64
votes
Accepted
Is there a maximum distance from a planet that a moon can orbit?
The concept you're looking for is that of a planet's Hill sphere. If a planet of mass $m$ is in a roughly circular orbit of radius $a$ about a star of mass $M$, then the radius of this "sphere&...
- 50.4k
63
votes
Accepted
Why does the Earth follow an elliptical trajectory rather than a parabolic one?
Now that doesn't apply on the orbit of the Earth. The gravitational force can be thought of as constant since the distance fron Earth to Sun can be thought of as constant too
You are correct that the ...
- 41.9k
59
votes
What does the Moon's orbit around the Sun look like?
Incorrect Path
I'm curious as to what does the moon's orbit around the sun looks like?
One might think the orbit (in the sun's rest frame) follows the path of an epitrochoid.
A (very) over ...
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49
votes
What does the Moon's orbit around the Sun look like?
The Moon's orbit must be concave toward the Sun.
The Moon's orbit with respect to the Sun is always convex. This is easily proven by comparing the minimum possible gravitational acceleration of the ...
- 41.7k
42
votes
Simulating solar system with Newton's law
You need to use a better numerical method. Euler’s method is notoriously bad for orbital mechanics because the numerical errors always accumulate. In particular, Euler’s method does not conserve ...
- 105k
41
votes
Accepted
If the 3-Body force problem hasn't been solved, how do rocket scientists plan orbits of spacecraft?
The three body problem isn’t “solved” in the sense that there is no known closed form solution that works for any general initial conditions.
However, when you have two massive bodies and one that is ...
- 119k
41
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 ...
- 57.5k
39
votes
Accepted
For a spacecraft orbiting a planet, orbital speed is inversely proportional to orbit radius. But speed must be increased to increase orbit radius?
The equation you have written there applies only for circular orbit but the orbit is not circular during the time the spacecraft is climbing to higher orbit. As the spacecraft climbs towards the ...
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30
votes
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Minimal velocity to throw an object to the Sun
The limitation to hit the sun is that the object has to have very little angular momentum. The reason for this is that as the distance to the sun gets smaller, the velocity in a direction ...
- 17.2k
29
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 ...
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26
votes
Why does the Earth follow an elliptical trajectory rather than a parabolic one?
The gravitational force can be thought of as constant since the distance fron Earth to Sun can be thought of as constant too, which by Newton’s second Law means the acceleration of Earth is also ...
- 15.4k
25
votes
If another planet was opposite Earth, would we be able to observe it?
We could certainly be able to infer its existence through tracking the motions of the planets we can see and then simulating the gravitational motions of those planets. Adding a similar sized planet ...
- 28.5k
24
votes
Proving Kepler's second law of planetary motion using conservation of angular momentum: What about gravity from other planets?
Deriving Kepler's laws in this manner is somewhat of an idealization that works because the perturbing effects of other planets are relatively small. If you consider more than just one planet and the ...
- 4,529
23
votes
Accepted
What's the actual path of the planets?
This is an interesting question, since it raises the problem of the reference frame where Kepler's laws are true, which is often neglected.
As a consequence of Newton's laws, in the inertial reference ...
21
votes
Why does an orbit become hyperbolic when total orbital energy is positive?
Intuitively, you expect that if your total energy $E$ is positive, then you have more kinetic energy than potential energy. Hence, the potential is not strong enough to ever bind the object into a ...
- 25k
20
votes
Accepted
Is it possible for a moon to have the same orbital period as its planet?
This occurs at the Lagrange points, where the moon is stationary in the rotating reference frame. A moon at L1, between the planet and the star, or at L2, on the "outside" of the planet's ...
rob♦
- 91.9k
19
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If another planet was opposite Earth, would we be able to observe it?
You have some good answers already, but neither touch on a critical issue with this proposal.
The wikipedia about Lagrange points clarifies that the Lagrange point in question (L3) is not stable. (See ...
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18
votes
Accepted
Proving Kepler's second law of planetary motion using conservation of angular momentum: What about gravity from other planets?
You're not wrong, strictly speaking we should consider the force of gravity from the other planets. However, the Sun is by a large margin the most massive body in the solar system, hence to first ...
- 21.5k
17
votes
Accepted
Why does an orbit become hyperbolic when total orbital energy is positive?
Is there any empirical reasoning as to why this is true?
I'm not sure what you have in mind, but I'll give it a try. See from the equations that:
$$E_k\ge 0$$
and
$$E_p \lt 0$$
So, if the total ...
- 59.9k
17
votes
Accepted
What would happen to the moon if we reduce its tangential velocity slightly?
No, the moon will not eventually fall to earth. Reducing the tangential velocity by a small amount will affect the orbital trajectory of the moon. Since the path followed by the moon is already ...
- 2,362
17
votes
For a spacecraft orbiting a planet, orbital speed is inversely proportional to orbit radius. But speed must be increased to increase orbit radius?
A simple way to calculate moving from one circular orbit to a larger one: Start by increasing the speed. The orbit becomes an ellipse. As Kirby points out, the speed decreases as the satellite moves ...
- 12.2k
16
votes
Can an atom orbit the Sun?
No, and radiation pressure is not the only reason.
The interplanetary space is not empty; apart from the optical photons it is in particular also flooded with the charged particles of the solar wind. ...
- 15k
16
votes
Accepted
What are the forces behind the orbit of the Earth around the Sun?
Yes, it does. Your description is correct. Other bodies than the Sun also pull in Earth with their respective gravities, though, but they are effectively negligible.
The elliptic effect is not as ...
- 51.7k
16
votes
Accepted
Mars' orbital period
For the "pure" two-body problem in classical mechanics, the period of the orbit is completely determined by the semi-major axis $a$, and is completely independent of the orbit's eccentricity....
- 50.4k
15
votes
What does the Moon's orbit around the Sun look like?
Before answering let me mention that there is a terrific free applet showing the orbits, including the velocity vectors of the system Sun/Earth/Moon:
https://phet.colorado.edu/en/simulation/gravity-...
- 17.9k
15
votes
Accepted
Kepler's 3rd law: ratios don't fit data
that equality should be a proportional to sign. In particular, in SI, the squared period has units of seconds squared, and the semi-major radius of of the orbit cubed is in meters cubed, so they can'...
- 41.7k
14
votes
Why are $L_4$ and $L_5$ lagrangian points stable?
As others have commented, including OP, the effective potential (consisting of gravity & the centrifugal potential)
$$V~=~ -\frac{Gm_1}{|z_1|}
- \frac{Gm_2}{|z_2|}
-\frac{\Omega^2 |z|^2}{2} \tag{...
- 208k
14
votes
Accepted
Under which conditions do two moving bodies start orbiting each other around their center of mass?
Unless other objects are "near enough" to complicate the motion, the bodies can always be described by a two-body solution whenever both are in freefall (nothing is pushing one of them). The only ...
- 41.9k
14
votes
WHY can't we use conservation of energy to find speed of the earth around the sun?
It is correct that
$$
-\frac{GmM}{R}+ \frac 12 mv^2= constant,
$$
but you assumed that the constant is zero. It is not necessarily so.
- 55.2k
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