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

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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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978 views

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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808 views

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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266 views

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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301 views

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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105 views

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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298 views

Derivation of Universal Variables

Does anyone know of link to the derivation of the Universal Variables? This is in regards to Kepler's equations. The Wikipedia link didn't have enough information for me, and the Colorado page ...
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2k views

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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372 views

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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594 views

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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309 views

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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677 views

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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324 views

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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4k views

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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124 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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228 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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248 views

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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523 views

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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752 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!
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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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246 views

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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2k views

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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287 views

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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627 views

Stable and Unstable Orbital Resonance

I was wondering if anyone can show me why some orbital resonances are unstable. For example in the asteroid belt there is a depleted distribution at 3:1 resonance with jupiter. What is the cause of ...
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236 views

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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176 views

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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817 views

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 ...
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For the long-term evolution of atmosphere/orbit, when is perihelion more important than mean distance?

When we want to figure out the long-term evolution of a planet's atmosphere/orbit, when is perihelion more important than mean distance? E.g. some processes (like Jeans Escape and escape of ...
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328 views

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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220 views

(Re-)use of a space elevator (basic mechanics and potential energy source)

It's said that if a space elevator were made then it would be much more efficient to put objects in orbit. I've always wondered about the durability of a space elevator though. I don't mean the ...
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710 views

How does an object falling into a plain Schwarschild black hole appear from near the black hole?

I know that when viewed from infinity (or from a very large distance from the black hole event horizon), an object that falls into the black hole will appear to slow down and will become more and more ...
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165 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 ...
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Time dilation factor for the circular orbit at 3/2 Schwarzschild radius

What would the time dilation factor be if a massive (as in rest mass>0) point particle orbiting a Schwarzschild black hole in the photon sphere? If I understand correctly, this is the only possible ...
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What is the precise definition of Gravitational Sphere of Influence (SOI)?

I am trying to understand the gravitational sphere of influence (SOI), but all I get by searching is the formula that you can find on Wikipedia, that is $$ r_{SOI} = a \left( \frac{m}{M} ...