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

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Orbital Velocity Question

I have a satellite in a stable trajectory around Earth, of a Mass $m$. I know that its velocity is: $$ v = \sqrt{mG/r}\, $$ But now it begins accelerating directly against the gravity vector (i.e. ...
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1answer
67 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 [closed]

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?
3
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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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1answer
281 views
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1answer
45 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 ...
6
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2answers
187 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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2answers
30 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 ...
4
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1answer
110 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
38 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
50 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 ...
2
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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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1answer
56 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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0answers
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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
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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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 ...
3
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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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1answer
70 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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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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0answers
87 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
47 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
48 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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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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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
79 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 ...
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2answers
84 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 ...
2
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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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0answers
22 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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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
75 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 ...
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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
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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0answers
70 views

Reduced Three-body problem

I know that three-body problem in celestial mechanics can't be solved analytically in general. But suppose that the 3rd body is much smaller than the others, so it does not perturb their orbits. This ...
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1answer
95 views

Do objects launched from Earth retain the Earth's lateral inertia (67,000mph)

We've probably all heard of the gun on a train theory. Fire a bullet that would normally travel 500mph on a train that's moving 200mph (in the same direction the train is moving) and you've now got ...
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1answer
54 views

What is the ultimate “goal” of two particles in a gravitational field? [closed]

What is the ultimate "goal" of two particles in a gravitational field? Will the particles eventually occupy the same point at the same time if nothing stops them? What stops them from achieving the ...
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1answer
115 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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2answers
153 views

Could a really tall tube suck garbage in to space?

When I was around 10 years old, I had this idea that was supposed to solve our waste problems; I imagined having tubes miles high that would stretch in to space. Every tube would have a door at the ...
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3answers
75 views

About Kepler's Law

When Earth goes near the Sun, its velocity increases and when it goes far from the Sun its velocity decreases. Then why according to Kepler's law is the time period $T^2 \propto a^3$, where $a$ is the ...
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4answers
86 views

Is trajectory the same as an orbit?

Is trajectory the same as an orbit? I wanted to know about gravity assists, but most books I find are talking about different types of orbits and such. Are they related?
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1answer
105 views

Maths behind gravity assist

What kind of maths is behind gravity assists and in general the theory of orbits, and how deep does it go? I am just wondering if I know enough prerequisites!
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1answer
57 views

How many times does the ISS celebrate New Year each year? [closed]

My question is, how many times each year do the crew of the ISS have an opportunity to celebrate New Year? Does it vary each year or will it be a fixed number? I tried to work this out for myself ...
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1answer
118 views

Could this planetary superalignment happen?

Here's the 'superalignment' I'm referring to: We've all heard the stories about 'mystical planetary alignments' that will increase/decrease the effective surface gravity experienced on Earth (one ...
4
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2answers
75 views

Reasons for decaying orbit for satellites and spacecrafts

As per newton's law, unless a force is applies, moving objects will continue to move in a straight line. A satellite which speeds at around 17.5k mph would be travelling in a straight line considering ...
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1answer
82 views

Why does the motion of the planet around a star cause a centrifugal force?

Please consider the differences in Newtonian physics and general relativity. Newtonian physics In Newtonian physics it makes sense that objects placed on a planets surface facing away from the ...
4
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2answers
203 views

Why is the Milky Way flat? [duplicate]

I read recently that the galactic "flatness" of the Milky Way is due to the rotation of the galaxy combined with a vast stretch of time. Yet, I also read where 1) the Milky Way rotates once every 225 ...
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1answer
160 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 ...
3
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1answer
139 views

What would have been required to boost Mir into a stable orbit?

In 2001, the Russian space station Mir was deorbited and burned up in the atmosphere, after $4.2 billion in expenditures. As it was orbiting within the thermosphere, it was encountering perpetual drag ...
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2answers
80 views

Initial Velocity For Orbital (Gravity) Slingshot At Hit Moving Target

In this problem we have three masses, Mass A is on the left side of the sun Mass B is the sun, and Mass C is on the right side of the sun. I want to calculate the initial velocity of Mass A to hit ...
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2answers
168 views

Calculate Initial Velocity For Orbital (Gravity) Slingshot

I am trying to find the initial velocity to slingshot a planet around the sun and through a gap. The green ball is the planet, and the yellow ball is the sun. In this trial I need to get the ...