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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Problems with Sun-Earth-Moon simulations in vPython
I'm trying to simulate the Sun-Earth-Moon system using the Verlet algorithm with vpython. I'm using natural units and a cartesian coordinate system, and am having trouble working out the physics.
I ...
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Radial motion of a photon in Schwarzschild spacetime
For photon worldlines in the equatorial plane of the Schwarzschild coordinate system ($\theta=\frac{\pi}{2}$) in Schwarzschild space-time, the metric equation is given by,
$$-\Big(1-\frac{2GM}{r}\Big)...
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Effects relevant to simulating LIDAR in LEO
I'm embarking on a research program to develop high-precision photon-counting LIDAR for the use in LEO.
As part of this, I'm planning on developing an accurate simulation of LEO and the level of ...
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2answers
73 views
Would the 2 orbiting black holes emit gravitational waves?
Would the 2 orbiting black holes emit gravitational waves even if they are moving at a constant speed in orbits? Here, can we consider the changing direction of black holes in their orbits as ...
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1answer
33 views
When is the effective potential equal to the total energy?
I have a question about the energy of a particle in orbit due to a gravitational attraction. The effective potential given by the gravitational force is defined to be
$$
U_{\text{eff}} = \frac{L^2}{...
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How to find the relative velocity and acceleration from a point on earth to a point in space?
Imagine a situation where you have a telescope on Earth, and you are trying to track an asteroid that is orbiting the sun.
How would I get the relative velocity and acceleration to the asteroid ...
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2answers
107 views
Can soneome help me understand this part of the Feynman's Lost Lecture?
Feyman's lost lecture
So at 17:38, 3Blue1Browns states:
We know that once the planet has turned an angle theta degree off the horizontal with respect to the sun, that corresponds to walking theta ...
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31 views
If motion is relative, can we say that the Earth doesn't revolve around the Sun? [duplicate]
Considering motion to be relative, consider these two cases as follows
An observer is standing on the sun and observing the earth and the earth has no background (no stars and stuff in the background)...
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1answer
30 views
Discrepancy of the Keplerian speed by a factor when calculated with different methods
I needed to derive today the Keplerian speed for a circular motion in a gravitational field. Just for the hell of it I decided to derive it once via the forces and once via the energies and strangely ...
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Calculating reentry of extremely low-denisty object
Assume I'm at an orbit similar to that of the ISS, going around 7.66 km/s around the Earth. There, using a foam sprayer or some similar contraption, I create a large, spherical, free-floating blob of ...
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1answer
31 views
Total Angular Momentum in an orbit
I have just learned that the total angular momentum of a system is measured by adding the angular momentum of the Center of Mass and also the angular momentum of matter rotating around the Center of ...
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3answers
790 views
Proof that the eccentricity of a planet in orbit is always greater than or equal to zero
I was looking into the formal proof of Kepler's laws of planetary motion and I happened to come upon this equation for the eccentricity of the orbit:
$$e=\sqrt{\frac{2EL^{2}}{G^{2}M^{2}m^{3}}+1}$$
For ...
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Saturn's moons - getting a stable harmonic model for Mimas and Encyladus
I have built a HTML/Javascript solar system model. It is working well with real time animation.
https://abetz-rouse.com.au/planetarium
I don't want to get into the deficiencies of my choice of ...
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0answers
27 views
Find semi-minor axis of elliptical binary orbit given semi-major axis and mass ratio
I'm working on a simulation of binary stars. I'm using Kepler's Laws to solve for the angular velocity given the semi-major axis $a$ and the masses $m_1$ and $m_2$ of the two objects in an elliptical ...
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1answer
60 views
Does Newton's Theory with Retarded potentials give rise to the motion of perihelion of Planets
If we take into account the retarded potentials and the motion of the Sun(due to the planet), does Newton's Gravitational theory give rise to the motion of Perihelion of planets (qualitatively, not ...
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1answer
172 views
Perturbation theory on perihelion advance
I'm trying to get a relativistic solution to Kepler's equation starting with
$$\frac{d^2 u}{d\phi^2}+u = \frac{M}{L^2}+3Mu^2$$
by ignoring the higher order terms;
$$u(\phi, \epsilon)=u_0+\epsilon u_1$$...
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1answer
67 views
How do I calculate the lagrangian of a planet orbiting a star and find its equation of motion? [closed]
So, it's basically what the title says. I was messing around with some systems that I found would be interesting to calculate their lagrangians, and one of these systems is a planet in an elliptical ...
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State equation for orbital trajectory?
My task is as such: I have a particle (or spaceship) and a planet. The planet exert a certain force $F$ on the spaceship and my goal is to define a few equations such that if these equations are equal ...
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Launching a satellite at an angle
A satellite is launched from a space station. The intended orbit for the satellite is
circular of radius R. The magnitude of the velocity required was correctly set at launch,
but the direction of the ...
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2answers
89 views
Is Acceleration of Earth Constant in its Orbit around the Sun?
According to this link , we can say that the Earth's acceleration is constant as the path is circular. But how ?
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2answers
78 views
Could two planets trapped between two stars orbit each other?
Say there are two stars, each exerting and equal force on a point in the midde of them. For simplicity, we'll say the two stars have the same mass and are equidistant from the point. Now suppose that ...
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27 views
How to move around an orbit?
Suppose I have a function $f(x)$ (for drawing purposes, I will image it to be $2D$). Is there some sort of dynamics/set of differential equations etc that allows me to move around the orbit defined by ...
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4answers
182 views
Satellite around a black hole
Let's say there's some satellite revolving around the Earth. Its orbital velocity would be
$$v=\sqrt{\frac{GM}{r}}.$$
Evidently, this is independent of the distribution of the mass of the earth, and ...
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2answers
20 views
How can you calculate the delta-v for a Hohmann transfer using potential gravitational energy?
I've been trying to calculate the delta-v required for a Hohmann transfer. I simply assume that, as no loss of energy happens on a vacuum, all you need to calculate is the sum of potential $(-GMm/r)$ +...
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1answer
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In a 2-dimensional sense, how do the perihelions of the planets in our solar system line up?
A bit of background, I'm currently making a 2d graphical representation of the planets orbits around the sun with Python for a university project which currently looks like the picture below (not ...
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Why can't the Chinese rocket Long March 5B keep revolving around the Earth without re-entering?
The out-of-control part of the Chinese rocket Long March 5B is expected to re-enter the atmosphere of the earth and crash on the earth in a few hours. (Today is May 8th, 2021) At the moment, it is ...
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1answer
35 views
Converting light-year to $m\cdot y/s$
For the solution to question $a$ of this problem, I'm confused with what that $3.0\times 10^8 m/s$ conversion factor is. I thought that light year is a measurement of distance, so why are we ...
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1answer
34 views
The speed of a particle when instead of pure circular motion it is forced to do a helicoidal-circular motion [closed]
Is it right that if a proton is trapped in a magnetic field it is forced to do a circular motion of a distinct radius.Now, if a quark inside that proton does a rotation inside the proton volume can ...
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0answers
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Fully General Relativistic treatment of Galaxy Rotation Curve
Over the years I have seen several approaches to this problem in the GR context: perturbations around a flat-spacetime, cancelation by hand of $\mathcal{O}(\partial_{\mu}\textbf{g}^{2})$ terms on the ...
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29 views
Is it necessary for the Sun to be “inside” the parabola in a parabolic orbit?
Can the sun be "outside" of the parabola of a parabolic orbit, but its focal point inside? Personally, I don't see a problem with this case, I was just curious and wanted to ask a quick ...
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2answers
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What is the reason for so many of uniform circular motions even after so many irregularities in phenomena like motion of planets?
A body remains in uniform circular motion around another body due to the centripetal force between them, when the first body keeps moving with a specific velocity.
This is more possible in an isolated ...
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Orbital mechanics: Landing azimuth
Consider a mission where we want to land on a specific ground location on Mars. As an example, we can take Eridania which has the coordinates $44.7^{\circ}~S, 140^{\circ}~E$. I understand that before ...
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3answers
51 views
Calculating where dropping a lead ball from orbit would land, if dropped perpendicular to the Earth, under very simplified conditions
This question has a lot of "what if"s, so let's simplify this:
Assume Earth is perfectly spherical
Assume no wind or anything, just plain atmosphere that is generally uniform (but will ...
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31 views
What is the logic behind this vis viva equation based calculation?
"If the moon were shrunk to having a radius of one meter, without changing its distance (of the apogee) from the earth, what would be the slowest it could be slowed down to and still orbit the ...
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2answers
380 views
Why does conservation of angular momentum explain why planet orbits lie in a plane? [duplicate]
I just learned about sector velocity and how you can manipulate the equation to show that angular momentum $L$ is conserved by $L/2M$. I know that sector velocity is constant and therefore angular ...
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0answers
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The Sun bends planets' trajectory and speeds up it towards the perihelion; does it both actions with light? [duplicate]
The Sun bends planet's trajectory and speeds up it towards the perihelion; does it both actions with light? If it speeds up light too, then does it mean that gravity is a consequence of a vortex that ...
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1answer
36 views
Numerical errors in highly eccentric motion in gravitational field
I am trying to solve the following problem:
A test particle at coordinate $\vec{r_0}=(1,0)$ is thrown with initial velocity $\vec{v_0}=(0,v)$ and is influenced by a gravitational field $\vec{F}=\frac{...
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4answers
96 views
If you could shrink the moon to one meter radius, how much could you slow the moon down by and have it continue to orbit the earth? [closed]
If the moon were shrunk to having a radius of one meter, without changing its distance (of the apogee) from the earth, what would be the slowest it could be slowed down to and still orbit the earth, ...
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3answers
47 views
Analysis of motion of a body following an elliptical trajectory
We are all familiar with a body traversing uniformly ( or non uniformly ) along the circumference of a circle. We get nice relations because of the symmetry of the figure and the distance between ...
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1answer
64 views
Were Kepler's Laws of Planetary Motion the first formal definition of an ellipse?
It seems to me that Kepler's Laws necessitate some definition of an ellipse in terms of a coordinate system. I am wondering whether Kepler's Laws mathematically defined what an ellipse is, or if he ...
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1answer
72 views
Could you use a balloon to show the drag from the gas/atmosphere of something orbitting near the ISS?
If a balloon were floating next to the International Space Station (ISS), how big, light, and/or dense would it need to be such that the gas/atmosphere at that distance from the earth's surface would ...
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5answers
519 views
Is circular motion possible for an object $A$ with some initial velocity being attracted by a much larger object?
A particle $A$ is initially given some velocity and is being attracted by a large object $B$ ($m_A\ll m_B$).
Do there exists an initial velocity so that the particle $A$ describes a circular motion ...
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1answer
35 views
A question on Newton’s analysis of Kepler’s laws
The three Kepler laws of planetary motion were established by analysis of Tycho’s measurements. The choice of coordinate system is important for Kepler’s laws. For example it is important that the ...
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2answers
53 views
Why is total energy not constant in a graph plotting potential and kinetic energy against distance?
The context is orbital mechanics (moving objects away/toward planets, for example).
The following graph confuses me:
How come total energy isn't a straight, horizontal line? Due to conservation of ...
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Why do planets move in elliptical orbits around the sun? [duplicate]
According to Kepler's laws, planets move in elliptical orbits around the sun. But why? What is the proof? Can we rigorously proof that planets move in elliptical orbits by deriving the equation of ...
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1answer
58 views
On figuring the eccentricity of an orbit knowing my launch speed [closed]
I want to check if I am reasoning a deduction correctly and am not missing some elementary part of the math.
I have a rocket that I launch at $10,000\; m/s$. Earth's escape velocity is $11,200\; m/s$, ...
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2answers
78 views
In what frame the three Kepler's laws are valid?
Three Kepler's laws of planetary motion were formulated by Kepler by analysing obervations of Tycho Brahe. I am wondering in what frame Tycho Brahe made his measurements and in what frame the Kepler’s ...
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2answers
60 views
Gravitational slingshots and energy conservation
I was watching YouTube video about gravitational slingshots and conservation of energy was explained as "planet loses its orbital energy around sun while spacecraft gains energy"
In solar ...
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1answer
35 views
How would I compute the gravitational radiation from two masses in an elliptical orbit? [closed]
I am looking at a research project that was suggested to me in another question. I would like some guidance. Thanks
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1answer
46 views
What is $v_{\infty}$?
So, you can calculate the trajectory of a celestial projectile by using this equation:
$$e=\frac{rv_{\infty}}{\mu},$$
where $\mu$ is the central body's Gravitational Parameter, so it is definable by $\...
