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

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34 views

Calculate the speed of Halley's comet at his perihelion [on hold]

Knowing that Halley's comet orbita the sun every 75,3 years, that the semi-major axes is 17.83 AU, the semi-major axes is 4.53 AU and at his perihelion he is 0.586 AU away from the sun. With these ...
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2answers
1k views

If we threw a baseball from the ISS, could we deorbit the ball?

Clearly this is a hypothetical question. Say we bring a star baseball player into NASA, prep them appropriately for a mission in space, and fly them up to the International Space Station. They go on ...
3
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1answer
16 views

How would I find the velocity of an object after it doesn't fully enter the gravitational pull of a planet and is kind sling shot out of its gravity?

Obviously that question doesn't have a lot of jargon having to do with math and physics. I am not a physicist, I'm not a mathematician, I'm trying to make a game and simulate some physics found in ...
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0answers
27 views

Is it possible for a particle to orbit a singularity inside the event horizon [duplicate]

Event horizon just means a distance from singularity, where there is no "going-away" from the black hole. But is it possible, that there are particles with enough momentum to actually orbit the ...
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13 views

Tidal heating of body

I am trying to make a plausible, though not necessarily accurate model of tidal heating of a body moving close by a gravitational attractor, not necessarily in orbit and not considering the spin of ...
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3answers
71 views

Experiment proving that the Earth is rotating around the Sun [duplicate]

Is there any simple experiment done on Earth proving that the Earth is rotating around the Sun? Something in the same spirit of what Foucault did proving that the Earth is rotating around itself. ...
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1answer
47 views

Mathematically calculate if a Planet is in Retrograde

How do you mathematically calculate if a Planet is in Retrograde when you are given both the Earth and the Planet Keplerian Elements value and rate? Keplerian Elements are: a - Semi-Major Axis; e - ...
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1answer
278 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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1answer
82 views

Simulation of relativistic probe passing through an external solar system

I recently read about the Breakthrough Initiative to launch "StarShot", a nano-probe that is designed to travel to Alpha Centauri at $0.2c$. One of the challenges to be solved involves the precise ...
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1answer
24 views

Which force transfers angular momentum in tidal locking?

The moon is in tidal lock with the earth, but a long time ago it was not. As the moon became tidally locked with the earth, its angular momentum changed and the delta went into it's orbit and possibly ...
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3answers
34 views

Relationship Gravitational Potential and the Tangential Velocity of a Satellite

So gravitational potential is given by $V(r)={\frac{GM}{r}}$ and the tangential velocity of a satellite is the square root of $V$, i.e. $\sqrt V$. So how do these two relate, if at all?
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39 views

Derivation of Bohr model equations (1) in his original paper

My question is rather straightforward. In his original paper ("On the Constitution of Atoms and Molecules") Bohr provides equations (1) for the frequency and major axis orbit: \begin{align} \omega ...
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1answer
23 views

Finding mass with an estimated gravitational force

As asteroids orbit the sun, they experience gravitational force exerted on them by the sun, and they in turn exert a very minute force back on the sun. Because of their small size, asteroids don't tug ...
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1answer
35 views

Vector interpretation of Kepler's 2nd law ( r X a = 0 )

I just read the vector interpretation of Kepler's second law and the conclusion put me in a confusion. The interpretation concludes by demonstrating that r X a = 0, where boldfaced r and a are ...
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4answers
62 views

Why are objects (such as planets) in motion and not static? [duplicate]

I am just curious, why are all the planets, rocks etc in motion? Would they fall into objects with larger gravity if they were not in motion? What is stopping the earth from falling into the sun or ...
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2answers
457 views

Kepler's laws to determine radius of circular orbit

"In nonrelativistic limit of general relativity there is a correction to the Newtonian gravitational potential energy $−h/r^3$ with $h = αL^2/(mc)^2$, where $c$ is the speed of light, $α = GMm$ ...
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1answer
41 views

How can a Satellite's position/orbit be calculated using only range measurements from ground stations?

This task is often done in a process known as Satellite Laser Ranging (SLR). SLR stations (of known coordinates) track satellites, recording range measurements to the satellite at known times. I would ...
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0answers
23 views

Orbital period and velocity around a Kerr black hole relative to fixed stars

I've been trying to make progress on some of the smaller pieces of this question about the environment around a Kerr black hole. In order to calculate the effects of special relativistic Doppler shift ...
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2answers
31 views

Why can't we detect the Earth's orbital motion when looking at the sky and stars?

After I read that speed of earth orbit around the sun is 30 km/s, I looked at sky and I didn't notice any change when compared to the start location. 30 km/s can be converted to (30 * 60 ) km/minute ...
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2answers
32 views

How to calculate the mass of the orbiting body given only its orbital information

A question asks the following: Using Newton’s Law of Gravity, show that the mass of a planet can be written: $$M = \frac{4\pi^2a^3}{ GP^3}$$ where $a$ is the semi-major axis and $P$ is the orbital ...
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1answer
27 views

How does the total change in energy being negative indicate the direction of the Force?

To be more precise consider the following situation: Suppose a satellite is orbiting at a distance of $r_1$ from the centre of the earth. After some time, rockets are fired such that the new distance ...
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1answer
66 views

Methods for handling close approaches in $N$-body simulations

In direct gravitational $N$-body simulations, what are the preferred methods for handling close approaches between bodies in order to preserve the accuracy of the evolution of the system?
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1answer
31 views

Orbiting in space (free fall) and centripetal force?

So basically astronauts are weightless b/c they are free falling. But to get to that state they need to be moving real fast. So why doesn't that speed along with the centripetal force affect them? I ...
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0answers
4 views

Deriving Stumpff functions for parabolic and hyperbolic orbits

I would like to know how I can derive Stumpff functions analytically for hyperbolic and parabolic orbits? It would be nice if you could tell me where I can read about it. Thanks, KS
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0answers
28 views

Can a satellite be put into orbit such that it will always remain directly over a city? [duplicate]

Isn't it possible if we just set it high enough so that it's angular speed matches with the earth's? I think that the city must be on the equator to make this happen. Am I correct? Please can anyone ...
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1answer
76 views

Can a satellite remain directly over a city?

Is it possible to put an artificial satellite into an orbit in such a way that it will always remain direct over a city (I mean at any specific place)?
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9 views

Calculating true anomaly of a hyperbolic trajectory from time

I'm creating a simulation for orbiting bodies with my primary challenge being calculating the true anomaly of a trajectory with respect to time. I have figured out circular, elliptical, and parabolic ...
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1answer
38 views

Show that Newtonian orbits are closed and periodic

I want to prove to show that the change of the rotation angle of a body in a two-body-problem is exactly $\Delta \phi = 2\pi$. I know that the whole energy of the system is given by $$ E = ...
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5answers
4k views

Difference between circular motion and rotational motion

Are rotational motion and circular motion different or the same? If different then when can we say that a body is in circular motion, and when it's in rotational motion? I find several answers where ...
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4answers
639 views

Why doesn't an orbiting body keep accelerating?

As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates ...
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1answer
299 views

What is the optimal burn direction to lower periapsis of hyperbolic orbit?

I am an engineering student who is interested in orbital mechanics. I am doing some self study before taking some orbital mechanics courses next year. I was learning about various orbit types ...
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1answer
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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60 views

How to visualize gravity fields? [closed]

I'm creating a tool for intuitively prototyping routes through space. Part of this requires visualizing gravity. This is the formula for working at how much gravity is at a particular location: ...
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3answers
339 views

Solving the two body problem numerically

I'm trying to solve the two body problem numerically, setting up $G$, $m1$ and $m2$ to be equal to 1. then I located each mass on positions -5 and 5 respectively along the $x$ axis and gave them both ...
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3answers
317 views

Apparent non-aberration of gravitational waves

Since GR assumes that gravitational waves travel at speed $c$, we expect we would be able to some day detect an aberration effect similar the that of light. Of course, gravitational waves are so tiny ...
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1answer
64 views

What would happen to the orbital radius of the Earth if the radius of the Sun is decreased but without any loss of its mass?

What would happen to the orbital radius of the Earth if the radius of the Sun is decreased but without any loss of its mass? According to Newtonian gravity the acceleration due to gravity will ...
2
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2answers
261 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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1answer
59 views

Can the constant $k$ from Kepler's third law be independent of the mass of the planet?

Consider Kepler's third law The square of the orbital period $\tau$ of a planet is directly proportional to the cube of the semi-major axis of its orbit $a$. $\frac{\tau^2}{a^3}=k$ The ...
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1answer
60 views

A simple explanation of Kepler's Third Law

Is there a simple way to explain how Kepler's third law follows from the inverse square law that of gravity (and laws of motion) For example for Kepler's second law we can say it's because Gravity ...
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1answer
57 views

How can we tell the potential from the orbit?

The orbit is $$r(θ) = a(1+\cos θ).$$ The orbit of the particle is in polar coordinates. How can we tell the potential $U(r)$ from this? $U(r)$ goes to zero at infinity.
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2answers
65 views

Is Keplers First Law a consequence of the conservation of angular momentum?

It would seem that once you have deduced that the angular momentum is conserved then you can deduce: $r^2\dot{\theta}=h$ is constant Combining this with the radial equation of motion then yeilds a ...
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1answer
46 views

Change in energy during orbital decay

Suppose we have a planet orbiting a star and the planet radiates away some amount of energy $\Delta E$. I want to find by how much the orbit decays (i.e the change in orbital radius). One way to do ...
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1answer
28 views

Setting up initial conditions of parabolic orbits, centre of mass frame

I am writing a simulation of 2 bodies in coplanar parabolic orbits in their centre of mass frame (in C++) and am having difficulties setting up the initial conditions for the velocities. The total ...
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3answers
3k views

How do you explain Kepler's third law in general terms without complex math?

I understand the first law-elliptical orbits, and the second-equal area in same time, but I need help with the third one. Note that I am not in an AP course or taking calculus at the moment so simple ...
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0answers
44 views

Do gravitational vawes deplete energy even if there's nothing they can affect?

I've read multiple times that one of consequences of gravitational waves being a thing is, that they make any orbit unstable. As long as the two or bodies orbit around each other, they create ...
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2answers
41 views

What is the reason for Earth's rotation and revolution?

Is it because of the gravitational effect of the other planets and the sun then why do the other planets rotate and revolve too? And well does the Sun rotate and revolve too?
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2answers
85 views

Why can't we put an object anywhere in the earth's orbit around the sun instead of Lagrangian points?

If we place an object in the earth's orbit around the sun, it should have the same orbital period right? For example, what would be the behavior of an object in orbit at point A1? It is at the ...
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1answer
166 views

What is the angular distance between Ptolemaic perigees of Mercury?

In his excellent treatment of the history of the science of astronomical distances and sizes, Albert van Helden says (p.29) that The complicated [Ptolemaic] model of Mercury has the curious ...
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39 views

How far inside a white dwarf Roche limit does the Earth have to be to start losing large chunks of rocks?

I have calculated that for a one solar mass white dwarf orbited by the Earth, the Roche limit is about 600,000 kilometers. I understand that any loose mass on the surface of the Earth would start ...
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12 views

Does Spin-Orbit resonance tune Mercury's eccentricity?

More fully, the resonance is remarkably close to friction locking of a fluid sphere, given Mercury's observed orbital eccentricity, while Mercury is instead a nearly elastic prolate spheroid. So is ...