37
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
Your intuition that two isolated objects approaching each other and not already in a closed orbit will either collide or will fly apart again is substantially correct. If the objects are not already ...
- 47.3k
24
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
Btw, here's an expertly drawn diagram that took 1000 hours in MS Paint to show things visually.
None of your three pictures really illustrates the actual physical scenario very well. (OK, picture B ...
- 13.3k
11
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
they can either miss each other and fly apart (if the velocity is enough and there's not enough gravitational attraction between them), or they can be attracted enough to each other that they ...
- 94.4k
7
votes
Can the Schwarzschild orbit equation be solved exactly?
Closed-form analytic solutions for bound timelike geodesics around a Schwarzschild black hole were first (to the best of my knowledge) given by Charles G. Darwin (grandson of) in 1959 in this paper (...
- 10.3k
7
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Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
Partly it's about how galaxies form (see another excellent answer about that).
But do also consider that you're seeing the survivor bias of 13.8 billion years. If they weren't in a stable orbit, the ...
- 2,531
6
votes
Accepted
Meaning of a Constant in the Unbound Orbit Equation
Your equation is close to the standard form, rewrite it with $\delta$ of zero, and $\alpha$ and $\beta$ as $a$ and $b$. Here is a figure from Wikipedia (Hyperbola article):
The distance $MF_1$ is ...
- 356
4
votes
Is Each Day the Same Duration?
Yes, the solar day length varies from 24 hours - ~22 seconds to 24 hours + ~30 seconds. Here's a graph for 2022, computed for apparent solar noon at Greenwich, using data from JPL Horizons
The ...
- 11k
4
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
chausies asked: "Why are there so many objects perfectly orbiting each other?"
Apart from the fact that most orbits are not perfectly circular but more or less elliptical: if two objects ...
- 10.9k
4
votes
Accepted
Why is the time from vernal and autumnal equinox different than from the autumnal to the vernal one?
as I think the paths are symmetrical parts of the elliptical orbit of the earth
No, they are not symmetrical in the way you think.
Perihelion and aphelion are separated by exactly $180°$
(by ...
- 36.2k
3
votes
Escape velocity work done problem
to provide velocity to send to infinite distance from gravitational pull of earth so for that we have to apply external force
This is called an “initial velocity”. The problem begins at the “initial ...
- 94.4k
3
votes
HW: particle subject to central force with exponential logarithmic orbit
Well, you know the trajectory to be a logarithmic spiral, and you have figured out the relation between the time $t$ and angle $\theta$. At the starting position, $t=0$ and $\theta=0$. If you look ...
- 211
3
votes
What is the motivation for supposing a pendulum exhibits circular motion?
I am aware that the central tenant of circular motion is that there is a centripetal force acting radially inward that takes on the form $$F = \frac{mv^2}{r}$$ and that the velocity along this path is ...
- 94.4k
3
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
And yet there are a zillion celestial objects perfectly orbit each other
This is survivorship bias. Based on our current model of how we think planets form, there were many orders of magnitude ...
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2
votes
How does the Dzhanibekov Effect change if replaced with a propeller?
A T-handle has three distinct mass moment of inertia values (indicated below in red, green and blue directions)
As you notice, about the z-axis (blue) the MMOI value of $47\;{\rm kg}\,{\rm mm}^2$ is ...
- 37.4k
2
votes
Whats the difference between the Photon Sphere and the Marginally bound orbit?
For a circular orbit around a large mass of mass $M$ under Schwarzschild geometry the energy of the the body of mass $m$ in circular orbit may be written as:
$$E=mc^2\frac{1-2 \frac{GM}{rc^2}}{\sqrt{1-...
- 719
2
votes
Is Each Day the Same Duration?
Yes, the length of the day varies.
This is graphically captured in the analemma, which I will display w/o explanation (other than the photo of the sun is taken at the same local time throughout the ...
- 31.4k
2
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
At first glance it may seem this way, but conservation of angular momentum sort of acts as a "restoring pseudoforce" to make orbits more likely.
If one object is traveling towards another ...
- 7,362
1
vote
Why is the time from vernal and autumnal equinox different than from the autumnal to the vernal one?
Consider the following:
The earth's orbit is an ellipse; the sun is located at a focus of the ellipse, not at the centre of the ellipse
The earth reaches perihelion in early January;
The earth ...
- 10.6k
1
vote
Accepted
What is the expression for strong field Schwarzschild circular orbit perihelion precession?
The periapsis precession for a circular geodesic with radius $r$ in the Schwarzschild metric is
$$ 2
\pi \left(
\sqrt{\frac{r}{r-6M}}-1\right)$$
The answer for a generic bound geodesic with (...
- 10.3k
1
vote
Why does the radius of orbit increase when a satellite increases it's velocity?
Technically, the future dynamical state of the orbit will depend entirely on the acceleration vector when the thrust is applied.
Simply stating that the velocity of an object in orbit has increased is ...
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