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Questions related to Lagrange points

For me, these two graphs are inherently different. The first graph portrays a "forbidden region" which is completely filled in, the other shows a collection of curves. Whats the difference here? ...
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1answer
49 views

Minimum energy required to remove the satellite from its orbit to infinity?

My book says that minimum energy required to remove the satellite from its orbit is equal to its total energy (K.E+P.E). But shouldn't it equal to only the potential energy difference of satellite in ...
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2answers
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Does the International Space Station always travels in the same path?

From the 3d visualization http://www.satflare.com/track.asp?q=25544#TOP (the right image with the red line indication the path of the ISS) it looks like always the ISS takes the same path. Is it the ...
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0answers
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What is exactly gravitational potential energy and explain P.E. $= -GMm/r$? [duplicate]

I was studying gravity and I came to know about $P.E.= -\frac{GMm}{r}$ which is derived by $GMm(\frac{1}{\infty} - \frac{1}{r})$ which the work done by the body to displace it from infinity to $r$. ...
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3answers
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What is the distance between two objects in space as a function of time, considering only the force of gravity? [duplicate]

What is the distance between two objects in space as a function of time, considering only the force of gravity? To be specific, there are no other objects to be considered and the objects in question ...
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1answer
62 views

Why does Goldstein's derivation of orbits from Newton's law not yield the orbit consisting of symmetric oscillation along a line thru center of Sun?

Why does Goldstein's derivation of Keplerian orbits from Newton's law of gravity not yield the orbit consisting of symmetric oscillation along a line passing thru the center of the Sun? The fact that ...
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49 views

Finding position with respect to time along a trajectory across a sphere (orbital mechanics)

When trying to find an object's position with respect to time on a ballistic trajectory along a curved surface, what equation should I use? I know that when adding force to an object to achieve ...
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0answers
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Can we use the planets and Sun to fling out a craft at relativistic speeds? [duplicate]

E.g. The Voyager crafts took various assists from the planets. Sun being much more massive, wouldn't a spacecraft gain much more energy from such a flyby on the correct trajectory? If so then what ...
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3answers
108 views

(How) can we determine mid-point on Earth's orbit?

The eccentricity of earth's orbit varies with time, but at present time its eccentricity is roughly mean e (0.0167). The position of equinoxes is far more complicated than I thought and it is not at ...
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1answer
36 views

Acceleration in an elliptical binary system

So I'm having a bit of a problem dealing with binary systems. I'm looking at acceleration in a stellar system and am not sure where to begin. Assuming both stars are of equal masses, they'd be ...
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2answers
53 views

Why does using the modified Kepler's 3rd law and using the gravitational parameter yields different results?

$p^2=\frac{2\pi a^3}{\mu}$ ($p$ is the orbital period in seconds) gives slightly different result from $p^2=\frac{4\pi^2}{GM_1}a^3$.
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1answer
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Units in gravitational N-body simulations

I use a code in Python to simulate a binary system interacting through gravity. You can find it here; The code works fine. I am however having problems with the units of length and velocity. I ...
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3answers
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What happens if you slow down a moon?

Let's say you'd put a whooping big rocket engine on the surface of the moon, and slow down its orbital velocity. Not to a complete stop, mind you. Just a bit slower than it was going before (a couple ...
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1answer
108 views

How do I calculate the effect of a prograde, retrograde, radial and anti-radial burn on the orbital elements of a two-dimensional orbit?

My relevant knowledge: This question works in two dimensions, with a two-body problem (see bottom for context). To my understanding, a two-dimensional orbit has the following orbital elements (3D ...
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2answers
106 views

Calculate the Earth’s velocity in its orbit (assumed to be circular) around the Sun [closed]

Data: GM of the Sun: $\text{GM} = 1.327 \times 10^{20} \;\mathrm{m^3 s^{-2}}$ Radius of the Earth’s orbit: $r_{Earth} = 1.496 \times 10^{11} \;\mathrm{m}$ Orbital period of a planet in seconds: $T = ...
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1answer
44 views

Can a natural satellite have a synchronous orbit?

I was thinking about space-elevators and large masses being put into geosynchronous orbit, when I considered the possibility of a natural satellite being in a synchronous orbit. I did a little digging ...
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2answers
155 views

Gravitational Null Point between Earth and Moon

I need help finding the gravitational null point point between the Earth and the Moon, the point beyond which you start falling towards Moon. I am having difficulty in taking into account the orbiting ...
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2answers
64 views

Confusion about proportionality in Kepler's 3rd law of planetary motion

I was reading about Kepler's third law on planetary motion and came across in two books $R^3\propto T^2$ and in the other $T^2\propto R^3$. So, I asked the following question on Math.SE. If both mean ...
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1answer
71 views

Why does Moon always poses the same face towards Earth?

If both Earth and Moon are rotating as well as revolving around some focus, shouldn't they have drifted out of phase with each other long ago? So, why do we always see the same side always?
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1answer
86 views

Is Voyager 2 slowing down?

Voyager 2 will leave the dominating gravitational influence of the Sun for a region where other stars have comparable influence on the craft. By the time it gets that far away, how much will it have ...
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3answers
3k views

Why do we launch rockets during the day?

The clips that I have seen of rockets launching all seem to be carried out during daytime. However, we learnt at school that rockets are fired closer to the equator and towards the east to take ...
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1answer
75 views

Can 4 collinear planets exist?

Imagine 4 planets, A has moon a and B has moon b. A and B are binary planets. Is it possible that a and b and A + B all have same the period, so that the 4 planets are collinear?
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2answers
387 views

Was Leverrier-Adams prediction of Neptune a lucky coincidence?

According to historians both Adams and Leverrier used Bode's law to guess the distance to Neptune, which led to a vast overestimation of its orbital period (Adams - 227 years, Le Verrier - 218 years, ...
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0answers
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Calculating stable orbital resonance and other factors into orbits

Firstly here is a brief summary of what I trying to accomplish. From a predetermined total solar system mass , star count in that system, per-star classification and mass I am building a system of ...
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1answer
68 views

Inverse square law in one dimension [closed]

A point of mass $m$ is at rest at position $b$ and subjected to a force $f(x) = -k x^2$. We are to show that the time required for the particle to reach the origin is $$ \pi \left( \frac{m b^3}{8 ...
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1answer
128 views

How “large” is a Lagrange point?

When placing an object at a L-point, the natural assumption, as with all things gravity, is that you needn't place it in an exact spot to achieve a stable configuration. How much room do you have to ...
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1answer
82 views

Which ellipse does the Earth's semi-major axis refer to?

In Wikipedia the semimajor axis of the earth is reported to nine digits of accuracy (nearest kilometer), and the eccentricity to eight. But to which ellipse exactly does that apply? Sun-at-the-focus? ...
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2answers
279 views

Planetary alignment of the gas giants?

There is this nice and new applet of the orbits of the planets around the sun: Solar System Orrery You can click and drag any planet and watch their relative orbits evolve in time. I was curious ...
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3answers
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Orbit of the Earth

The question I have really is in a few parts. First what if anything could cause the orbit of the Earth to start to diminish start to go towards the Sun closer on each revolution? ( edit to remove ...
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1answer
269 views

How does the Pluto-Charon orbital 'dance' affect Pluto's elliptical orbit around the Sun?

Like many Scientists (and people in general), I have been watching the New Horizons mission results with great interest. One aspect in particular caught my attention - the Pluto-Charon orbital ...
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1answer
43 views

Observations of erratic rotation of asteroids

An asteroid generally has an irregular shape, therefore, one would expect its rotation is quite erratic in some sense. Are there any observational examples?
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Anomalous orbit of pluto [duplicate]

Can anyone explain, why, like unlike all planets, Pluto does not have a regular orbit? Why does it have an orbit that meets the orbit of Neptune? Why does it never collides with Neptune? Is it ...
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0answers
46 views

Gravity between Moon and Earth [duplicate]

It's known that the greater the mass the stronger its gravitational force. Hence, Sun's gravity is definitely stronger than Earth's. So the question arises that why does the Moon orbit around the ...
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1answer
108 views

Why does planetary spin affect the stability of orbits?

Reading about the Hill Sphere I notice that "the region of stability for retrograde orbits at a large distance from the primary, is larger than the region for prograde orbits at a large distance from ...
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2answers
87 views

Deriving the velocity for circular orbital motion

I'm trying to derive the (circular) orbital velocity for a given height from the center of mass of a body, like Earth. First I used the equation of the circle $x^2 + y^2 = r^2$ to get $y = \pm ...
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3answers
756 views

Do the planets really orbit the Sun?

This is a duplicate of this question on Space Exploration.SE. So why would I ask it again here? Read below. The question reads We often say that the planets orbit the Sun, which is usually a ...
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2answers
103 views

Physical Meaning of Cone used in Conic Section for Orbital Mechanics

Does the polar angle (complement of $\theta$ below) of a cone which intersects a plane to yield a conic section have a physical meaning in orbital mechanics? Note that the angle of incident ...
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0answers
148 views

Elliptical path of planets [duplicate]

Why are the planet's orbits in the form of an ellipse and what is the proof that earth moves in an elliptical path with the sun at its foci? Initially it was thought that earth moved in a circular ...
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3answers
468 views

How often does the earth rotate around the common center of mass with the moon?

I could not find anywhere how long does it take for the earth to rotate around the center of mass of the earth moon system, which is located inside the earth but off-center. And does this motion have ...
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2answers
93 views

Why are L4 and L5 Lagrange points stable as points and not part of a circle?

I read this Phys.SE thread which is similar Why are L4 and L5 lagrangian points stable? but I did not want to necro that thread. It seems that most discussions of a three body problem are presented ...
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2answers
94 views

Gravity effect on moving bodies

If we imagine two suns of equal mass, and a small object in their combined center of gravity, which is not moving, it will stay there forever. If the object is displaced a little bit towards one of ...
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0answers
43 views

Minimal set of invariants to specify a Kepler orbit

In the Kepler problem, we know that there are various invariants, including: Energy Angular momentum vector Runge-Lenz vector All together these consist of 7 parameters. On the other hand, the ...
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3answers
56 views

Foci of elliptical path

I have read the Kepler's laws of motion where I came across the term foci of elliptical path. But what is really a focus? Can anyone please explain what is a focus (maybe with a diagram) and why a ...
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1answer
295 views

Determing Velocity of Moons

I have a question that I believe is relatively easy to answer, I am working on an $N$-body simulation of a fictional star system and am having trouble finding the velocity of moons so that they will ...
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2answers
158 views

In the time of the dinosaurs the Earth rotated once in 17 hours rather than about 24 hours, where did the rotational energy and angular momentum go?

where did the rotational energy and angular momentum go? Some claim that the angular momentum went to the Moon. Astronauts put a corner reflecting mirror on the moon and reflected a Laser and timed ...
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1answer
112 views

Do 2-body elliptic orbits precess in special relativity?

Einstein famously explained the anomalous precession of Mercury by showing that in general relativity elliptic orbits precess even in the 2-body problem. But apparently in the early days of quantum ...
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2answers
223 views

If Earth and Jupiter are orbiting around Sun in same orbit, will they have same time period?

Let us suppose that Earth and Jupiter are orbiting around the Sun in same orbit, If we talk about at any particular point. (Which is not possible but for the sake of question) I was wondering that ...
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2answers
572 views

Earth-Sun distance on a given day of the year

The Earth-Sun distance on a given day of a year, can be calculated using the formula (source pdf): $$\frac{d}{\rm AU} = 1 - 0.01672\cos(0.9856({\rm day}-4))$$ where $\rm day$ is the count of days ...