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

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2answers
194 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
125 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
28 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. ...
3
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3answers
87 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 ...
1
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1answer
55 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
109 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 ...
4
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3answers
140 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 ...
2
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2answers
102 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
102 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
106 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
58 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 ...
1
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1answer
145 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 ...
1
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2answers
182 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 ...
0
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3answers
81 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 ...
1
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4answers
92 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?
4
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1answer
231 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!
0
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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 ...
1
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1answer
155 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
89 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 ...
0
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1answer
87 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
506 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 ...
0
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1answer
234 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
152 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
99 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 ...
2
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2answers
246 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 ...
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1answer
88 views

Non-geodesic circular orbit? [closed]

From N. Straumann, General Relativity Exercise 4.9: Calculate the radial acceleration for a non-geodesic circular orbit in the Schwarzschild spacetime. Show that this becomes positive for ...
0
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1answer
54 views

Are magnetic orbits possible?

I have a small ball with lots of magnets embedded in it with all the north poles facing out and I have a big sphere with lots magnets embeded in it with all the south poles facing out. I set the ...
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2answers
105 views

Calculating the velocity of an elliptical orbit

I need an explanation as to why my solution to this problem doesn't work (please do not give me an answer or tell me exactly how to do it as this is a homework question that I need to do myself, hints ...
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1answer
180 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 ...
-1
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1answer
40 views

How could the lifetime of a low earth orbit satellite be extended [closed]

How could the lifetime of a low earth orbit satellite be extended? I am studying for a test and wish to know a few methods. Thanks. Edit: You are allowed to work with anything related to the ...
1
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1answer
83 views

Delta-v required to get to Medium Earth Orbit?

Does anyone know what's the delta-v you need to get to Medium Earth Orbit (the delta-v for 7,000 km high orbit for example)? I know that to get to LEO you need around 9.5 km/s (including gravity and ...
1
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1answer
135 views

Why does orbiting matter form an accretion disk? [duplicate]

Why does matter in orbital motion around a central body tend to form an accretion disk, as opposed to some other configuration like a sphere? I know this has something to do with angular momentum ...
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2answers
216 views

What would Earth have been without the Moon?

Would Earth rotation have been more slowed down because of the tidal effect from the Sun, as seems to be the case with Mercury and Venus? Due to the giant impact hypothesis the angular momentum from ...
0
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2answers
87 views

What happens to an orbiting body moving with the Earth's angular speed at various altitudes?

I was learning about inertial frames amongst other things, and I somehow came up with this question. Imagine we have a pole, made of imaginary very strong material that will never bend, placed at the ...
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1answer
35 views

Reg position of satellite

Is it possible to put an artificial satellite into an orbit in such a way that it will always remain direct over a city (I mean at any specific place)?
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2answers
399 views

How does the Moon stay in orbit?

How does the Moon stay in orbit? The Moon has not reached escape velocity from the Earth, then how does the Moon stays in orbit?
12
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3answers
2k views

Why don't stars have Keplerian orbits?

In a comment to Rob Jeffries' answer to this question on spherical galaxies, Incnis Mrsi commented There should exist the entire range of orbits in a spherically symmetric system: near-circular, ...
11
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1answer
178 views

Are the orientations of spin-axes and binary/planetary orbits random or is there any relationship with the Galactic plane?

In an answer to another question, a claim has been made that orbit/spin orientations are random (at least within our own Galaxy), except perhaps towards the Galactic centre. I have dabbled in this ...
2
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1answer
51 views

Is the orbit in Schwarzshild metric a path with maximal proper time?

In curved spacetime particles follow timelike geodesics, which should have maximal proper time (at least locally). I thought this path usually corresponds to a global maximum, and there are only ...
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0answers
84 views

How to calculate orbital eccentricity from the ratio of satellites' velocities?

I have a problem with working out how to calculate the orbital eccentricity from the ratio of two satellites' linear velocities. We know that two satellites encircles the Earth in two elliptical ...
0
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2answers
203 views

How can Rosetta spacecraft orbit an object with such a low mass?

Comet 67P Churyumov–Gerasimenko's mass is 11 orders of magnitude lower than Earth's. That means that the comet's gravity force is also weaker than Earth's in the same proportion. Provided that also ...
3
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1answer
148 views

Why does the Cassini probe experience jerky acceleration in deep space?

I was looking at this plot of speed over time for the Cassini probe. What's going on at the right, after mid-2004? Why does it keep slowing down and speeding up again?
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1answer
29 views

Is simultaneous pole-to-pole stacked orbit of planets around a star possible? [closed]

I read recently that mercury, mars and earth once had concentric simultaneous orbits pole-to-pole under each other; all of which orbited under Saturns south pole around the sun. In sort of a stacked ...
1
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1answer
21 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 ...
0
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1answer
54 views

Newton's gravity formulas for ellipses

A few times I've come across formulas, which are identical for circular and elliptical orbits, except that for the second ones you substitute $r$ with $a$, where $r$ is the radius of a circular orbit ...
0
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3answers
139 views

Angular momentum

The satellites are revolving around a planet in circular orbits by themselves (no external source to maintain their speed). Are we able to make them revolve in elliptical orbits by themselves? Do ...
1
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1answer
55 views

Reduced mass and energy representation?

If we have a gravitational system where $m<<M$ then we can write down the energy of $m$ as follows: $$E=\frac{1}{2}m(\frac{dr}{dt})^2+\frac{L^2}{2mr^2}-\frac{GMm}{r}$$ but if $m$ is not small ...
22
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5answers
6k views

Build a ring around Earth, then remove the supports

What would happen if we decided to build a giant ring that managed to wrap around the whole world, end to end that was supported with pillars all along the ring and then the supports all suddenly ...
0
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1answer
71 views

Is there anything interesting about an n-body system whose potential energy is constant?

I am curious about a system of gravitating bodies with particular characteristics. Before describing the characteristics of the system, let me say what I want to know about it: Can this be a ...
2
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1answer
42 views

Change in velocity of a circular orbit?

For a body in a circular orbit will any (i.e. however small) decrease in velocity mean it falls to earth or will it go into an elliptical orbit? I originally thought that it was the first (i.e. falls ...