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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Path Equation for Central Forces [closed]
I needed help in part (c) of this question. I have got the equation for $u=A\cos(wt)$ for some arbitary constants A and w but what interpretation can we make from there.
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Inclination angle of a ray in a static spacetime
In accordance with Synge (equation 8) of the ray with respect to the radial direction in a static Schwarzschild spacetime is
$$ \cot \psi = \left(1 - \rho^{-1} \right)^{-1/2} \rho^{-1} \frac{d \rho}{d ...
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Angular velocity in planetary motion
Torque about centre of sun is zero.
$$T=Ia$$
So angular acceleration is zero too, so angular velocity should remain constant.
However it is not the case. Please tell where I went wrong.
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What are the conditions that produce various shapes in 2D motion?
I have read that projectile motion is parabolic in nature. I know that the equation of projectile motion represents a parabola. But when do we get a parabolic curve? Does it happen when there is ...
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Does the integral of the vis-viva equation have any meaning?
If orbital speed of an elliptical orbit can be described by
$$
v(r) =\sqrt{GM\left(\frac{2}{r}-\frac{1}{a}\right)},
$$
then what would the meaning of its ($\mathrm{d}r$) integral be?
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How does one interpret the relative motion of an object in orbit as it compares to to the object it is orbiting?
How does one interpret the relative motion of an object in orbit as it compares to to the object it is orbiting?
In flat spacetime, it's pretty easy to determine relative motion. If Alice sees Bob as ...
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Where on the orbit of 101955 Bennu would an impact deflection mission have the most chance of success
Asteroid Bennu has a slight change of impact with Earth in the year 2135 (or 2182) and thus is a prime candidate for a future deflection mission using an impact spacecraft.
Given that the orbit of ...
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Two-Body Problem as a function of $t$
I'm writing an orbital simulator program and I'm struggling to apply the two-body problem.
To simulate it properly I need values for the $x$, $y$, and $z$ coordinates for both bodies. Ideally, these ...
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How do we know when the earth completes an orbit?
Two bodies in space always orbit their center of mass. So the relative motion of the Sun and the Earth happen in the same line, save for the rotation of the Sun. So, how do we measure
The time taken ...
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Do all bodies in a 3-body system orbit their center of mass with respect to each of the other bodies?
Scenario
Consider an empty universe with just the Earth, Moon and the Sun. The Earth and the Sun will rotate about their center of mass, which is inside the Sun. The Earth and the Moon will orbit ...
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Will the ball fall down?
I just start learning Physics.
The picture shows the ISS orbiting Earth.
Suppose now we (or rather, God) put a baseball behind the ISS. The ball is not moving with the ISS, we just put it on the track ...
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Retrograde burn vs. Radial Burn for a 'Rods from God' reentry profile, which would be more fuel efficient
So as item of personal curiosity, if I were to have a rod from god say a 10 ton rod of tungsten orbiting in a orbit identical to the ISS for arguments sake, would it make more sense to 'fire it ...
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Plotting ground Tracks with Python only using trigonometry [closed]
I'm trying to plot a ground track in Python from a TLE file without using explicit AstroPy or other packages. I've encountered a problem with the code that I can't figure out. The issue pertains to ...
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How much energy is required to remove Earth from it's orbit and exit the solar system under perfect conditions?
Ok, this is my first question on this site. But it's one I've been thinking about for a while.
Say through whatever means, we place a device capable of generating thrust/ kinetic energy on the surface ...
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Runge-Lenz vector when the earth is neither at the aphelion nor at the perihelion
Assuming the earth is either at the perihelion or at the aphelion, it is easy to see the Runge-Lenz (RL) vector is directed along the line joining the perihelion and aphelion. Since the RL vector is a ...
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Ground track's equations for latitude and longitude?
I've been having trouble finding equations to calculate latitude and longitude in books or other materials. I want to understand how they are mathematically expressed and attempt to use them with the ...
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Will a very long space ship orbiting the Earth appear to have gravity to someone inside?
My friends and I have several disagreements about this scenario:
Imagine a rigid cylinder that is the length of the diameter of the earth. At either end of this cylinder is a capsule with a person ...
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Escape velocity when Sun is present
When we calculate escape velocity for an object from earth, what we do is, we conserve energy. So if $v$ is the escape velocity, we write
$$-\frac{GM_em}{R_e}+\frac{1}{2}mv^2=0$$ since we are assuming ...
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Basic: calculating a satellites height from its angular speed
A few days ago, while loooking at the night sky, I saw a satellite and I wondered if it would be possible to tell how far it is just by looking at it. The only possible naked-eye measurement that I ...
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How to add kinetic energy to gravitational energy to obtain total energy?
Cambridge Pre-U 9792/03/M/J/22
Examination question: What is the total energy E of the binary star system?
Given: The kinetic energy of star X is $E_x = \frac {2GM^2}{9D}$
Working:
$E_Y = \frac{GM^2}{...
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What is the cross-section impact probability for an extended object moving trough a field of randomly moving particles?
In trying to get an estimate of the probability for an earth orbiting (LEO) satellite to collide with small debris particles.
So I need to understand what is the impact probability for an orbiting ...
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Will a man acquire orbit if we suppose Earth is rotating fast enough?
if we consider that the rotation of earth is mush faster (30000km/h), so if a man standing on earth jumps 1 meter above will it acquire orbit if we ignore atmospheric friction
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How to calculate the energy in a hyperbolic orbit?
I'm recently reading a book about rocket science which involved orbital mechanics. I know that in an elliptical orbit, the energy $ E=-\frac{GMm}{2a}$, and therefore can get the vis-viva equation: $ ...
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Conservation of Angular Momentum in Elliptical Orbit: simple yet confusing [closed]
Problem
A satellite orbit is to change from elliptical to circular with radius $2 R$. The satellite is at point $A$ on the elliptical orbit as shown in the figure. Determine the speed of the ...
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In orbital mechanics why is the angular momentum $\bf{h}$ constant?
In the context of an object moving under the influence of gravity, in Bate, Mueller, White it says, sect. 1.4.2
The expression $\bf{r} \times \bf{v}$ which must be a constant of the motion is simply ...
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How to derive the period of non-circular orbits? [closed]
By conservation of mechanical energy:
$$
E(r_0)=-\frac{GMm}{r_0}+\frac{1}{2}\mu \left (\dot{r_0}^2+r_0^2 \omega_0^2 \right)
$$
where $r_0 =r_{max}$. Because our body is located at the apoapsis: $v_r = ...
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Earth's motion in the universe
In the context of working with atomic clocks I have to obtain the orientation of the Earth for every given Julian date. I am trying to obtain a 3d vector summing up all of earth's motions in the ...
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How would I observe the trajectory of the planet Mercury from an inertial frame of reference?
If i were to make an observation of the orbital motion of the planet Mercury from an inertial frame of reference, would I observe the precession of Mercury's perihelion? or would I observe it moving ...
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Centrifugal barrier in modified Kepler potential
In the case of a single particle of mass $m$ and angular momentum $l$ moving in a central potential, the Lagrangian is
$$L = \frac{1}{2} m \dot r^2 - \frac{l^2}{2mr^2} - U(r),$$
where $r$ is the ...
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If another planet was opposite Earth, would we be able to observe it?
Imagine another Earth-sized planet, in the exact same orbit as Earth, but 180 degrees out-of-phase. In this arrangement, at all times, you would be able to draw a single straight line through space ...
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Why free fall motion is parabolic?
Consider no air resistance. If we throw a ball vertically upward from my point of view it goes vertically up and down and moving along straight line. But from point of view observer in outer space it ...
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Would there be any way to avoid gravitational waves emission in some orbital configurations?
In principle every object orbiting another (e.g. a planet revolving around a star) would emit gravitational waves, relaxing the orbit over time.
However, this would not happen if the orbits had a ...
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Three-body problem with multiple systems?
The three-body problem has been known for a long time (https://www.spacedaily.com/m/reports/On_chaos_drunks_and_a_solution_to_the_chaotic_three_body_problem_999.html), in which two celestial bodies ...
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In a binary black hole system, can one of the black holes get ejected before merging in some contexts?
As it is said here (https://physicsworld.com/a/couple-emerges-from-trio-of-supermassive-black-holes/) a system of two orbiting black holes could disrupt the gas and stars at the center of the galaxy ...
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Why do the planets tend to spin in the same direction as they orbit the center sun?
I mean, why do the spin angular momentum and the orbit angular momentum of a planet tend to have the same direction?
As we all know, a planetesimal $m$ orbiting a sun with mass $M_{sun}$ at $r$ will ...
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How to calculate the trajectory of a high speed projectile on earth?
Let’s say you launch a high velocity ($2-8km/s$) projectile from the earth at the equator. How do you calculate the trajectory of the projectile in the absence of drag? Is there a simple formula that ...
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Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? [duplicate]
Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? I imagine it should be absolutely massive so that tidal forces are minimal.
And if all this is ...
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Why doesn't the centre of mass of the solar system move away from the sun? [duplicate]
Consider our solar system, in the frame of the sun (i.e. "the sun is stationary"), with a simplified 5 planets and nothing else. Suppose that for a brief moment, all of the planets aligned (...
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How strong of a gravitational field do you need for a projectile to make a full loop?
How strong of a gravitational field do you need for a projectile to make a full loop? By full loop I mean it curves once around the by dot, and then it ends up on the same trajectory as it was one ...
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Deriving the Equation of a Light Body orbiting a Heavy Body
If a light body orbits a heavy body, the orbit of the light body in classical mechanics is given by:
$$ \frac{d^2}{d \phi^2} \bigg( \frac{1}{r(\phi)} \bigg) + \frac{1}{r( \phi) } = \frac{GM}{h^2} \ ...
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Do only gas planets have discs or even rocky planets may have them orbiting around?
Do only gas planets have discs or even rocky planets may have them orbiting around? If rocky planets are great in volume is then a higher chance for an orbiting disc to exist in the planetary orbit?
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Conditions for the Virial theorem
I've been investigating the Virial Theorem, and I've found different conditions, some more restrictive than others, for it to be applicable to a given system. According to my professor, said theorem ...
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Does the conservation of angular momentum depends upon the choice of point about which you are calculating it?
I know that torque is the rate of change of angular momentum.
Suppose a planet is revolving around the sun. Then its angular momentum about the common center of mass of the planet and the sun will ...
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Can kinetic energy be extracted from an object moving in vacuum using a gravitational slingshot?
Not really sure if physics question or engineering question. If we can apply energy to make an object in space move faster, the reverse should be possible - we should be able to extract energy while ...
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Why, if the potential is different from the Coulomb one, but has spherical symmetry, the eigenvalues of the system are non-degenerate?
I have found the eigenvalues of the following systems: $H=-\frac{1}{2}\Delta+V_1$ and $H=-\frac{1}{2}\Delta+V_2$, using NDEigensystem by Wolfram Mathematica.
In the ...
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Is it possible to determine if a planet can have a moon based on its mass and gravitational pull?
I'm curious, if based on what we know with Newton's law, can we determine if a random planet, knowing it's mass and gravitational pull, can hold a moon in it's orbit.
Or to phrase it another way, is ...
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Number of Geostationary Orbits
It is stated that there is only one geostationary orbit whose height can be calculated using:-
$H = [\frac{GM_ET^2}{4π^2}]^{\frac{1}{3}} - R$
But there can be more than one geostationary orbits if I ...
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Why are the trajectories velocity specific? [duplicate]
Consider projecting a particle from or above the earth surface (at a distance $r$ from center of earth) with velocity $v$. My teacher told me that if $v<v_0$ particle will follow elliptical path, $...
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Satellite angular velocity at an angle
Suppose I am observing a satellite that is not at my zenith. I know the altitude(α) and azimuth(γ) of my telescope and I was able to get a relative angular velocity of the satellite.
Based on this ...
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Is gravity assist a 2-body or 3-body problem? [closed]
I know this question has actually been answered before in a couple of places such as Here
Unfortunately I am dealing with an irascible and impatient person who simply will not bother to read any more ...
