The Newtonian model of gravity in which the force between two objects is given by GMm/r^2.

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Question on motion of vehicles

What slows us down while we are climbing in a sloped road, and what makes us faster while sliding down? Friction and what else?
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1answer
31 views

How would you go about solving this graphical mass problem? [on hold]

I've tried finding the x and y components of the vectors created by each mass to find the resulting vector's magnitude. However, my answer of 0.354 N keeps getting marked wrong. Any ideas on how to ...
5
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1answer
51 views

Dynamics of pairwise distances in the $n$-body problem

Consider the $n$-body problem where we are interested in describing the time evolution of $n$ masses interacting through a potential $U$. Let $D$ be the matrix containing all pairwise distances ...
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0answers
45 views

Potential Energy = mgh. What is the name of this principle and did Newton discover it?

Somebody I know keeps trying to convince me that Potential Energy $PE=mgh$ is one of Newton's Laws (as well as the closely related idea, Work Done = force x distance moved). I am fairly certain that ...
2
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1answer
102 views

What is the significance of the Inverse-square law? [duplicate]

Considering its occurrences in various fields like Electrostatics, Gravitation, Acoustics etc. how does the law bind these topics together?
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2answers
57 views

Free fall vs throw with air resistance

If I let a stone drop from a certain height and throw a stone from a certain height, with air resistance, which will reach the ground first? When I draw a free body diagram the air resistance in the ...
59
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5answers
6k views

If dark matter only interacts with gravity, why doesn't it all clump together in a single point?

I'm a complete layperson. As I understand, dark matter theoretically only interacts with the gravitational force, and doesn't interact with the other three fundamental forces: weak nuclear force, ...
18
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3answers
2k views

Gravitational force when standing on an infinite disc

If a person were to stand on a flat disc of thickness 1 meter but infinite diameter, would they experience finite or infinite downward force? There is an infinite amount of mass, all of which ...
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0answers
5 views

Acceleration as a function of time in Newtonian gravity [duplicate]

In Newtonian gravity, you have acceleration as a function of separation distance $r$ as $a(r) = GM/r^2$. I need to derive acceleration as function of time, i.e. $a(t)$. PS I got into this when I ...
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1answer
125 views

What's my $\mathrm dM$? Gravitational Potential inside a circle of mass

I'm trying to find the gravitational potential for an arbitrary point within a ring of uniform mass density. The point is constrained to be in the same plane as the ring. So we start with: $$\Phi=\...
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12answers
2k views

Is the distance between the Sun and the Earth increasing?

M = mass of the Sun m = mass of the Earth r = distance between the Earth and the Sun The sun is converting mass into energy by nuclear fusion. $F = \frac{GMm}{r^2} = \frac{mv^2}{r} \rightarrow r =...
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2answers
919 views

Is Earth's orbit around the Sun affected by the ~8 minutes light delay?

Gravitational change occurs at the speed of light. As a consequence, we experience on Earth the gravitational attraction of the Sun based on its position relative to us ~8 minutes ago. How does this ...
3
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1answer
68 views

Gravitational force between Earth and Sun is decreasing

According to one of the most famous equations in physics, i.e. $E=mc^2$, the mass of the Sun is decreasing as it emits energy. So there must be some kind of disturbance in planetary orbits, and if ...
56
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5answers
8k views

Why do archery arrows tilt downwards in their descent?

In the movies, arrows shot into the air rotate so that during the descent, the arrow head hits ground first. What is the source of this angular momentum? It would seem that the bow string exerts a ...
1
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2answers
42 views

How well-defined is the infinite-sheet-of-mass computation?

When computing the gravitational force from an infinite plane (or the electrical field from an infinite sheet of charge), it is standard to begin by making a symmetry argument to say that the ...
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3answers
691 views

Infinite grid of planets with Newtonian gravity

Assuming only Newtonian gravity, suppose that the universe consists of an infinite number of uniform planets, uniformly distributed in a two-dimensional grid infinite in both directions and not moving ...
4
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1answer
58 views

Details of Newtonian Prediction for Mercury's Precession

Could anyone point me to a book or outline the methods used to actually calculate the 532 arcseconds per century that Newtonian theory apparently predicts for Mercury's precession. I am completely ...
5
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2answers
57 views

How much mass must Earth lose to lose its Moon?

Maybe I am wrong about the basic concept here, but for my curiosity: how much mass would need to leave the Earth (like satellites and rockets) to create an imbalance between the Earth and Moon so that ...
3
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1answer
43 views

Maximum range in projectile motion (elliptical path)

Elementary Newtonian mechanics tells us that if a projectile is shot at 45 degrees from the ground, and a downward gravitational field is acting on it, it will follow a parabolic path and achieve ...
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42 views
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3answers
96 views

Gravity effects when deleting stars or planets

In one of the latest SCIFI movies, they collect a star absorving it entirely in a kind of planet size gun/machine. As mass cannot disappear, I assume it was just concentrated inside their machine (...
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8answers
10k views

Would it help if you jump inside a free falling elevator?

Imagine you're trapped inside a free falling elevator. Would you decrease your impact impulse by jumping during the fall? When?
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2answers
492 views

Kepler's laws to determine radius of circular orbit

"In nonrelativistic limit of general relativity there is a correction to the Newtonian gravitational potential energy $−h/r^3$ with $h = αL^2/(mc)^2$, where $c$ is the speed of light, $α = GMm$ and $...
6
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1answer
320 views

Derivation of Universal Variables

Does anyone know of link to the derivation of the Universal Variables? This is in regards to Kepler's equations. The Wikipedia link didn't have enough information for me, and the Colorado page doesn'...
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1answer
55 views

Are lighter molecules in the air more affected by earth gravity?

Or: Why are raindrops falling? In vacuum a heavy (big mass) object is attracted by gravity with the same speed as a light object as shown on the moon with the hamer and the feather. But on earth ...
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6answers
256 views

If gravity is additive, then how does it cancel itself out?

I understand that gravity, as far as we know, is always attractive. Also, it has additive qualities - i.e. the size and strength of the field are proportional to the quantities of mass. This seems to ...
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2answers
499 views

Escape velocity at an angle

Comparing the work required for a mass to escape the Earth's gravity to the necessary initial kinetic energy gives us the escape velocity from the surface of the Earth of around $11\;\mathrm{km\cdot s^...
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Predict position of a body in an elliptical orbit in Cartesian coordinates [closed]

A spaceship is orbiting a star on a 2-dimensional plane. I know: The orbit is elliptical The mass of the star Where the star is in x,y coordinates Where the spaceship is in x,y coordinates. The semi-...
4
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2answers
142 views

Weight Distribution of granular piles

I was recently at a farm watching piles of grain being formed in the shape of enormous cones. Each of these grain stacks weighs in excess of 50 tonnes. I am not a physicist but I am very curious as to ...
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6answers
3k views

Gravity - What happens when two objects of unequal masses fall freely towards the ground? (Revisited)

The common perception regarding what happens when two objects of equal sizes but unequal mass are allowed to fall freely towards the ground is that - both the objects make contact with the ground at ...
76
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8answers
9k views

Could a “living planet” alter its own trajectory only by changing its shape?

In Stanislaw Lem's novel Solaris the planet is able to correct its own trajectory by some unspecified means. Assuming its momentum and angular momentum is conserved (it doesn't eject or absorb any ...
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0answers
17 views

How can I measure the stability of a many body gravitational system?

Suppose I have an N body planetary system interacting via gravity. Suppose I know the positions and momenta at t=0. How do I know if this system is stable (indefinitely)? By stable I mean the ...
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1answer
74 views

Relation between gravitational field and gravitational potential

The gravitational field is the negative differential of the gravitational potential. Now the gravitational potential due to a particle at a distance $r$ is $-Gm/r$ where $m$ is the mass of the ...
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2answers
655 views

Tension in string and gravitational force on bob relative strength

When calculating time period of simple pendulum (an approximation of SHM at small amplitudes) we take gravitational force greater than tension in string and resolve gravitational force in two ...
2
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1answer
48 views

Tidal effect on planet with two moons

If an Earthlike planet had two moons, one relatively smaller and closer while the other was bigger and farther away, and one had a prograde orbit while the other had a retrograde orbit, in what ways ...
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3answers
235 views

Does center of mass affect how an object falls?

Suppose you drop an object which has two ends, of which one is heavy and the other is pretty light. Will the object fall with its heavier end downward or with the lighter one? Why does it happen?
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1answer
27 views

Solar balloon vs hydrogen or helium filled balloon

This is my very first post here and I used the search engine to make sure this set of questions was not asked before. Sorry if it is the case for some reason. Feel free to delete my post. Here are my ...
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0answers
29 views

Why does the inverse square law cause elliptical orbits? [duplicate]

I've seen it printed multiple places, here for example, that the reason orbits are elliptical is because the gravitational law has an inverse square of the radius. Why does this make the orbits ...
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3answers
5k views

Derivation of Kepler's laws

How can analytically be derived the Kepler's laws? I found some extremely synthetic equations which from the Newton's laws (in particular $\mathbf{F} = m \mathbf{a}$) tried to obtain the Kepler's ...
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0answers
34 views

Mathematical proof for elliptical orbit of planets [duplicate]

Elliptical orbits are stable for planets. But how to mathematically derive this result that a planet travels in an elliptical path? How are circular orbits less stable than elliptical orbits for ...
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2answers
82 views

Negative Gravity Fields and Time Dilation [duplicate]

Question: Some physicists believe that it is possible to have negative mass. My questions is would this negative mass create a negative gravity field, exerting a negative force on positive masses? And ...
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2answers
49 views

Problem with derivation of potential enery of two body in Gravitational energy

Maybe what I'm going to ask sounds stupid but it means a lot to me that's why I'm asking. I've problem with just a single step in derivation. Let's start. I'm keeping in mind the direction of each ...
2
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2answers
111 views

Equation for a falling body including terminal velocity

I'm making an app that times how long it takes a pebble to fall, then calculates the distance it fell. I noticed that the simple $f(t) = \frac{1}{2}gt^2$ was becoming increasingly inaccurate as the ...
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2answers
230 views

Confusion about gravity

I understand the “rubber sheet” model of Relativistic gravity is just an illustration, and beyond the initial issues of mixing three dimensional objects with a two dimensional representation of 3D ...
0
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1answer
30 views

Where does gravity get it's energy to cause tides? [duplicate]

The moon's orbital radius is fixed as a function of its velocity (I know it is actually drifting..). Since there is nothing in space to resist this velocity, it will continue orbiting "forever". Now ...
0
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4answers
363 views

Inertia and Rocket Propulsion

We were taught in school that the law of inertia indicates that an object tend to stay the way it is, so if you throw something in space it will tend to go on forever and ever. The reason an object ...
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0answers
28 views

Average of the velocity vector along a Keplerian orbit

I would like to show that the average of the velocity vector $\mathbf{v}$ along one Keplerian orbit vanishes, i.e. $$ \frac{1}{2 \pi}\int_{0}^{2 \pi} \!\!\!\! \mathrm{d} M \, \mathbf{v} = \frac{1}{T}\...
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1answer
29 views

Rolling motion of a rigid object

I have the situation described in this picture I know the speed of the ball at the top of the loop ($v_{top} = 2.38 m/s$), and I have to demonstrate that the ball does not fall from the track at ...
3
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1answer
318 views

Marvin the Martian vs. the Death Star: how much energy will they actually need to disintegrate the Earth?

According to a detailed analysis by Dave Typinski, Marvin the Martian’s Illudium Q-36 Explosive Space Modulator will require $1.711 \cdot 10^{32}~\text{J}$ to shatter the Earth into a gravitationally ...
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3answers
535 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...