The path a body takes while moving through space under the influence of the gravitational forces of other bodies

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158 views

My python trajectory calculator for a small mass in a gravitational field - why is energy conservation violated?

I wrote this thing to calculate the next position of a small mass, given its current position and velocity, and a vector field determines acceleration. It sort of works - except I can never get the ...
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1answer
114 views

Is there any relationship between the $E=mc^2$ equation and the $a_n=\kappa v^2$ formula for the normal component to acceleration?

To clarify, I know very little about physics and don't pretend to have any insight whatsoever into relativity beyond what has entered the popular imagination; my knowledge is more or less at the level ...
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3answers
233 views

Gravity on the International Space Station - General Relativity perspective

My question is an extension to this one: Gravity on the International Space Station. If all the outside views of the ISS was sealed, then the crew inside would not be able to tell whether they were ...
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1answer
66 views

Is it possible to have a black hole in empty space?

If the escape velocity of two very massive objects is near the speed of light, and those objects are orbiting each other (let's ignore the Roche limit for this exercise), is it possible that the ...
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1answer
24 views

Orbital variations [on hold]

My question relates to relativity and the warping of spacetime. If the geodesics approaching the star are coplanar with the ecliptic how can polar planetary orbits form?
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1answer
107 views

What made Kepler think that orbits are not circular which came to be elliptical?

Kepler formulated his laws in a sort of time where human began to believe in heliocentric universe and telescope was not yet invented/ discovered. So what made Kepler think that orbits aren't ...
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1answer
49 views

What is a nongeodesic orbit?

I have read that in the Schwarzschild spacetime for a nongeodesic circular orbit the radial acceleration becomes positive for $r<3r_S$. Intuitively, the acceleration should be negative, pulling the ...
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2answers
186 views

Will an object falling into Earth's orbit start spinning?

Assume an object falls towards Earth (I've drawn a hyperbolic orbit, but this would apply to any orbit). The object starts at $A$, and at this point it is not rotating i.e. an observer on the object ...
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1answer
55 views

Prove that orbits are conic sections

How does one prove that an orbit of a satellite around a planet of significantly greater mass than the satellite is a conic section (i.e. an ellipse, circle, hyperbola, or parabola)? Also, there is ...
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1answer
44 views

Does the Moon have rotation about its axis?

As I understand, the Moon is following Earth's curved space. If that's the case, shouldn't the Moon have no rotation if it's tidally locked, and only appear to have rotation? If the Earth suddenly ...
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1answer
117 views

Calculate orbit height from tangential velocity

Is it possible to calculate the altitude of a satellite orbiting a planet, just from the planet's mass and the satellite's velocity, assuming that the satellite is in a perfect circular orbit? If so, ...
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2answers
27 views

Would a black hole's rotational axis precess in orbit around the sun?

The earth rotates, and its axis of rotation precesses due to the gravitational pull of the sun and moon and other planets upon the mass of the earth. If an earth-sized, rotating black hole was in ...
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3answers
121 views

Does gravitational time dilation affect apparent mass?

Suppose I'm on a highly elliptical orbit around some massive body. As I get closer, I start to experience time dilation due to the object's gravitational field - time starts passing slower for me than ...
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1answer
84 views

Orbital mechanics: hyperbolic trajectory: periapsis

The question is formulated as follows: A satellite is some distance, r, from the centre of the earth, traveling at a speed $2v_e$, where $v_e$ is the escape velocity. The angle between the velocity ...
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0answers
131 views

The Solar System explosion in the Nice model

This video depicts one variant of the Nice model (pronounced "neese", like the city in France). I'll briefly describe it in case the link ever dies. Here is the initial configuration: The four ...
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1answer
37 views

Kepler's laws: show the planet always stays in the same plane?

I know angular momentum $L=q \times p$ is conserved, where $p=L_{\dot q}$ is linear momentum. How to apply this to a planet orbiting the star, described by the position vector $q$ relative to the ...
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2answers
48 views

Air Drag in orbit

Artificial satellites don't orbit the earth forever. Eventually the Earth's atmosphere, thin as it may be up there, will bring them down. But did you know the linear speed of a satellite in a near ...
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1answer
25 views

Coexistence at Lagrange points

I was wondering how precise the location of an object in a Lagrange point needs to be to maintain stability, since it seems that several natural objects (asteroids) exists together in some of these ...
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4answers
3k views

Can a balloon float into space? (+orbital velocity)

After watching the recent "space jump" a question arose. Why can a balloon not float into space? Can one be made/designed to do this? Next, everything in orbit is falling back to earth. It only ...
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0answers
15 views

How did Kepler “guess” his third law from data? [migrated]

It is amazing that Kepler determined his three laws by looking at data, without a calculator and using only pen and paper. It is conceivable how he proved his laws described the data after he had ...
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1answer
68 views

Can the epicycles of the geocentric model of the solar system be dismissed due to the laws of physics?

With enough epicycles, the motions of the planets can be accounted for in a geocentric model, but do the laws of gravity make such motions impossible? Did Newton's laws not only provide a simpler ...
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1answer
19 views

In astronomy, what is a 'reflex orbit'?

In astronomy, what is a reflex orbit? The term is used in one of my books, but u don't find a definition for it. Googling it gives me articles about 'Oculocardiac reflex' which is not what I want. ...
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1answer
68 views

Why doesn't no rotation imply tidal locking?

That I know of, in most parts of physics 0 movement means the body is resting, all the forces are in equilibrium. Why in orbital mechanic 0 rotation speed doesn't mean tidal lock as it would be the ...
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2answers
93 views

Finding sphere of influence in multibody system

I would like to draw a boundary illustrating the sphere of influence of each body in a 3 body system. What is the best way to find such a boundary? My understanding is at the edge an SoI is the ...
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2answers
3k views

Might a planet perform figure-8 orbits around two stars?

Might a planet perform figure-8 orbits around two stars? I'm thinking that if the two stars were equal mass (and not orbiting each other) then a planet that were to go right between them would ...
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1answer
62 views

Clearing up confusion about orbital mechanics

When I see an orbital mechanics problem, I recall the following things from my "toolbox": Angular momentum is conserved for a body orbiting a planet, since the torque due to gravity is 0. Kinetic ...
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5answers
98 views

How gently could a comet/asteroid/meteorite “hit” Earth?

Could an object from outer-space with the right velocity and orbit come into contact with the surface of our planet in a manner that wouldn't cause it to burn in our atmosphere?
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6answers
1k views

Can orbital energy be a source of perpetual power?

A thought just came to me, and I want to comfirm it here: If we figured out a way to harvest the energy from the orbit of the Moon, would that be perpetual? The Moon has been orbiting the earth for ...
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3answers
5k views

Orbital speed for a circular orbit?

I wanted to look up the formula for orbital speed for a circular orbit on Wikipedia, and I found 2 formulas: All bounded orbits where the gravity of a central body dominates are elliptical in ...
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2answers
57 views

Correlation between equations of elliptical orbits and pendulums

The equation for the period of a pendulum is: $$T=2π\sqrt{\frac{L}{g}}$$ Where 'g' is the acceleration due to the gravitational field and 'L' is the length. The equation for the period in of a body ...
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1answer
20 views

Relating Angles in Elliptical Orbit

I've been trying to model the orbit of a comet of arbitrary mass around our sun from having a known initial condition with $r_0, v_0$ with angle $\alpha$ at $t_0$ around our sun. I've been able to ...
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1answer
134 views

Is it possible for a solar system to have planets orbiting the star(s) in a spherical pattern?

By the question I mean that the planets spin in their ellipse but all ellipses describe the surface of a near-sphere shape around a star. Same question but for a solar system with 2 stars of ...
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6answers
4k views

Throwing an object around the Earth. Is it possible?

Some of you might be familiar with the cartoon called Astérix. In one of the episodes, Obelix (the really strong fat guy in the stylish striped pants) enters a spear throwing competition. He beats the ...
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3answers
2k views

How does Newtonian mechanics explain why orbiting objects do not fall to the object they are orbiting?

The force of gravity is constantly being applied to an orbiting object. And therefore the object is constantly accelerating. Why doesn't gravity eventually "win" over the object's momentum, like a ...
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1answer
69 views

Why do planets not stop revolving around the Sun? [duplicate]

Why do planets revolving around the Sun not stop revolving? Note I am not asking why planets do not collapse with Sun.
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5answers
9k views

Why don't planets have Circular orbits?

This might be a completely wrong question, but this is bothering me since many days ago. Given the mass (Sun) curves the space around it, gravitation is the result of such curved space (Correct me if ...
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0answers
86 views

What are the equations of motion that model near light speed orbits of a massive body about incredibly massive bodies?

In Kip Thorne's recently published book, The Science of Interstellar, he describes, by means of an illustration, the complex nature of a spacecraft orbiting a massive black hole with velocities ~ ...
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1answer
45 views

Calculating eccentric anomaly using the Newton-Raphson method

Yesterday I asked a question on calculating the eccentricity of an exoplanet only knowing the radial velocity vs. phase graph an the mass of the star (question). The answer I got helped me a lot, but ...
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1answer
78 views

Calculating the eccentricity of an exoplanet

I'm wondering how to calculate the eccentricity of an exoplanet by its radial velocity vs. phase graph. To clarify my question I will take an exoplanet called WASP-14b 2 as an example ...
2
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1answer
47 views

How did Kepler formulate his second law from data?

It's amazing that Kepler derived his three laws emperically and then Newton rederived them from his own laws of motion. Its conceivable how Kepler derived the first and third laws, but the second law? ...
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2answers
82 views

Why are planets in unstable equilibrium in a stable orbit

It is well known that a planet in stable orbit is in unstable equilibrium. If e.g. the moon was just a few m/s slower in velocity, or a few m closer to the earth than it is, the gravity would ...
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8answers
5k views

How does the earth move?

My son who is 5 years old is asking me a question about how the earth moves around the sun. What answer should I give him?
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1answer
94 views

Solving the Kepler problem

I'm trying to solve the Kepler problem using the Lagrangian, $$L = \frac{1}{2} m (\dot{r}^2 + r^2 \dot{\phi}^2) - U(r) $$ which after quite a bit of fiddling with, by noting that the angular ...
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1answer
266 views

Satellites and gravitation

A satellite with mass $m$ orbits a planet of mass $M$ in a circular path with radius $r$ and velocity $v$. Due to some internal technical failure, the satellite breaks into two, similar parts with ...
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21 views

Obtaining angular velocity of a general orbit

Provided you are given a effective potential function i.e. $$ V_{eff}=\dfrac{J^2}{2ml^2sin^2(\theta)} + mgl(1-cos(\theta))$$ how do you obtain the angular velocity for different types of orbits; i.e. ...
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3answers
64 views

Why does reduced mass help when talking about two body problems?

I hear people say that reduced mass, $\mu$, is used for two body problems, but what sort of problems? Is it so that the two body system can be treated as one body or is it to simplify calculations ...
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3answers
162 views

How many celestial bodies could be in stable orbit at roughly the same distance from a star?

How many planet-like celestial bodies of roughly the same mass (say within 50%) could orbit a star at roughly (say within 10%) the same distance from the star and be in stable orbits. By stable I ...
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1answer
47 views

Orbital configuration for two bodies at fixed distance from each other

Suppose two bodies are orbiting about their common center of mass, and the distance between the bodies is a fixed distance $d$. Surely one possible configuration is the following: each body moves in a ...
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2answers
73 views

Orbital mechanics problem

Here is a problem from the 2009 $F=ma$ contest on orbital mechanics: Two stars, one of mass $M$, the other of mass $3M$, orbit their common center of mass. When the stars are collinear with the ...