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

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How far would an arrow go in a space station and still be deadly?

So I was answering a question on the WorldBuilding SE site and one aspect of my answer made me wonder. Imagine you are on a massive space station of unlimited size. If you were to fire an arrow from ...
2
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3answers
72 views

Why does weight on Earth have a tangential component?

I read in Pulsar's answer of this question that weight has a tangential component due to the rotation of the (assumed spherical) Earth but I don't understand this. Can someone expand on it please?
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1answer
1k views

Understanding the math behind a falling object attached to a parachute

I'm trying to understand the mathematics behind calculating the total speed and force of a $40 kg_f$ object hooked up to a parachute, falling to Earth. From what I understand, the formula for this is ...
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1answer
117 views

As The World Turns 2

When dinosaurs roamed the Earth was the Earth rotating faster creating less gravity to allow for their size? How much would 100 kg weigh then?
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4k views

How the apparent weight varies due to the rotational motion of Earth?

I learned that as the earth rotates about its axis, the bodies on the earth also follow a circular path. In most books I read, they give the example of a person standing on a weight balance at the ...
0
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1answer
29 views

Weight Detection Under Concrete/Asphalt [closed]

Consider that a weight sensor was embedded in a road. Would cars that drive over it trigger the sensor? I was thinking it'd look something like this (if we ignored the downward force that the ...
52
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6answers
7k views

Why is the Moon considered the major cause of tides, even though it is weaker than the Sun?

You have likely read in books that tides are mainly caused by the Moon. When the Moon is high in the sky, it pulls the water on the Earth upward and a high-tide happens. There is some similar effect ...
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1answer
48 views

Newton's 1st law [closed]

If all of a sudden the gravitational force and gravity disappears then the planets would still continue to rotate and revolve ? Give reason
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2answers
853 views

$1/r^2$ gravitational force of triangles in 2D

Suppose I have two triangles relatively close together (so they probably shouldn't really be treated as point masses). I want to calculate the gravitational force (and potentially torque?) generated ...
5
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1answer
65 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 ...
23
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4answers
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How does gravity work underground?

Would the effect of gravity on me change if I were to dig a very deep hole and stand in it? If so, how would it change? Am I more likely to be pulled downwards, or pulled towards the edges of the hole?...
3
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2answers
65 views

How deep does a gravity well need to be to remove particles from a planetary body?

I almost considered asking this question on WorldBuilding, however I wanted the brute mathematics on the subject, so please excuse the theoretical nature of this question. I understand the basic ...
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1answer
42 views

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

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 ...
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0answers
55 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
126 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?
0
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2answers
62 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
votes
5answers
7k 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, ...
20
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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 ...
0
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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
127 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=\...
11
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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 =...
5
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2answers
931 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
votes
1answer
73 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 ...
57
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5answers
9k 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 ...
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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 ...
13
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3answers
693 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 ...
5
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2answers
63 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
votes
1answer
50 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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1answer
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97 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 (...
18
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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?
0
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1answer
67 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 ...
0
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6answers
271 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 ...
2
votes
2answers
505 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^...
4
votes
2answers
144 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 ...
8
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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 ...
77
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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 ...
0
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0answers
18 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 ...
0
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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 ...
2
votes
1answer
49 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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vote
1answer
31 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 ...
0
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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 ...
1
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2answers
90 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
50 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 ...
0
votes
1answer
32 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
366 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 ...
0
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0answers
30 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}\...
1
vote
1answer
32 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 ...
1
vote
3answers
545 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 ...
5
votes
4answers
533 views

Are elliptical orbits really elliptical?

I have wondered for a long time how elliptical orbits can work. It seems awkward for a freely-moving object to come very close to a source of gravity and then return to the exact point where it ...