# Questions tagged [orbital-motion]

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

2,236 questions
Filter by
Sorted by
Tagged with
13 views

### 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 ...
20 views

### 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,...
6 views

### 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.
• 1,304
1 vote
56 views

### 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 ...
77 views

### 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 $c$ ...
• 263
141 views

### 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: ...
• 291
50 views

### 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 $r_0$ ...
1 vote
14 views

### 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 ...
• 111
22 views

### 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 $c$ ...
• 263
1 vote
62 views

### 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, ...
• 11
40 views

### 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 ...
• 103
1 vote
53 views

### 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 ...
• 11
28 views

### 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
56 views

### 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, $L$ ...
• 390
57 views

### 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 ...
• 653
78 views

### 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 ...
1 vote
52 views

### 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 ...
• 11
79 views

### 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 ...
117 views

### 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? ...
• 83
24 views

### 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 ...
• 121
1 vote
60 views

### 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 ...
• 11
69 views

### 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 ...
• 101
1 vote
73 views

### 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 ...
66 views

### 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 ...
1 vote
106 views

### 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 ...
95 views

• 16.2k
14 views

### 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 ...
48 views

### 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 ...
58 views

### 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 ...
17 views

### 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 ...
117 views

### 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 ...
• 270
19 views

### 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 ...
• 101
51 views

### 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 ...
• 11.4k
19 views

### 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 ...
• 35
525 views

### 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:...
• 31
116 views

### 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 ...
• 5,968
1 vote
150 views

### 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 ...
• 316
171 views

### 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 ...
• 4,852
36 views

### 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?
• 323
1 vote
57 views

### 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 ...
• 323