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

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In how lmuch time will the year be exactly 365 days? [on hold]

I understand that the number of days per year has changed throughout the history of the Earth. Apparently there were once over 400 days per trip around the sun. How long will it take approximately ...
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19 views

Calculating initial velocity to achieve orbital motion using verlet integration

I'm attempting to build a simple computer programme which models bodies orbiting other bodies. I've implemented a Verlet integrator (https://en.wikipedia.org/wiki/Verlet_integration) and I can ...
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2answers
2k views

Why we don't see time dilation in stars orbiting black hole?

We have images of stars orbiting black holes or black holes destroying near stars, but why do we see the stars moving normally? I mean, if time dilation does exist, shouldn't we see that stars slow ...
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1answer
47 views

Can stable non-circular orbits exist in 2 or 3 dimensional hyperbolic space

I know that stable non-circular orbits in euclidean space exist only in 3 spatial dimensions but what about if the spatial dimensions are hyperbolic instead? Are there any stable non-circular orbits ...
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1answer
128 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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27 views

Earth “satellite” breadcrumb: Have we ever placed an object orbiting our Sun and the Sun only?

Have we ever placed an object orbiting our Sun and the Sun only? like a breadcrumb of our orbit... I was reading about VLA for satellites and wouldn't this breadcrumb be a viable solution to create a ...
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1answer
30 views

What velocity do I need to get the moons orbit perfectly aligned with the earths center [closed]

I have a simulation for universal gravity with two objects. How can I calculate the velocity or instantaneous force I would need to apply to object 2 (the moon) to get it to orbit so that the origin ...
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23 views

Central Force Scattering in Goldstein

On page 108 in Goldstein 3rd edition in the paragraph after equation (3.94) he says that $\psi$` can be obtained from the orbit equation (3.36) using the limits as $r_0=\infty$ $r=r_m$ which the ...
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1answer
68 views

How do spacecraft gain kinetic energy by passing near planets? [duplicate]

When a a spacecraft like Voyager travels close to Jupiter, it somehow gains kinetic energy. I'm not sure how this energy isn't simply lost again as it moves away from Jupiter. I'm also hoping this ...
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3answers
118 views

General Relativity 2-Body Closed Form

Is there a closed form solution in general relativity to the 2-body orbit problem?
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4answers
126 views

Calculating how fast a mass needs to travel in order to launch itself from a hill

Today I was driving on a hill side and on the opposite lane this very careless gentleman was traveling at a very high speed on a large truck that I surely thought his truck would of lifted off the ...
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1answer
91 views

Black Hole surface area at Schwarzschild radius is half?

I have been interested in black holes for some time, and am still trying to wrap my head around some of their more obscure properties. Now I know that the Schwarzschild radius is $r= ...
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1answer
55 views

Drag in low earth orbit

So I'm looking at the following problem; Arrow type configuration in orbit. Each end of the arrow has a mass and a cross sectional area (we can assume the head and tail are connected by a ...
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1answer
32 views

Can a Space tether be made from AmSteel (Samson Rope’s Dynameen)?

AmSteel is a high strength poly-ethylene fiber. Its strength passes that of stainless 316/8 and is considerably less mass per foot. A 4 inch piece could support a length of 160 miles if the ...
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1answer
34 views

If we were to observe a cluster of planets from a star's magnetic north, which direction would they appear to orbit? Clockwise or counter clockwise?

I have a question, and it's been a topic of great discussion amongst my peers. If we look at galaxies or clusters of planets around stars, they appear to be moving both clockwise and counter ...
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1answer
64 views

What is the velocity of Sun due to Earth alone?

If Earth and Sun were in a isolated system, will the Earth's motion around Sun will be similar? What will be Sun's and Earth's velocity when Earth is at its aphelion? Please note that it's not a ...
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0answers
30 views

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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30 views

Hyper/parabolic kepler orbits and “mean anomaly”

In an elliptical kepler orbit there is an easy recipe to describe the motion/position of a satellite at time $t$. One just follows the following steps - an important detail for me is that the ...
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33 views

Bertrand's Theorem: Perturbative Methods Leading to $1/r^3$ Solution

My professor and I have been working on a proof of Bertrand's Theorem using perturbative methods. We have arrived at a solution yielding 1/r^3, which we had presumed to be an incorrect result. While ...
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2answers
108 views

Does an orbiting body accelerate?

Wikipedia says that : "Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get a ...
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2answers
80 views

What is the binding energy in General Relativity?

In general relativity, the potential energy is given by $$V(r)=\frac{h^{2}}{2r^{2}}\left(1-\frac{2M}{r}\right)-\frac{M}{r}.$$ Solving $V^{\prime}(r)=0$, there are two points where circular orbits ...
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1answer
22 views

Rendezvous Orbits [closed]

If I have two orbits, Orbit 1 and Orbit 2, and the spacecraft with Orbit 2 is trying to dock with the spacecraft in Orbit 1, but does not have a stable orbit (it will crash into Earth) how will this ...
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1answer
38 views

Planetary hohmann transfer epoch [closed]

For an exam I was asked to derive the follow equations for epoch departure $t_1$ and epoch arrival $t_2$. (planet 1 has a smaller orbit, eccentricity/inclination can be assumed 0) $$t_1 = t_0 + ...
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2answers
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Do we know what event caused the Sun and Solar System to form?

Some stellar formation theories suggest that stars are formed by shock waves from trigger events such as supernovae. This excerpt from Star Formation basically gives the background to my question: ...
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43 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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2answers
38 views

Falling into the sun, a thought experiment for trying to understand reference frames

If someone were transported out into empty space, idk like hundred of thousands of miles straight "up," would they fall into the sun? It would depend on their velocity right? If they were moving at an ...
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1answer
96 views

Calculate orbital changes after acceleration

With the vis-viva equation I can calculate the orbital speed at any position on the ellipse. I want to calculate the opposite way. Assume a satellite with an apogee of 600km and a perigee of 400km is ...
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1answer
27 views

How may one calculate the escape velocity of a binary system at a given radius from the COM?

Apologies if this is a bit general, even some pointers in the right direction would be great (reading material etc.) Given an object of mass $m_3$ travelling outward at speed $v$ from the centre of ...
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33 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
61 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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2answers
1k views

Is the Earth the center of the Solar System? [duplicate]

Alright guys, so I attracted you with the title. Now, to preface the question, I am fully aware of the work of Copernicus, as well as the concepts of Heliocentrism and Barycentric Coordinates. I have ...
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2answers
348 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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63 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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33 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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1answer
27 views

Orbital motion (in a plane) Speed at a given mean anomaly

For a small simulation I'm working I'm in need to provide an instantaneous speed (and acceleration). The system is a basic "2 dimensional" orbit system. The orbits follow kepler's law of orbits. ...
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3answers
129 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
54 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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27 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
36 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
51 views

Can I launch an object into orbit using only a cannon?

My friends and I were reminiscing about our intro physics classes and decided to revisit an old problem were we were required to calculate the orbital velocity of a cannonball fired from 1 meter above ...
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1answer
95 views

Drift of Earth's orbit?

How much has Earth drifted (inwards or outwards) from its orbit about the sun? Or has Earth has not moved at all, compared to, say, 1000 years ago? 10,000 years ago?
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1answer
63 views

Time to fall in a non-uniform gravitational field

In an uniform gravitational field the loss in potential energy (the work done) by gravity is given by $\text{-}mg\Delta h$ and the time to do so (assuming no friction and no initial velocity) is given ...
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3answers
108 views

What makes an orbit stable or unstable?

I have an assignement, where I have a given central potential $V(x)=-\frac{K}{6r^6}$ and object with an angular momentum $L$. I've calculate the radius of a circular orbit, which I've done by ...
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1answer
72 views

Velocity of an object in a decaying orbit

The velocity of an object in a stable orbit is well known and (relatively) easy to derive. I have a problem involving a decaying orbit. An object, M2, in a vacuum is orbiting another object, M1, but ...
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0answers
41 views

How do you calculate perihelion precession in the general spherically symmetric space time?

I am trying to find the approximate solution of the differential equation obtained for the the motion of massive particle around Riessner-Nordstrom-AdS solution, equation and its solution are given in ...
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3answers
135 views

Since the gravitational force is only attractive, why does matter not just concentrate into a small sphere?

This doubt has been wandering in my head for a long time. The gravitational force is only attractive force not a repulsive force. Since gravitational force is only attractive force, why not the ...
2
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1answer
47 views

How did the Moon survive next to the Earth since earth and Moon came into existence?

What mechanism(s) prevented the gravitational effect of the earth on the moon from shattering the moon when it was closer to the earth than the Roche Limit some 4.5 billion years ago?
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1answer
62 views

Gravitational Force vs. Centripetal Acceleration

Can someone please explain this conceptually: Suppose we have two probes, one one the surface of the earth and one in geosynchronous orbit. Since $a_c = \omega^2r$, the probe that is further out, ...
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1answer
87 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
103 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 ...