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Questions tagged [celestial-mechanics]

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1answer
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Two-body problem - point of closest approach

I am reading through an exercise : One of the hints to solve this problem is that at the point of closest approach the comet's velocity must be tangential only, why is this the case ?
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3answers
73 views

Radius of the Sun

Is it possible to calculate the radius of the sun with minimal amount of physics? I couldn’t find resources on the internet that gives me an answer using a theoretical formula. You are given values ...
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1answer
44 views

Is there any model explaining why would a particle revolve around another one in an elliptical orbit? [duplicate]

The reason for asking this question is to understand the elliptical orbits of planets and why aren't they circular, we know that if a particle moves with an initial velocity perpendicular to the ...
0
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1answer
32 views

How was the equation for a gravitational assist derived?

Im currently writing a paper about a hypothetical probe meant to escape our solar system and I want to analyse how gravitational assists would be beneficial for its mission. I found a website with an ...
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2answers
58 views

What's the nicest proof that two isolates masses orbit their center of mass? [duplicate]

Although it seems intuitive, I haven't found proof of this fact in my textbooks from a purely mathematical standpoint. I was wondering if anybody knows of a particularly elegant proof of this fact, ...
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1answer
51 views

Why doesn't the Earth slowly collapse into the Sun? [duplicate]

I understand that the sun exerts a force on the earth and that if that was the only force exerted on the earth then the earth would have already crashed into the sun a long time ago. The reason the ...
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2answers
51 views

How come planets with different masses can orbit at the same velocity at the same altitudes?

Angular momentum is equal to r × p and angular momentum is also what gives planets with lower orbits a higher speed (because angular momentum is conserved). So as r decreases either m or v (p=mv) has ...
2
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2answers
33 views

How can I determine a planet's mass based only off of information about its orbit and its parent star?

I'm coding a video game with procedurally generated planetary systems and I want some and I want to make sure I'm at least somewhat scientifically correct. I've reached the part in my code where I ...
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4answers
114 views

Kepler's third law is unintuitive

Kepler's third law states that the ratio between the period of a planet in orbit round a star squared over the average distance to that star cubed, is constant. And in the case of an elliptical orbit, ...
1
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1answer
65 views

Two black holes colliding (classical mechanics)

I had this question come up in my exam where two identical black holes are in orbit around each other. There is a loss of energy via gravitational waves : $$\frac{d E}{d t} = kr^4\omega^6$$ where $k$ ...
2
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0answers
47 views

Horseshoe orbit cycle times

I asked on Worldbuilding originally, but was directed here instead I've been working on a habitable moon system for a story, and I'm now trying to populate the other moons around the parent planet. ...
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3answers
151 views

Why does angular momentum being constant prove Kepler's first law?

So I was watching this video and this video on Kepler's first law in order to understand the proof of Kepler's first law. He started off by saying that for an ellipse, the distance from a focus point ...
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0answers
61 views

Mass distributions within two bodies such that the orbit is no longer Keplerian?

The trajectories of two point masses or spherically symmetric masses with respect to their center of mass are conic sections or Kepler orbits. Consider that the bodies have finite size with respect ...
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1answer
55 views

On Planets orbiting binary stars

Several years ago a discovery was made of planet orbiting a star of a binary system (two stars orbiting each other). Since binary star systems are plentiful in our galaxy, I presume we will be ...
2
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1answer
82 views

'Harmony of the Spheres' or 'Harmony of the World' - is it debunked? [closed]

I sincerely apologise for this vague question but I'm writing an essay for my music class on musical harmony and it's historical origins. I came across the Pythagorean notion of Harmony of the Spheres ...
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2answers
17 views

What is meant by “instantaneously aligned” with regards to rotating reference frames/coordinate axes?

I'm trying to understand a set of lecture notes I found online from MIT which describe the derivation of the equations of motion for an object in a rotating reference frame, this is for an essay on ...
1
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1answer
62 views

What is the second $r$ in this equation for the Two Body Problem?

$$r=\frac{r^2\frac{\mathrm d\theta^2}{\mathrm dt}}{\frac{Gm_2^3}{\left(m_1+m_2\right)^2}\left(1+e\cos\theta\right)}$$ I have this equation for the radial distance of a planet from the barycenter. But ...
2
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2answers
89 views

Mass versus rotation Curves

Is there an equation that describes the relationship between the mass of the Galaxy and rotation curve? I found V versus R graphs and equations that describe their relationship (kind of). But I ...
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0answers
28 views

Restricted 3-body problem - Rotating coordinate system

I'm trying to follow the formulation of the restricted 3-body problem in Taff's "Celestial Mechanics" book as I'm writing an essay on Lagrange points and am confused by the transformation into the ...
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5answers
102 views

What is holding things like the Earth and the Sun in one dimension?

I was thinking last night: for most of my life I’ve been taught that the planets in our solar system orbit the Sun, which insinuates that the Sun is in a fixed point in 3-dimensional space, and that ...
1
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1answer
30 views

Barycenter of a binary star system

It is said that the barycenter of 11 Draconis (Thuban) and 10 Draconis which compose a binary star system is a central point. Is this central point a material or immaterial object? Does the size of ...
2
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1answer
63 views

Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?

In the book of Classical Mechanics by Goldstein, at page 88, it is given that However, the orbit might not be bounded, so there might not be two turning point; just one. In such a case, how can we ...
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1answer
27 views

The shape characteristics of gravitational wells given different masses and spread of objects

I am curious as to research that calculates the shape of gravitational wells, and their limits, and affect on time, for different masses and spread of mass. The actual question is st the end. For ...
2
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1answer
41 views

Solar System Position and Velocity data

I'm trying to create an nbody simulator and to test it I'd like some real world data. A good test would be the solar system. I've come across the JPL Horizons software but if cant seem to figure out ...
2
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0answers
41 views

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
107 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
136 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\...
0
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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 ...
1
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1answer
28 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
89 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. ...
1
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1answer
44 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
58 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
602 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
279 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
121 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
118 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
70 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
74 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
93 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
52 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
54 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
50 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....
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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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0answers
12 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
50 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
73 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
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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
294 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 ...