# Tag Info

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
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### 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

### 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 ...
• 15.7k

### 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

### 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
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### 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

### 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
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### 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 ...
• 808
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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

### 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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### 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

### 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

### 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
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### 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 ...

### 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
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### 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 ...
• 91.9k

### 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 ...
• 7,536
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### 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
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### 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
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### 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

### 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 ...
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### 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. ...
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
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### 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....
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### 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
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### 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'...
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