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

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Kepler problem in time: how do two gravitationally attracted particles move? [duplicate]

Two particles with initial positions and velocities $r_1,v_1$ and $r_2,v_2$ are interacting by the inverse square law (with G=1), so that $$ {d^2r_1\over dt^2} = - { m_2(r_1-r_2)\over |r_1-r_2|^3} $$ ...
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When and how were relative distances to the planets first measured?

I understand that the absolute distance to a planet can be measured using earth-baseline (e.g., diurnal) parallax, and that the first reasonably accurate such measurement was made for Mars by Cassini ...
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Radial fall in a Newtonian gravitational field [duplicate]

Suppose an object of mass $m$ starts at rest at a radial distance $ r_0$ from a perfectly spherical mass $M$ (where $m << M$), $r_0 > R =$ radius of $M$. Can we analytically determine when ...
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Forces on objects orbiting a black hole?

Firstly, please excuse my elementary knowledge and lack of eloquence when writing about astrophysics. I am a dentist, who occasionally thinks about the how the universe works. I'm both fascinated and ...
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Why aren't there more natural satellites orbiting the Earth than just the Moon?

Considering that there's a lot of debris in space and that impacts fling out rocks into space all the time, why do we only have one large natural satellite - the Moon? Shouldn't there be all kinds of ...
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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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How to derive Kepler's equation?

The Internet lacks, so far as I know, a derivation of Kepler's equation $$ M = E - e\text{sin}(E) $$ where $M$ is the mean anomaly, $E$ the eccentric anomaly and $e$ the eccentricity. Since there ...
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How many celestial bodies could be in stable orbit at roughly the same distance from a star?

How many planet-like celestial bodies of roughly the same mass (say within 50%) could orbit a star at roughly (say within 10%) the same distance from the star and be in stable orbits. By stable I ...
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Finding interplanetary flight trajectory using calculus of variations?

Consider two orbits $x(t),\space y(t)$ representing the origin and destination for some spaceflight of interest. These could be, for example, cycloids describing LEO and another orbit circling, say, ...
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Earth-Moon orbiting each other after being engulfed by Red Giant

Recently some exoplanets were discovered which are thought to be the leftover cores of giant planets that had survived a star becoming a Red Giant and then shrinking back to a subdwarf. If giant ...
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Is there a mathematical relationship here or am I looking for relations when there are none?

When I was taking classical mechanics, we dealt a lot with pendulums, and orbiting bodies problems. This lead me to think about the two situations depicted above. Left: Shows two balls of equal mass ...
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Convert latitude of lowest altitude to argument of perigee?

I am designing an orbit around Mercury. I know the values I want for the semi-major axis, eccentricity, inclination, and RAAN. I want the altitude of closest approach (periapse) to occur at ...
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Lyapunov stability of circular orbits

I'm studying Classical mechanics on Arnold's "Mathematical Methods of Classical Mechanics". In a problem i'm asked to find for which $\alpha$ the circular orbits in the central field problem are ...
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Elliptical orbit changing as a star's mass increases

I'm studying Kepler's Laws, specifically the orbit of the Earth around the Sun. I know that if the Earth was more massive, the orbit would not be significantly affected. If the Sun was more massive, I ...
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Calculus used by Gauss to find Ceres' position?

With very little data, the great mathematician Gauss was able to predict the exact location of where to find the asteroid Ceres. If possible I would like a reconstruction of his work, from the data ...
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Why GPS is at LEO?

Why GPS/GLONASS/Galileo satellites are on low earth orbit? Why geostationary orbit is so bad? Sattelites might be placed there 'statically' and more precise... The only problem I can see is ...
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Are elliptical orbits really elliptical?

I have wondered for a long time how elliptical orbits can work. It seems awkward for a freely-moving object to come very close to a source of gravity and then return to the exact point where it ...
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Is the escape velocity at Geosynchronous Earth Orbit 0km/hr?

Follow-up question to How long must escape velocity be maintained? Is the escape velocity at GSO 0?
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If the moon was rapid enough would it be able to orbit the earth from a close distance?

If the moon was close in orbit that it's surface was like 100 km away from the earth's surface. And it had a large enough angular velocity will it be able to hold orbit? If this was possible, is ...
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Deviation from Earth's orbit

How much orbital deviation is required for the Earth to get knocked out from current orbit so it either moves away from Sun or towards the Sun?
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Why are people weightless whilst in orbit around the Earth? ISS? Satellites? [duplicate]

Had physics for 2 years now on highschool, but there is a thing I am wondering about. You know the in the height above the earth surface around where the satellites are (Or the ISS), I've calculated ...
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Why the center of our galaxy doesn't absorb us?

Depending on the theories, the center of our galaxy is a super massive black hole, this is easy to accept as a truth, but what I couldn't simply devour is how the solar system is orbiting around it ...
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Orbit in the vacuum

As the space is a vacuum and there is no friction in space, Can we assume that, if we place an object in gravity in exactly the right distance from a planet with gravity and in the right acceleration, ...
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Does mass affect speed of orbit at a certain distance?

Does the mass of both the parent object, and the child object affect the speed at which the child object orbits the parent object? I thought it didn't (something like $T^2 \approx R^3$) until I saw ...
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Would a considerably big asteroid be disintegrated by the Earth's Roche limit?

If there was a big asteroid with a diameter of say 50km+ in a collision course with the Earth (not orbiting), would it disintegrate into smaller chunks due to the Earth's Roche limit, or the time it ...
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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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Is such an orbit possible that allows a satellite on Earth and another on Mars to always be in direct line-of-sight?

If not always, how much "most of the time" could it get? Or would a multi-satellites setup be more suited?
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Orbital speed for a circular orbit?

I wanted to look up the formula for orbital speed for a circular orbit on Wikipedia, and I found 2 formulas: All bounded orbits where the gravity of a central body dominates are elliptical in ...
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Runge-Lenz vector and Keplerian Orbits

Is the loss of closed Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?
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Measuring acceleration of earth due to its fall around the sun

Every orbiting of a satellite around a mass is nothing else but a constant fall - and therefore acceleration - towards this mass. In a way it is a "falling around" that mass. My question Is it ...
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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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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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Why are orbits around black holes stable?

Black hole theory involves space (or space-time), itself, being sucked into the black-hole, with the event horizon marking the point at which space/space-time is moving faster than the speed of light. ...
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Can an elliptical orbit take the same time as a circular obit?

In the picture below you can see two orbits of potential pbjects. The main aspect of the orbits is that they have a collision point at the maximum of the elliptical orbit. My question is, could the ...
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Calculating specific orbital energy, semi-major axis, and orbital period of an orbiting body

Is it possible to calculate the specific orbital energy $ϵ$, the semi-major axis $a$, and the orbital period $T$ (or $P$) without any of them being available to you? The values I do have available to ...
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How to calculate linar velocity of planet orbit?

I try to simulate a solar system with planets (with random mass) placed randomly around a sun with a mass $X \times \text{solar mass}$. The simulation is going well when I use real data ...
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Is it possible for the planets to align?

We've all heard the statement that on the 21st of December, the planets in the solar system will "align" from the point of view of the Earth. I assume this means that they would all be in the same ...
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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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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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Is tripleaxis planet possible?

Imagine. Our solar system. Our sun. Then earth and moon orbiting it. And you have "powers" to create any planet you want, any size, any density, any weight and any velocity. Would it be possible for ...
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Does Kepler's law only apply to planets?

Does Kepler's law only apply to planets? If so why doesn't it apply to other objects undergoing circular motion? By Kepler's law I'm referring to $T^2 \propto r^3$
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Do stars of higher metallicity have more planets in highly-inclined Pluto-like orbits?

In an answer to a previous question of mine, one that asked about the planar orbits of inner planets, I was told the following (emphasis mine): On the subject of different solar systems, I would ...
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Orbital mechanics of Dragon's Egg

In the novel Dragon's Egg, the human crew use one asteroid to swing other asteroids in place to counter the gravity of the neutron star. I understood that it was similar to a gravity sling shot, but I ...
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Why isn't the time between apogee and perigee constant?

I've assumed since the translational speed of the moon along its orbit undergoes the same boosts and reductions over its orbital course, the time between the apogee and the pedigee (and respectively, ...
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Is the fuel burn for a satellite launch affected by the position of the moon relative to the launch site?

The gross mass of a satellite rocket is tiny compared to that of Earth, and Luna. Between them, however, the two bodies set up tides in bodies of water which itself is again considerable mass. At ...
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Increasing mass' effect on the balance between centripetal force and centrifugal force

Okay, this is nothing more than a thought experiment which popped into my head while driving home from work today. Take the case of a single body orbiting another, larger body, as in a planet and a ...
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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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Is the Moon freely falling towards the Earth?

The Moon is revolving around the Earth and its centripetal acceleration is towards the Earth. Does it mean that the Moon is freely falling towards Earth? What is the cause of the Moon orbiting around ...
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Could the Earth be ejected when the sun burns out?

My younger brother came home from school today and told us at the dinner table that when the sun burns out the Earth could be ejected from its orbit. Skeptical, I asked his source. He quoted his ...
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What's the reason for the seasons?

In the diagram, it shows that the fundamental reason for different seasons is when the northern hemisphere is titled towards the sun there's summer in northern hemisphere and winter in southern ...