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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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-1 votes
1 answer
55 views

Why particle is certain to escape the conservative field when the mechanical energy is positive?

It is generally said that the particle is bound into the conservative field when the mechanical energy is negative and zero is the limiting case and the particle will escape the field when the ...
1 vote
1 answer
301 views

Potential Energy for Non-conservative Forces

I was studying for the GRE and came across the problem below. A small puck of mass $M$ is attached to a massless string that drops through a hole in a platform, as shown in the diagram above. The ...
22 votes
3 answers
2k views

Can perfectly stable orbits exist in GR?

Defining "stable orbit" between two bodies as one where, in the absence of other bodies or non-gravitational forces, the distance stays between some value pair $r_{min}>0$ and $r_{max}$. ...
3 votes
1 answer
505 views

How accurate does the ISS's velocity and altitude need to be to maintain orbit?

We know the the ISS is not drifting weightless in space, but rather is constantly falling as it circles the Earth. To do this it must be at a specific altitude and moving with a specific velocity. ...
0 votes
2 answers
82 views

What would happen to the moon's orbit if we reduce (instantaneously) its mass? [closed]

In my opinion the moon's orbit shouldn't change, because an orbiting body is a free falling object and the trajectory of a free falling object is not affected by its mass (because the inertial mass ...
4 votes
5 answers
1k views

The validity of the Longitude of Perihelion

As I understand it from Astronomical Algorithms, by Jean Meeus, the Longitude of Perihelion is a very common numeric value associated with planets, even used as one of the planetary orbital elements. ...
3 votes
3 answers
555 views

Why does atmospheric drag speed up satellites?

I've read that old satellites slowly lose altitude when encountering the very thin atmosphere, and strangely enough they speed up. My theory is that the work done by the drag force is insignificant in ...
1 vote
2 answers
147 views

Doubt on conservation of angular momentum for Kepler's laws

Just before proving Kepler's laws, my Professor claimed that if $\vec{F}$ is a central force with center $O$ and it is the only force acting on a point $P$, then the trajectory of $P$ is a curve plane....
1 vote
0 answers
62 views

Why does a moon's orbit get more circular with time?

I understand that there is a transfer of energy between a moon and a planet depending on whether the moon is orbiting faster or slower than the spin rate of the planet. This would obviously change the ...
1 vote
1 answer
386 views

How can I obtain the position of the Earth on the orbit for given date?

I would like to be able calculate (or at least download some time-series data of) the position of the Earth on it's orbit at given date. For my purposes, it would be sufficient to account for the ...
0 votes
1 answer
270 views

Derivation of the equation of a hyperbolic orbit from the conic section expression derived via the orbit equation

So I'm looking to derive the equation of a hyperbolic orbit from the general expression for a conic section $$r=\frac{l}{e\cos\theta+1}$$ that you get out of solving the orbit equation for an inverse-...
0 votes
1 answer
62 views

Has our knowledge of astrophysics and gravity reached the point where we can accurately calculate Lagrange points?

is it possible for us today given the knowledge we possess of gravity and our success with inserting satellites in to steady/ geosynchronous orbit and any knowledge we have on the relative size (and ...
2 votes
1 answer
88 views

Are we certain of the mass we calculate for supermassive black holes?

If astronomers have concluded that the rotation speed of objects held firmly within a galaxy but far from a galactic center is too great to be explained by the visible matter of the galaxy alone, what ...
0 votes
3 answers
579 views

Two particles rotating about their center of mass

Two bodies each of mass $m$ are rotating about their center of mass where the radius is $r$. Here centripetal force of each body is $\frac{mv^2}{r}$ where $v$ is the linear speed. Now, gravitational ...
1 vote
2 answers
98 views

How can it be known what the Earths periods of eccentricity, perihelion and obliquity are when the observational data only cover at most 3,000 years?

How can it really be known what the earths periods of eccentricity, perihelion and obliquity are when the observational data only cover at most 3,000 years? What I mean is that these parameters ...
3 votes
1 answer
225 views

Geodesic equations and Carter constant: how can I derive the right equations?

Introduction Suppose the Hamilton-Jacobi equation: $$\frac{\partial S}{\partial \lambda} + \frac{1}{2}g^{\mu\nu}\frac{\partial S}{\partial x^{\mu}}\frac{\partial S}{\partial x^{\nu}}= 0. \tag{1}$$ Now,...
0 votes
5 answers
697 views

Regarding the objects in free fall in the ISS

There are lots of information about this topic, but I'm still greatly confused about something: Astronauts in the ISS are in free fall all the time because they have only gravity acting on them, but ...
2 votes
1 answer
225 views

Question about Lagrange's solution for the three-body problem

The original text in my textbook, written in short: "By Newton's second law, $$\ddot{\mathbf{x}}_1=-Gm_{2}\frac{\mathbf{x}_1-\mathbf{x}_2}{|\mathbf{x}_1-\mathbf{x}_2|^3}-Gm_{3}\frac{\mathbf{x}_1-...
2 votes
1 answer
43 views

Trajectories of projectile based on different speeds of projection [duplicate]

So my teacher was teaching gravitation and an interesting fact that he mentioned was the trajectory of a projectile projected from Earth at a speed equal to escape velocity, is parabolic. Also, he ...
0 votes
3 answers
82 views

Pseudo Orbital motion only due to Coriolis force

Planet, say of mass M and radius R is rotating with some angular velocity ω and a object of mass m (initially on the surface and rotating with the planet) was launched with velocity v vertically ...
1 vote
1 answer
895 views

How do I use Kepler's Laws to propagate an orbit for a Two-Line Element (TLE) Set?

I need to propagate a large number of orbits (get a satellite's position at a certain time) from TLEs (two-line element sets) using Kepler's laws. Ordinarily I'd use a real propagator like SGP4/SDP4, ...
0 votes
1 answer
257 views

Energy in central force orbit

Given a mass $m$ moving under the central force $$F(r) = -\frac{k}{r^n}$$ and a circular orbit passing through the force center, I want to show $n$ must equal $5$. I ultimately arrive at the ...
4 votes
1 answer
164 views

Would the Moon move away if the Earth were frozen with no liquid tide?

The moon is moving further from the Earth. To the extent that after 600 million years we will no longer enjoy full solar eclipses as it will be too far away to completely block the sun. The reason the ...
2 votes
4 answers
2k views

Projectile/orbital motion over very long distance

We know the optimum angle for greatest horizontal displacement when launching an object with projectile motion is 45 degrees. How to solve the angle when it is real long distance around the earth ...
0 votes
0 answers
31 views

Better equations for modeling and simulating a halo orbit?

I'm trying to model a halo orbit at low altitude (10m from surface). The satellite is using propulsion to trace the circular halo path. It looks like this "from the top" (the blue ball is ...
0 votes
0 answers
31 views

Restricted 3-body: one large mass and two smaller ones

A restricted 3-body problem is usually understood as two large bodies and one much smaller one that doesn't affect the motion of the other two. I am curious about a 3-body problem with one large body, ...
4 votes
2 answers
783 views

Good sources to get velocity/position vectors for all planets and moons in the Solar System for building an orbital simulator?

I’m building an $N$-body simulator, and I have everything ready to begin simulating. But my issue is is that I have no idea how to get all the starting positions and velocities for the celestial ...
6 votes
7 answers
1k views

What changes the velocity perpendicular to radius in an elliptical orbit?

I'm working currently on a problem that asks to justify that angular momentum and kinetic energy conserves for a planet in an elliptical orbit. Although I've been taught that angular momentum should ...
3 votes
1 answer
430 views

Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?

In the book of Classical Mechanics by Goldstein, at page 88, it is given that: $$ \frac{d^{2} u}{d t^{2}}+u=-\frac{m}{l^{2}} \frac{d}{d u} V\left(\frac{1}{u}\right) . $$ The preceding equation is such ...
2 votes
1 answer
688 views

Deviations from purely circular orbit for an object in a Yukawa potential

I am struggling with the logic for completing the following problem. The problem is part b of 3.19 in Goldstein's Classical Mechanics book. A particle moves in a force field described by the Yukowa ...
3 votes
1 answer
1k views

Why does the Earth orbit its axis in the same direction it rotates the Sun?

Suppose you are the young Earth that is being formed in the early solar system. Let's say north is up, so left of you is the (soon to be?) sun, since the Earth orbits the sun counter clockwise. Stuff ...
1 vote
3 answers
100 views

Escape Velocity from Moon to escape Earth-Moon System

So the escape velocity at Earth is roughly 11.2 km/s, but with the escape velocity of the moon it says that it is 2.38 km/s but since the moon is orbiting the Earth, wouldn't the effective escape ...
1 vote
1 answer
122 views

Which of Kepler's laws would remain true if the force of gravity were proportional to the product of squares of each masses?

I was asked this question recently on which of the Kepler's Three law would remain if we changed the force of gravitation to be proportional to the product of squares of each masses instead of just ...
0 votes
1 answer
61 views

Find eccentricity of orbit given the velocity and the semi-major axis

Is it possible to calculate eccentricity of orbit knowing only the semi-major axis and the velocity of both celestial bodies? If not, what other additional information is required. Does the fact that ...
0 votes
1 answer
132 views

Deflecting a lunar mass with consecutive nuclear explosions [closed]

I'm looking for help in determining the amount of deflection an object with a mass of roughly $7\times10^{22} \,\text{kg}$ (a lunar mass) needs from colliding with a planet. Let's stipulate that the ...
0 votes
1 answer
44 views

The magnetic force between the earth and the sun

There is a magnetic field around the earth and a stronger one around the sun. I guess there should be a magnetic force between the sun and earth. Now, shouldn't we take the magnetic force into account ...
1 vote
4 answers
160 views

Gravitational attraction between two bodies

While the gravitational force between two bodies is directly proportional to their masses, and inversely proportional to the distance between them is understandable / seems logical, how did Newton ...
0 votes
1 answer
85 views

Questions about speed of gravity [duplicate]

If gravity "travels" at $c$, and the sun is travelling "forward", does it mean the planets are actually orbiting various points "behind" the center of the sun? Does it ...
2 votes
0 answers
37 views

When are two object guaranteed to keep getting further and further away?

In a two-body problem, it is known (if I understand correctly) that if the specific orbital energy of the system is $\varepsilon \geq0$, then the objects must eventually escape each other. My question ...
0 votes
1 answer
48 views

Would an Hypothetical Ringworld Positioned Inside the Moon's Orbit Around Earth, gravitationally affect Earth?

If a ringworld were to encircle Earth within the orbit of the Moon, would it induce any gravitational alterations on Earth? I grasp that inside a circular structure, there might not emerge a ...
0 votes
2 answers
83 views

Initial positions and velocities for the three-body problem

I have made a simulation of the three-body problem, it follows the euler's method of solving differential equations. I have tried some initial positions and velocities of the bodies and have observed ...
15 votes
2 answers
512 views

Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?

I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
16 votes
4 answers
9k views

Where does tidal energy come from?

Kind of an odd, random question that popped into my head. Tidal energy - earth's ocean movement, volcanism on some of Jupiter's moons, etc. - obviously comes from the gravitational interaction between ...
18 votes
3 answers
11k views

Why does the Moon drift away from Earth?

I once saw on TV that the Moon is slowly drifting away from the Earth, something like an inch a year. In relation to that the day on Earth what also increase in time. I wonder why is that?
0 votes
0 answers
51 views

Despite tides the Moon, as far as I know, doesn't slow down. Where does the energy come from? [duplicate]

Hy, I don't have anything to do with physics, so please forgive me if I explain my question in a weird way ;) As the Moon rotates around the earth it is creating tides and waves on the earth. IE it's ...
0 votes
1 answer
48 views

Speed of satellite in elliptical orbit [closed]

A satellite $S$ orbits a planet of mass $M$ in an elliptical orbit. At perihelion, $S$ has a tangential velocity of $v_1$ and is distance $r_1$ from the planet. At aphelion, $S$ has a velocity of $v_2$...
0 votes
0 answers
37 views

With what vel. would you have to launch an object vertically up from the earth's surface for it to land back again at it's initial launching point?

[Can skip reading this part] First of all, Newtonian gravity shall be considered whilst trying to solve this question. It's been on my mind for a long, long time and has been bothering me since. I ...
1 vote
2 answers
67 views

How do two things attracted to each other move in mechanics?

Okay very simply: If you have two objects in 1D and they're both attracted to each other by some force (say there's a spring pulling them both towards each other, or Coulomb's Law or something)... How ...
1 vote
1 answer
196 views

The shape characteristics of gravitational wells given different masses and spread of objects

I am curious as to research that calculates the shape of gravitational wells, and their limits, and affect on time, for different masses and spread of mass. The actual question is st the end. For ...
5 votes
1 answer
4k views

How to show circular orbit as a precessing ellipse

A uniform distribution of dust in the solar system adds to the gravitational attraction of the sun on the planet an additional force linear in $r$ where m is the mass of the planet, k is a constant (...

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