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

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How to find velocities given Force

I have one large and one small body orbiting eachother, I can easily find the objects velocity $$v=\sqrt{aR}\hat{R}_\perp$$$$a=F_G/m$$ But if I add a third force how do I model the velocity, since it ...
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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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24 views

Throwing the object around the Earth [closed]

You have to throw an object to a point diametrically opposite od Earth surface, take that Earth does not rotate and that it is perfect sphere. What angle to the ground and velocity must object have? ...
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1answer
28 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
32 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
62 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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28 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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23 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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32 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
103 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
76 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
21 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
36 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
1k views

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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0answers
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
37 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
73 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
25 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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31 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
57 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
325 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
58 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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28 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
25 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
118 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
53 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
33 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
46 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
91 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
62 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
103 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
69 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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40 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
128 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 ...
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1answer
45 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
55 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
82 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
102 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
54 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
72 views

What sort of propulsion technology would allow spaceships to lift off the surface of the Earth and ascend into space like we see in sci-fi movies?

In many sci-fi films, spacecraft are easily capable of lifting off the surface of a planet like a Harrier and ascending into space. It's clear that the propulsion system/jet engines aren't your ...
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2answers
138 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
106 views

Where does the angular momentum of the solar system come from? [duplicate]

We inhabit a system with significant angular momentum: http://www.zipcon.net/~swhite/docs/astronomy/Angular_Momentum.html If our solar system formed by gravity gathering its material together to ...
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1answer
35 views

Working out length of taut rope orbiting the earth remaining straight and radially directed [closed]

A taut rope is orbiting the earth with angular velocity $a$. It remains straight and radially directed. If the midpoint is located at radius $r$, find the length of the rope. I can't even imagine ...
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2answers
90 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 ...
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0answers
65 views

Escape velocity for Schwarzschild metric

I can't fill in the gaps in my solution to this and assistance or a reference would be appreciated. The question begins with the straightforward derivation of the EoM for a massive particle orbiting ...
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1answer
17 views

Superposition of accelerations in multibody problem

I am currently trying to design a game that implements Newtonian gravity, and am trying to code something that draws the trajectory of a small mass being acted upon by the gravity of much larger ...
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1answer
33 views

How do we find the cone angles of the conic sections that are the Newtonian orbits?

In planetary motion, when the eccentricity of a conic section and its semi-latus rectum are known, how do we find out the cone's semi-vertical angle and angle of cutting of the cone by plane?
3
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2answers
734 views

Why aren't satellites increasing speed because of gravitational acceleration?

Satellites orbiting the earth are experiencing almost as strong gravitation as we do, but they don't hit the earth because of their velocity outwards and the earth's curvature. But if they're ...