets speed up when getting closer to the sun, but they speed up because they have an elliptical orbit, and they have an elliptical orbit because they speed up. Why did they have an ...
2
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1answer
63 views

Solar Flares hitting Earth [duplicate]

When the earth is hit by solar flares, will it make the earth move faster through space when the magnetic field bends?
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1answer
256 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 ...
0
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1answer
103 views

About Kepler's 2nd Law

Kepler's 2nd Law states that the area swept by the line joining the Sun and the Earth is constant per unit time. And here the Sun is at fixed position. (first statement) How about the area swept by ...
7
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2answers
119 views

How could the precession of Mercury be known so accurately in the 19th century?

The discrepancy between the observed precession of the perihelion of Mercury and the value predicted by Newtonian theory was known in the 19th century to be approximately 43 arcseconds per century. ...
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0answers
144 views

How is the precession rate of planets calculated? For which planets do we know the precession rates?

From what I've read, precession rates of Earth, Mars and Moon are known. Why is that? And how is it calculated?
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1answer
528 views

Einstein field equations (EFE) $N$-body simulator

I made a $N$-body simulator and it works well, but it uses Newton's gravitational equation, which is nice, but I want it to simulate Einstein field equations. Speed of gravity should be simple enough, ...
0
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1answer
88 views

Problem: Spectroscopy of a binary system

The Problem is: For a binary system (2 Stars) with Orbital Period of $P =4.822 days = 416620.8 second$ and inclination $i=90$ and with speeds very less than $3 .10^8 m/s$. Their orbital planes around ...
2
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2answers
211 views

Multiple star system, stable orbits?

Inspired by worldbuilding SE, I know that there are relatively stable star systems with two or three suns, but any more than that and they start to become very unstable (e.g. trapezium systems), but I'...
3
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3answers
214 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 ...
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1answer
311 views

Negative eccentricity in orbital motion

$e=0$ represents circular motion $0<e<1$ for elliptical $e=1$ for parabolic motion $e>1$ for hyperbolic Does negative eccentricity ($e<0$) have any meaning too?
0
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1answer
183 views

Can there be an orbit beyond the Geostationary orbit?

I am interested in knowing if we can place a satellite beyond the geostationary orbit. I know that we can send objects beyond that, but can a normal satellite do all its functionalities in that case?
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0answers
50 views

Sun constant formula derivation using Kepler's laws of planetary motion [duplicate]

Well, my previous question was re-asked at the Mathematics StackExchange. It was about the derivation of this formula: $$\text{G}_\text{sc}\left(\text{A}\right)=1367\cdot\left(1+0.03\cos\left(\frac{...
4
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1answer
154 views

Kepler's first law; mathematical way of finding the eccentricity

We know that Kepler's first law of planetary motion is defined as: $$\text{r}=\frac{\text{p}}{1+\epsilon\cos\left(\theta\right)}\tag1$$ Now, for $\epsilon$ I have (see wikipedia): $$0\space<\...
3
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1answer
130 views

Kepler's first law; mathematical way of thinking

I have Kepler's first law of planetary motion: $$\text{r}=\frac{\text{p}}{1+\epsilon\cos\left(\theta\right)}\tag1.$$ Now, for $\epsilon$ I have: $$0<\epsilon=\sqrt{1+\frac{2\cdot\eta\cdot\text{h}...
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4answers
98 views

How does the law of gravity work?

I was taught that if I wanted to find the attraction force between two objects I would use the formula: $F=(G*m_1*m_2)/d^2$. Where $d$ is the distance from the center of object $m_1$ to $m_2$. I find ...
3
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1answer
145 views

Stable disk for $N$-body simulation

I want to simulate a Galaxy of $N$ particles which I have to generate first. What I have done so fare does not lead to the result I want to see. I probably did an error and don't see it. Here comes ...
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1answer
108 views

Can there be a perfect planetary circular orbit?

All of the observed planetary orbits are ellipsoid. Is there any possibility that there will be a perfect circular orbit in this universe? Also what are the requirements for a circular orbit?
1
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1answer
197 views

The mass and separation of binary system with only information about one star [closed]

If we can observe that a star and an unmeasurable planet are in circular orbit around a common center of mass. If we know the speed of the star to be $100\,m/s$, the mass of the star to be $2 \cdot 10^...
1
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1answer
56 views

How can it be known what the Earths periods of eccentricity, perihelion and obliquity are when the observational data only cover at most 3,000 years?

How can it really be known what the earths periods of eccentricity, perihelion and obliquity are when the observational data only cover at most 3,000 years? What I mean is that these parameters ...
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0answers
108 views

Double star system; relative orbit in the case of elliptical orbits

In my physics book they say that the relative distance between two stars (that both have elliptical orbits) in a double-star system equals $4.0 AU$ in the pericenter, and $16.0AU$ in the apocenter. ...
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6answers
832 views

Does the Earth orbit the Sun's current location, or its location from 8 minutes ago?

... and how could we empirically test this? Notable commentary: "... the sun isn't where it was a millisecond ago, and we are revolving around where it was. It's a little like swinging a yoyo on ...
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1answer
478 views

Why Earth's orbit is elliptical though gravity makes body rotate in circular orbit?

As we know that gravitation makes a body rotate in circle So sun should also make earth rotate in circular orbit But why earth rotates in elliptical We not think that it is to cover equal areas in ...
2
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1answer
3k views

How to derive inverse square relation in Newton's Law of Gravitation from Kepler's laws?

I read Feynman's Lost lecture a while ago. In that spirit, I'm trying to do a more simplified version of coming up with the inverse square relation. Using Kepler's 2nd, $ A_1 = \frac{1}{2}r_1^2\...
0
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2answers
98 views

Angular momentum for planet is constant [closed]

In this excersie we look at the system of the dwarf star Gliese 536. Gliese 536 is 10 Parsec away and has half the mass of the sun. (I guess, they mean our sun). There are hints, that there a so ...
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1answer
69 views

Orbit of stars in a galaxy

Do all stars orbit around the galactic center? If yes what makes them orbit around the center , what object creates such a massive force which makes stars millions of light years far away from the ...
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0answers
82 views

Stability of solar system

As far as I understand, the stability of the Solar system means that planets do not collide and will not in near future. The only thing that is stated on Wikipedia is that scientists are concerned ...
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1answer
95 views

Upper limit of gravity

Now I don't mean maximum gravity because there is no maximum gravity. What I mean is what is the escape distance? In other words, how far would I have to be from a mass to get away from its gravity? ...
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0answers
31 views

Gravity assisting [duplicate]

I watched Passengers movie yesterday. There was one detail which stroke my eye. Does it really make sense to use gravity assisting for interstellar travel? I'd imagine that the spaceship would have ...
2
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1answer
113 views

Gravitational $n$-body problem with tidal forces

This year I'm working on modelling the gravitational $n$-body problem using Newton's law of gravity where I assume that for large enough distances, planetary bodies can be modelled as point masses. ...
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4answers
80 views

Do planets on other star systems form ellipse orbits like in our solar system?

In solar system we have all planets roughly on the same plane. Is it true for all of the star systems (or at least for those that we have observed so far) with multiple planets in our galaxy/other ...
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1answer
93 views

Shape of planetary orbits

What makes Venus' orbit almost circular, though mercury's is highly elliptical,even though it is closer to sun ? Further, Why is mercury's orbit most elliptical right after Pluto ?
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2answers
657 views

Motion of planets: inverse square law

If a body is acted on by a force which obeys the inverse square law, will it mean the body follows an ellipse, if so, equating Newton's law of universal gravitation $(f=(GMm/(r^2)))$ to centripetal ...
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1answer
186 views

Voyager Speed After Launch

I am learning about gravity assist. Therefore I am interested in the flight of voyager 2. i found this diagram from Wikipedia and I have trouble understanding the massive acceleration of voyager after ...