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Questions tagged [celestial-mechanics]

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A question about almost stationary orbits

For an orbit around the earth with period equal to a sidereal day with eccentricity $e=0$ and inclination $i=0$, the path on earth would be a single point on the equator. I have done some simulations ...
2
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1answer
88 views

Why is ʻOumuamua traveling so slowly?

Imagine a space rock that starts at rest at the Lagrange point between the sun and our nearest stellar neighbor, Alpha Centauri. That would put it at about 2 light years away from the sun. Now, it ...
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2answers
104 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
31 views

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
26 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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0answers
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Axial tilt stability

The moon is suspected to stabilize earth's rotation axes so that we don't have extreme climatic variations. This is due to the interaction of the tidal forces with earths oblateness. The moon exerts ...
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2answers
85 views

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
43 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
52 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
460 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
99 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
115 views

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
103 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 ...
2
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1answer
53 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
69 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
84 views

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. ...
2
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1answer
48 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
50 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
49 views

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....
3
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2answers
64 views

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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0answers
25 views

Angular momentum in Rotating Frame for satellites

I am working on satellite orbit propagator, I am propagating the satellite position and velocity in the inertial and rotating frames. To validate my propagator, I am checking the angular momentum and ...
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2answers
22 views

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
66 views

What's keeping the Moon in its orbit when the Sun's gravity is greater? [duplicate]

Just as the title says, what's keeping the moon in its orbit around the earth while sun's gravity is greater, why doesn't it deviate and take an orbit (purely elliptical without moving around the ...
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0answers
11 views

celestial coordinates, elliptic plane

When looking up earth orbital elements often I see non zero inclination which seem odd because earth orbit is reference so should be zero. Now I guess for mean orbital elements which give elements to ...
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1answer
49 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
50 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 ...
0
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1answer
52 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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2answers
3k views

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
130 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
50 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 ...
0
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1answer
39 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 $L_4$...
2
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2answers
99 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
57 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 $\...
3
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1answer
164 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
44 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
41 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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0answers
35 views

could someone explain how were the coordinates obtained for the following dumbbell system?

Context: The following is a dumbbell satellite setup, and the objective is to obtain the equations of motion of the system. The mathematical representation of the system. Two types of coordinate ...
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0answers
23 views

How would one show the effects of potential well barriers on a dumbbell satellite system in an earth orbit?

I guess this "Potential Well" explains what a potential well is to an extent, if you could explain it better and in detail, please do so. But, I am looking for Potential well barriers in the context ...
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0answers
14 views

Is it possible to achieve a stable Low Lunar Orbit? [duplicate]

I have been researching on Lagrangian points, and also Low Lunar Orbits. However, following what I have read, LLO is unstable and can easily be perturbed from its orbit. On the other hand, I have also ...
2
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3answers
85 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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0answers
75 views

Angular Velocity in a Gravity Turn

I am trying to simulate a gravity assisted ascent of a rocket. One of the differential equations I need to use for this is the sum of forces transverse to the axis of the rocket (gravitational and ...
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3answers
3k 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
67 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
108 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
147 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
174 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
130 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 ...