Questions tagged [orbital-motion]

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

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Find interval between scucessive conjunctions

The maths here doesn't seem to be too hard, but for some reason I can't quite figure out what to do: Consider two planets orbiting a star in circular orbits with periods $T_1$ and $T_2$. What is the ...
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Orbital animation

I'm no long able to follow the differentials and derivation of orbital mechanics. Given a heavy star like mass W located at (x1, y1, z1) and a small mass at (x2, y2, z2) with a motion/velocity of (dx,...
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Delta-v for orbital changes around a Kerr black hole

What's the Delta-v to change between the Marginally bound orbit and the innermost stable circular orbit around a Kerr black hole.
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A problem Understanding how a two-body system of planets starts rotating around barycentre

Consider,We are Creating a Two-body system in free space,Where no other mass exists,Let's Take First Mass M1 and hold it,Now bring Second Mass M2,hold it up,Now we are giving a suddenly impulse To M1 ...
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Are there any other significant radii around Schwarzschild black holes besides the four I know of?

A Schwarzschild (non-rotating, non-charged) black hole has an event horizon with radius $r_s = \frac{2 G M} {c^2}$, where $M$ is the mass of the black hole, $G$ is the gravitational constant, and $c$ ...
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What is the component of gravity other than curvature?

This question started long, but it summarizes as follows: there is light there is mass These are 'many' things for the purpose of a single force, gravity. Yet there are 'many' components of gravity: ...
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How velocity affects different orbits?

Assume a sun with mass $M$ and a planet with mass $m$. Assume at $t_0$ the planet is $r_0$ (distance) away from sun and has an initial velocity of $v_0$. Also, let’s assume the angle between the $r_0$ ...
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Does the Lagrange Point $L_3$ exist in practice in the multi-body solar system?

Lagrange Points ($L_1$ through $L_5$) in a restricted 3-body system are well documented. Traditionally body 1 (M1) is the central object with a mass much greater than the other two objects. M2 is ...
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Is there an equation for retrograde equatorial orbital radii around a Kerr black hole as compared to a Schwarzschild black hole?

A non-rotating, non-charged, Schwarzschild black hole has an event horizon with radius $r_s = \frac{2 G M} {c^2}$, where $M$ is the mass of the black hole, $G$ is the gravitational constant, and $c$ ...
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Which time interval is this question referring to? [closed]

Question: The acceleration due to gravity on another planet is $25 \text{ m/s}^2$. A ball is projected vertically upward with a velocity of $75 \text{ m/s}$ from a platform 100 m above the surface, ...
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Generalized projectile motion [closed]

Toss an object from the surface of earth at speed $V_1=\sqrt{MG/R}$. Here $R$ is the radius of the earth and $M$ is the mass of the earth and $G$ is universal gravitational constant. How long will it ...
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How to calculate the new position at time $t$ of celestial bodies with variable acceleration?

Intro For an $N$-body simulation of celestial bodies I need to calculate on the one hand the accelerations of the celestial bodies based on the received gravitational forces [done] and on the other ...
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Satellite Collision with other objects

I am looking for a detailed physical study on the collision of satellites with other objects while moving in their orbit
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Deriving the Kepler's first law

I am following this video lecture for the proof of Kepler $1$st law and lastly left with this differential equation. $$\frac{d^{2}r}{dt^{2}}-\frac{L^{2}}{m^{2}r^{3}}=-\frac{GM}{r^{2}}$$ Here, $L$ ...
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The unlikely marriage of orbiting bodies

O.k. so we have an orbiting body such as the Earth around the sun or the moon around the Earth. The fact that they are orbiting does not fascinate me, it is my intuitive sense that there is a much ...
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Why is the shape of the orbit of the Earth as it is?

My View: I think that if the sun were only force acting on earth (as a centripetal force), the earth would have a circular orbit. Since other planets also exist , there also exists gravitational force ...
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How does one generate a formula(s) for an artificial satellite's location at time $t$ given a set of known locations at discrete times?

Given a set of spatio-temporal points in space {(Lat_1, Lon_1, Alt_1, Time_1), ... (Lat_n, Lon_n, Alt_n, Time_n)}, I need a function (i.e. a formula) that takes these points (or subset of points) as ...
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How fast would a rocket have to go to maintain in the earth orbit without falling down? And how frequent would rocket boosters be needed? [closed]

I was thinking how fast would a rocket have to go to maintain in the in earth orbit? I was thinking of the ISS going 7000kph with rocket boosters every 6 months. What is the most efficient way to ...
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2 answers
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Do 2 masses orbiting the same barycenter have the same period?

If I were to have a system of 2 masses that rotate around their barycenter such that $m_1$ has a radius of $r_1$ and $m_2$ has a radius of $r_2$, what would the ratio of the periods of the planets be? ...
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Why do moons not get pulled into the planet while they clear their neighborhood? [duplicate]

Today, my 6 year old and I were discussing dwarf planets and their characteristics. We were talking about how, to be a considered a planet, the planet needs to clear it's neighborhood (as explained in ...
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Determining initial conditions for central force question [closed]

Question: A particle of unit mass is acted on by an attractive force of magnitude $k/r^2$ directed toward origin O. It is projected from infinity with speed $v$ along a line whose perpendicular ...
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Orbital Mechanics

Suppose we have an object orbiting the Earth with a circular orbit of radius $R$. We then change the velocity by an angle $\alpha$, without changing the speed. The textbook then asks what orbit will ...
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Thomas Precession on Neutron Stars

We know that Thomas Precession is a relativistic correction that is applied to a particle spin that adds an angular velocity to the spin of the particle that moves along a curvilinear orbit linked to ...
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How to solve Newton's Law of Gravitation? [duplicate]

Imagine you have Newton's Law of gravitation. How would you solve this differential equation. $$ \frac{\mathrm d^2 r(t)}{\mathrm d t^2 } =-\frac{GM}{r(t)^2} $$ I know the solution of this equation is ...
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Is Bertrand's Theorem Consistent with GR?

Bertrand's Theorem - Please observe the gif of orbits with different exponents in the denominator. (I couldn't get the image upload feature to work for this) Note, the orbit with a 1.9 exponent ...
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What explains the descrepancy between Asaph Hall's equation for Mercury's precession and GR?

In regard to What is the weight equation through general relativity?, the answer is: $$F=ma=\frac{GMm}{r^2}\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}.$$ This source provides a different equation: $$f \approx ...
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Could a moon keep orbiting a planet forever?

Our Moon orbits the Earth further away each year due to the tidal forces but could there be a moon orbiting a planet where somehow keeps going further away by the tidal forces but its attracted again ...
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What would happen if a spaceship would pass near a completely stationary astronomical object?

Imagine a completely stationary astronomical object (e.g a planet) and assume it has no movements of any kind (no rotation, no orbits around a star or even a galaxy... a completely still planet) If a ...
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Hohmann Transfer Starting Point

Suppose that we wanted to get to a planet orbiting at a radius $r_1$ and we can launch from either a planet at $r_2$ or $r_3$, with $r_1>r_2>r_3$ (for example, getting to Jupiter from either ...
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Necessary mass and speed of asteroid required to make Venus spin

Suppose we are going to push a large asteroid (or two) from the belt and use them to make Venus rotate at approximately the same rotational speed as earth. Here are some questions regarding that: If ...
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Change in Path of a satellite on changing its velocity

When the speed of a Satellite travelling in a perfectly circular orbit is increased does the path of the satellite remain circular and the radius is increased OR does the path of the satellite follow ...
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How can satellites change direction without any medium in space? [duplicate]

How can satellites change direction without any medium in space? How do spaceships move in space if there is no medium? How does Newton's third law of motion work in space?
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Are orbital eccentricities in a binary system always the same?

Some excercises on Kepler laws and binary system use this relation $$\frac{r_1}{r_2} = \frac{a_1}{a_2},$$ where $r$ is the distance from the center of mass to each object and $a$ is the semi-major ...
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Can I please get the proofs for different trajectories of a satellite when projected at different velocities? [duplicate]

I recently came across a question about the trajectories of satellites, I have tried many resources for the proofs but couldn't find them. For example, a satellite will have an elliptical orbit if (...
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Harmonic and subharmonic orbits in central fields

Using Newton's theorem of revolving orbits one can easily obtain orbits for central forces containing inverse cube terms, such as $$F(r)=F_0(r)+\frac{(1-k^2)|B|}{r^3},$$ from known orbits for $F_0$. ...
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Wobble of an unbalanced fan suspended from the ceiling

A fan hangs several feet from the ceiling by a ball-in-socket joint, and it has one fan blade that is heavier than the others. When you turn on the fan, the additional centrifugal force of the heavy ...
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Kepler's laws of motion [duplicate]

I have studied Kepler's Law of Motion but I always think how did Kepler arrive to those laws and what were the basic thinking behind it? I just want to know the basic physics behind his ideas. I know ...
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How to solve second order ODE from a simplified version of the two-body problem?

While thinking about the motion of a particle being attracted to another massive particle and considering that the acceleration of that particle is not constant, I found myself trying to solve this ...
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Active Balance on L1

Could you have a spacecraft on L1 say the earth-moon system and then extend a weight on a string to the moon and a weight on a string to the earth and keep the spacecraft in balance at L1 just by ...
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Angular position as a function of time for elliptical orbits

It is a well-known fact that there is no analytical solution to the two-body problem as a function of time. However, I wanted to derive the differential equation for the angular position of an ...
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Scaling up a theoretical super Solar system arrangement into a Star system

Recently an article came out about the maximum number of planets in an artificial Solar System. See below the image for the full article link . It suggests that if each planet is placed at a distance ...
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What is the extra kicks to accelerate a spacecraft during gravity assist?

Suppose a spacecraft coming from behind a planet during a flyby, it gets a boost in speed and also change in direction of travel but where does this extra kicks come from? Now that I understand ...
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What is the Smaller Alignment Index (SALI)?

I was reading the following paper where the use the Smaller Alignment Index (SALI) to determine when orbits are chaotic and when they aren't. I was confused on what the deviation vectors are and how ...
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Why is angular momentum not conserved in this case?

I've been trying to figure out how the angular momentum is preserved. From what I could understand, there needs to be no external torque about the said point. What I could not get into my head is this:...
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Does the gravitational field of a planet affect it's own orbit?

According to GR, masses (such as the Sun and the Earth) cause space to curve. Then planets such as the Earth follow geodesics on this curved space. However, if we consider the Earth and the Sun both ...
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Is the motion of an electron bound into an atom inertial?

When a particle moves on a gravitational potential subject to no contact and tidal forces, the particule clearly is in inertial movement. But what about the "motion" of an electron bound ...
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How to make the Moon spiral into Earth?

I recently watched a video of what would happen if the Moon spiraled into Earth. But the video is pretty sketchy on the physics of just what would have to happen for that to occur. At first I thought ...
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Free fall and the period in keplerian motion [closed]

What is the time it takes for a free fall compared with keplerian time period? Is it half the orbital period or a quarter?
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Why Laplace-Runge-Lenz vector in a circular motion is $0$?

This vector is the sum of two vectors, and I understand why their direction is opposite, but I don't understand why their magnitude is the same. I know that the direction of this vector is always the ...
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What are the equations of motions for a planet in a corotating reference frame?

Imagine standing on the sun and always keeping a polar corotating reference frame. Start at the perihelion (when earth is closest to the sun). The velocity of the earth is perpendicular to the radius ...
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