Questions tagged [celestial-mechanics]

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2answers
167 views

Is the geodesic equation independent of an initial condition?

The following argument is used to determine the unknown factors (e.g., $A(r)$ and $B(r)$) in the Schwarzschild metric. $$ \lim_{r \to ∞}A(r) = \lim_{r \to ∞}B(r) = 1 \space\space\space\space\space\...
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1answer
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Can we ever calculate the exact period and semi-major axis for an orbit with strong perihelion precession?

To calculate the period of an orbit with strong perihelion precession we could just pick an arbitrary point in the sky, and time how long it takes for it to pass it again. But wouldn't we get ...
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1answer
45 views

Can a planet have multiple significant sized moons?

The Earth has one moon at about 1/80 of Earth's mass. Is it possible to have two moons large enough each to subtend a >30 minute disk as viewed from the surface? I have tried with various ...
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2answers
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How do astronomers explain trajectories of planets?

I'm wondering how astronomers can explain the trajectories of planets because: planets spin, so have angular kinetic energy. Thanks to the mass-energy relationship this means space-time curvature. ...
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1answer
48 views

Confirmation / interpretation of unphysical(?) Kepler orbits

The following two pictures show the Kepler orbit of two masses $m_1, m_2$, where $m_1/m_2=7/3$, as I calculated them using $$ r(\varphi)=\frac{a(1-\varepsilon^2)}{1+\varepsilon\cos\varphi},\quad\...
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2answers
87 views

Centripetal Acceleration to find Orbital Velocity

When presented with a problem asking for the orbital velocity of an object $1,000 km$ above the Earth's surface, the formula I know you can use is $$v=\sqrt{\frac{G*m}{r}}$$ However, I was thinking ...
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5answers
772 views

What is $R$ in the formula for escape velocity?

From the escape velocity formula $$v_e = \sqrt \frac {2GM}R.$$ Some sources say it is the distance between two objects with mass $M$ and $m$. Some examples I have read, only used radius of the $M$. ...
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3answers
362 views

Why is angular momentum of the Earth/Moon system conserved?

Why is the angular momentum of the Earth/Moon system conserved, apparently unaffected by external forces such as force of the Sun?
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3answers
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Why should the trick solution to the problem of how long it takes to fall into the sun work?

There is a famous problem which asks: Suppose an object is held at 1 au from the Sun and released from rest. How long does it take to fall into the Sun (neglecting the size of the sun)? The trick ...
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4answers
144 views

How to find angle something turns as it orbits in orbital mechanics? [closed]

Short version: Take a look at this animation really quick. https://commons.wikimedia.org/wiki/File:Orbital_motion.gif The direction in which the arrows for $\alpha$ and $\nu$ is adjusted as the ...
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1answer
96 views

Kepler's Second Law: Why do we calculate the area of a triangle rather than the area of a sector?

Kepler's Second Law states that equal areas are swept in equal times. When calculating this area, why do we use the formula for the area of a triangle rather than the area of a sector?
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1answer
82 views

Is a complex Keplerian eccentricity $e=\sqrt{1+\frac{2\varepsilon h^2}{\mu^2}}$ possible?

Wikipedia provides the following formula for the Keplerian orbital eccentricity: $$e=\sqrt{1+\frac{2\varepsilon h^2}{\mu^2}}$$ Considering that a bound object means negative energy, if the magnitude ...
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2answers
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So, DO All Things Float In Space, Or Not?

Incredibly, I cannot find an answer to this anywhere. The experts say that planets etc don't actually float in space, but instead continuously 'freefall' around the object they're orbiting and so on. ...
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1answer
57 views

Lagrange points and gravity

I have just found an article talking about the L1 to L5 equilibrium positions of gravitation around stars, planets, etc. As far as I could learn from this website and other research I have done the ...
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2answers
58 views

Can Kepler's laws apply for circular motions?

Can Kepler's laws apply for circular motions? (First law states planets take an elliptical orbit)
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3answers
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Energy of a planet moving around the Sun

In chapter 13 of volume 1 of The Feynman Lectures, Feynman is discussing how the work done in going around any path in a gravitational field is zero. Here's the link: http://www.feynmanlectures....
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2answers
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Parker Solar Probe top speed

All the news articles say it'll orbit the sun at 430,000 mph. How do they get that? It seems too low. Isn't orbital velocity proportional to $1/\sqrt{r}$? Parker will be 4 million miles above the "...
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2answers
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How can I calculate the ratio of distance between 2 longitudes at different latitudes?

Suppose i have to calculate the ratio of lengths of AB and CD where A(0° N,0° E) and B(0°N,30° E), and C(30°N,0°E) and D(30°N,30° E) the values are just as an example.Is it possible to get the ratio ...
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1answer
57 views

What would happen to the Moon if the Earth stopped providing it with a centripetal force owing to its force of gravity?

Would the Moon really only travel in a straight line then? What about the other planets and their forces of gravity? Wouldn't they prevent this rectilinear and undisturbed motion of the Moon?
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1answer
84 views

Good sources to get velocity/position vectors for all planets and moons in the Solar System for building an orbital simulator?

I’m building an $N$-body simulator, and I have everything ready to begin simulating. But my issue is is that I have no idea how to get all the starting positions and velocities for the celestial ...
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1answer
55 views

Earth's movement around the Sun

My question is - because of sun's movement around the milky way, Earth never reaches at the same point where it started from. Then how can we say that it circles around the sun in 365 1/4th days.
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If the 3-Body force problem hasn't been solved, how do rocket scientists plan orbits of spacecraft?

What methods would they use to predict what would happen in a situation when a probe is being acted upon by the gravity of two stars, say?
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3answers
454 views

Computerised Solar System Simulation [closed]

In school I am doing a project where using python I simulate the solar system The physics I know so far is newtons laws and Kepler’s laws and I have done a lot of research but there appears to be ...
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1answer
73 views

Barycentre of two planets and calculating velocity shift

I find my self puzzled by this question, and I cant see anything wrong with my derivation, which leads me to believe that there is something I am missing within how the velocity shift is calculated. I ...
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1answer
63 views

How to understand $L_4$ and $L_5$ Lagrange points gravity balance? [duplicate]

It's relative easy to understand gravity balance of Lagrange points $L_1$, $L_2$ and $L_3$. But I am having a hard time to understand how a body would be "kind of" balanced out on Lagrange points $L_4$...
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2answers
158 views

Total angular momentum of a planet orbiting a star [duplicate]

Would the total angular momentum of a planet orbiting a star while rotating on it's axis be the sum of the orbital rotational momentum and the rotational momentum about it's axis?
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0answers
85 views

Planar Precession Frequency of Orbit

What is the general relation between orbital precession $\Phi$, orbital frequency $\Omega$ and a radial perturbation frequency $\omega$? For certain cases the answer is "clear", for example: 1) If $\...
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1answer
238 views

Feynman's Lost Lecture: what is the significance of $\frac{d\mathfrak{v}}{d\theta}=-\frac{GMm}{\left|\mathfrak{L}\right|}\hat{\mathfrak{r}}?$

My question pertains to a fact used by Richard Feynman in his so-called Lost Lecture. http://books.wwnorton.com/books/Feynmans-Lost-Lecture/. I have only skimmed the book, so I have much more to learn ...
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1answer
50 views

Spirals in newtonian celestial mechanics?

I know Kepler's laws, Newton's laws, and that conic sections are the trajectories of noncolliding two point masses. But I wonder about a point mass A eventually colliding with point mass B. In ...
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2answers
10k views

Can an atom orbit the Sun?

Is it possible for a molecule or atom to orbit a star (e.g. the Sun)? Or is there always too much outward force imparted by solar radiation compared to the inward force of gravitational attraction?
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1answer
43 views

What happens in between planets?

I was wondering in an area of space where there arent enough planets around it to suck an object in with gravity, does the object just float there? And if it does just float there will other objects ...
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3answers
90 views

How would a gradual joining of the Earth and Moon affect their orbits?

My 5 year old asked a question today that I wasn't sure how to answer, "What would happen if people took so many pieces of the Moon that it was gone?" I'm curious specifically about what a gradual ...
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4k views

Minimal velocity to throw an object to the Sun

What is the minimal velocity to throw an object (material point) to the Sun from Earth, with no specific restrictions?
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1answer
73 views

Can a satellite park between the Earth and Sun?

If you put a satellite at Geostat altitude travelling the wrong way, will it remain between the Earth and Sun?
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1answer
54 views

Is the speed of an orbiting object at a given distance enough to uniquely classify an orbit's eccentricity?

As in the title, I am having trouble with part ii and iii of the linked image. So far i have found the semi-major axis and the period of the orbit both using the vis-viva equation along with proving ...
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3answers
129 views

Why does planet's mass affect it's speed around sun?

Let's assume that planet orbits sun with a perfect circular orbit. If force by which sun pulls planet is $\frac{GM_1m_2}{r^2}$, and $F=ma$ than $a = \frac{GM_1}{r^2}$. Now we also know that for ...
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1answer
349 views

Which Kepler laws might change with the Universal Gravitational Constant?

I was recently asked the following question: Which of the Kepler Laws change if the Universal Constant Of Gravitation is changed? And why? I list the 3 laws of Kepler below: The Law of Orbits: ...
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1answer
29 views

Force on moon & what will happen next?

The moon is rotating around the earth. It is feeling a force by earth due to gravity. So if I some how manage to exert some force into moon, what is be the scenerio? I can think of: The moon will go ...
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1answer
268 views

Speed at the perihelion [closed]

Hale Bopp has a period of 2400 days, with a mean distance from the sun at 174 AU and 1AU away in perihelion and 357 AU away in aphelion, what is its speed at the perihelion? what formulas do you need ...
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3answers
206 views

Does it take energy (in joules) to keep the moon in orbit around the Earth?

If energy is force times distance and I use the Newtonian formula to calculate the force between the earth and the moon $$ F=\frac{G m_1 m_2}{r^2} , $$ then multiply it by the circumference of the ...
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1answer
52 views

How can I obtain the position of the Earth on the orbit for given date?

I would like to be able calculate (or at least download some time-series data of) the position of the Earth on it's orbit at given date. For my purposes, it would be sufficient to account for the ...
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2answers
124 views

Why can large objects at greater distance be treated as a point particle?

Why can large objects at greater distance be treated as a point particle? "The bodies of our solar system are so far apart compared with their diameters that they can be treated as particles to an ...
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1answer
650 views

How to calculate a planet's tangential velocity moving in an elliptic orbit? [duplicate]

Consider a planet of mass $m$ moving around the Sun of mass $M$ in a circular orbit of radius $r$. By equating the centripetal force to $\frac{mv^2}{r}$ to gravitational attraction $\frac{GMm}{r^2}$, ...
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1answer
59 views

Can three bodies be collinear all the time under the influence of gravity?

if a spacecraft is set into orbit around a binary star system such that it is collinear with the two stars. if the distance of the spacecraft from each of the stars is $R$ and $r$ then what will be ...
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0answers
47 views

Sign of the action for the harmonic osccilator?

I am confused about the derivation of the action $S(x,\mathbf{J})$ for a harmonic oscillator as given at page 219 in "Galactic Dynamics", J.Binney-S. Tremaine, 2nd Ed. 2008. The part of the derivation ...
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1answer
60 views

During which part of the year does the Earth move toward the galactic centre?

The Earth orbits around the Sun which in turn orbits around the center of the Milky Way. In which part of the year is the Earth is moving away from the center of the Milky Way?
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2answers
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Mercury's precession

I read in an article about Mercury's precession that Newton's law of gravitation predicts such precession of planets ;but fails to caluclate the precession of Mercury.But most of popular science ...
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0answers
53 views

Flyby anomaly observations: the Pluto case

Recently, the flyby anomaly was back in the Juno probe. I was wondering if the New Horizons probe also observed it. Any references for the New Horizons probe? Any idea if New Horizons could test it on ...
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4answers
736 views

Why doesn't gravitational potential energy cancel out?

If you have 2 stars of mass $M$ and seperated by a distance $2R$, and a planet of mass $m$ is equidistant between them, the potential energy of the planet is given by: $$E_p = \frac{-2GMm}{R}$$ This ...
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1answer
312 views

Planet Orbit in General Relativity

A single planet orbits a sun. With Newton's classical gravity formula, sun moves in a ellipse, with the gravity force always pointing toward the focus/sun. With General Relativity model, how does ...