# Questions tagged [celestial-mechanics]

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### 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 ...
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 $M$. ...
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?
3answers
123 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 ...
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 ...
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?
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 ...
2answers
105 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. ...
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 ...
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)
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....
2answers
76 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 "...
2answers
26 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 ...
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?
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 ...
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.
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?
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 ...
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 ...
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 $L_4$...
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?
0answers
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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 ...