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

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23
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5answers
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Build a ring around Earth, then remove the supports

What would happen if we decided to build a giant ring that managed to wrap around the whole world, end to end that was supported with pillars all along the ring and then the supports all suddenly ...
0
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1answer
47 views

Why do we have to use an integral in this scenario to figure out $v_{max}$? [duplicate]

$$\int_0^R mg\frac{r}{2}dr=\frac{m}{2}v_{max}$$ and can't write $$\frac{m}{2}v_{max}=mgR$$ don't we usually equal potential energy to kinetic energy? A stone is falling through a tunnel towards the ...
0
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1answer
89 views

Is there anything interesting about an n-body system whose potential energy is constant?

I am curious about a system of gravitating bodies with particular characteristics. Before describing the characteristics of the system, let me say what I want to know about it: Can this be a ...
4
votes
2answers
1k views

Platform diving: How deep does one go into the water?

I am a platform diver. I am trying to figure out how deep in the water I go depending on which platform I dive from. The platforms are 1m, 3m, 5m, 7.5m and 10m above the water surface. By ignoring ...
2
votes
2answers
4k views

Why does the acceleration $g$ due to gravity not affect the period of a vertically mounted spring?

For a vertically mounted spring, I was looking at the formula $ T= 2\pi \sqrt{m/k}$ for a period. Why doesn't the gravitational acceleration $g$ factor in?
0
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2answers
60 views

Human between two bodies of large mass

What if a person is put between two identical dense spherical bodies (well, not as dense as black holes, but definitely 100 times more than earth) with mass $M_1=M_2=10^{30}kg$, exactly in the middle ...
0
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2answers
214 views

Correlation between equations of elliptical orbits and pendulums

The equation for the period of a pendulum is: $$T=2π\sqrt{\frac{L}{g}}$$ Where 'g' is the acceleration due to the gravitational field and 'L' is the length. The equation for the period in of a body ...
8
votes
7answers
928 views

Distribution of Gravitational Force on a *non-rotating* oblate spheroid

Suppose a person is standing on a non-rotating$^1$ oblate spheroid of uniform density. He first stands on one of the poles, then on the equator. In which case is the gravitational force greater? In ...
0
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3answers
410 views

How much does the Earth's population affect the force of gravity? [duplicate]

If everyone on earth except one person were to gather up in one location, say the North Pole, and jump at the exact same time and stay airborne for about 1.5 sec. And that one person who did not jump ...
3
votes
2answers
276 views

Kepler's First Law of Planetary Motion: Whats at the other focus? [duplicate]

Kepler's first law states that the orbit of every planet is an ellipse with the Sun at one of the two foci. Is there anything significant about the location, or any unusual properties about the other ...
1
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1answer
60 views

Projectile motion. Is there a point where sum of the forces is 0?

Body of mass m, is thrown with initial speed, at an angle α from a horizon. Neglecting wind resistance, is there a point on the trajectory where the sum of forces is 0? I don't think so, but maybe at ...
0
votes
1answer
108 views

Two-Body problem confusion regarding equations of motion

I'm reading John Taylor's Classical Mechanics text, and I'm a little confused about something in chapter 8, which deals with the two-body problem with central forces. The issue is with the equations ...
0
votes
1answer
233 views

Question regarding calculating acceleration due to gravity on planet Mercury [closed]

I was asked to calculate the acceleration due to gravity on planet Mercury, if the mas of Mercury is $2,99 \times 10^{22} kg $ and its radius is $2,42 \times 10^{3} \ km$. The mass of the object is $...
6
votes
4answers
609 views

Can the gravitational constant $G$ be calculated theoretically?

We know all that the gravitational constant is $$G=6.67428±0.00067\times 10^{-11}\mathrm{m^{3} \:kg^{-1} s^{-2}}.$$ But can we calculate it theoretically?
-1
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1answer
1k views

how can an egg be balanced on a nailhead on equator [closed]

How can an egg be balanced on a nail head on equator? Why only on equator and not on different latitudes?
4
votes
2answers
354 views

What is the cause of planetary rotation. Not orbital rotation [closed]

I am a senior in high school, sixteen years old. I think differently than most in my class. Recently, I have been thinking about alternative causes for the rotation of our planets. My current thought ...
1
vote
2answers
381 views

What is the jerk due to gravity with ascent? [closed]

Acceleration is defined as the rate of change of velocity with time. Jerk is defined as the rate of change of acceleration with time. What is the jerk due to gravity with ascent?
1
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2answers
118 views

Does a ball spin more from left to right than it does from right to left?

I swear that in a manual on tennis published by the German Tennis Association (Deutscher Tennis Bund) it stated as fact that all things being equal a ball will move more from left to right than from ...
-1
votes
1answer
256 views

Explain the terminal velocity equation [closed]

As explained by Method 1 on WikiHow, the equation for Terminal Velocity is: $$ V_T = \sqrt{2 \times m \times g \over ρ \times A \times C} $$ Some parts of this equation are self explanatory, and ...
2
votes
3answers
740 views

Can Newton's Law of gravity be deduced using dimensional analysis?

I tried using dimensional analysis to deduce Newton's law of gravity but I wasn't able to do so as one of the equations were $0=-2$ which is a contradiction. But I thought that we can't do that ...
15
votes
5answers
11k views

How fast would someone have to run to travel vertically up a wall?

I am currently doing a physics project on the effects of so-called 'super-speed'. I was wondering how fast you would have to run to vertically travel up a wall? That is, to negate the force of gravity....
3
votes
1answer
93 views

Why does matter gather as discs around massive objects? [duplicate]

Why do discs, like rings of Saturn and the spiral shape of our galaxy form around massive objects, instead of just a (spherical?) cloud of matter?
4
votes
3answers
295 views

Why is $\pi$ used when calculating the value of $g$ in pendulum motion?

I am trying to intuitively understand why $\pi$ is used when calculating the value of $g$ using the harmonic motion of a pendulum: $$g ~=~\frac{4\pi^2L}{T^2}.$$ Does it have something to do with the ...
0
votes
1answer
116 views

What is $g$ when traveling quickly around a planet?

I am trying to model a rocket orbiting a planet. I want to simplify the problem so that the rocket is travelling along an infinitely long flat surface with a $g$ along the $y$-axis. This is what I ...
2
votes
3answers
760 views

While finding escape velocity, does human mass counts as the mass of Earth?

Escape velocity depends upon the mass of earth. my doubt is whether human mass adds into it or not? If it add then Earth's escape velocity would be increasing!
5
votes
6answers
4k views

Why does the moon stay with the Earth?

Naturally, I know it to be true that the moon goes around the Earth and that the Earth goes around the sun. However, attempting to picture this has confused me a bit. Why doesn't the moon just get ...
6
votes
4answers
31k views

Why is Earth's gravity stronger at the poles?

Many sources state that the Earth's gravity is stronger at the poles than the equator for two reasons: The centrifugal "force" cancels out the gravity minimally, more so at the equator than at the ...
10
votes
2answers
1k views

Why heavy elements don't sink to the core?

If earth assembled out of space dust, how come we find heavy elements like gold, silver, uranium and bunch of others that are heavier than iron on the surface? I mean silicon (Si mass 28.084) being ...
0
votes
1answer
159 views

How would the solar system change if the Earth were removed

I was reading a closed question with the same title and wondered if it would be on-topic with the following change: Could a large-mass object from interstellar space pass through the inner solar-...
1
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5answers
1k views

Why is kinetic energy stored as potential energy in a body during its motion against gravity?

Everyone knows kinetic energy is converted to potential energy in the body when it moves up against the earth's opposing gravitational force. But I am facing some problem with this. What I learnt ...
0
votes
3answers
9k views

When does acceleration due to gravity equal positive/negative? [closed]

For example a projectile is launched at an angle. What would $a$ in $y=vt +.5at^2$ be? Let's say I choose up to be positive. How do you not confuse yourself whether to use positive or negative $a$?
0
votes
2answers
703 views

Space Elevator: how would you keep the end of a Space Elevator's cable rigid?

I had a discussion with my wife about physics behind a Space Elevator. Imagine a cable rising 60k into the firmament for its elevator to climb. The cable would have to rotate in unison with the earth, ...
0
votes
1answer
36 views

Correcting for oblateness of the Earth [duplicate]

I'm trying to model numerically the effects of the Earth's oblateness on satellite orbits. I'm seeing precession of the orbit, but not in the plane that I'm expecting. Here's my corrected grav. ...
2
votes
3answers
371 views

Two bodies of finite size treated as two point masses in Newtonian gravity

When discussing gravitation between two bodies of finite size, for instance Earth around the Sun, we suppose the mass of Earth and the Sun to be perfectly localized at the center of each body. Is this ...
0
votes
1answer
110 views

Why is $d$ generally not used instead of $r$ in Newton's derivation of force of gravitation? [closed]

In Newton's law of gravitation we take distance between two bodies $r$ and represent it in the form of $r^2$? Why don't we take distance as $d$?
3
votes
1answer
188 views

Modifying Newtonian gravity to fit observed precession of Mercury's orbit

The idea is to modify Newtonian gravity so that it fits measurements of orbits around the sun. For example the precession of Mercury's orbit unlike Newtonian $n$-body simulations. I'm currently not ...
4
votes
1answer
216 views

How big can a cube-shaped planet be? [duplicate]

There can be small cube planets or asteroids, but as they get bigger, the gravitational force compresses them to a sphere. But what is the maximum size?
2
votes
2answers
371 views

Does the gravitational acceleration change value with height?

My prof asked me to do a graphic of a given function and I have to just to vary the gravitational acceleration $g$ and the height $H$. If I know the interval in which $H$ is defined :$[500,2000]m$, ...
2
votes
1answer
376 views

How to show circular orbit as a precessing ellipse

A uniform distribution of dust in the solar system adds to the gravitational attraction of the sun on the planet an additional force linear in $r$ where m is the mass of the planet, k is a constant (...
3
votes
2answers
5k views

How did Isaac Newton figure out how the law of gravity worked? [duplicate]

There are this and this similar Phys.SE questions, but I didn't find what I'm looking for, nor was the person's question specific enough. How did Newton figure out $$F=GMm/ r^2~?$$ What was his ...
1
vote
3answers
336 views

Two bodies of equal mass thrown from a height-Practical physics question

I have a doubt about this question: Two bodies of masses $M$ and $m$ are allowed to fall from the same height. If the air resistance be the same for each of the bodies, will the two bodies reach ...
1
vote
2answers
1k views

How did Newton discover the universal law of gravitation?

I am having trouble comprehending how anyone could come up with this formula: $$F = \frac{GMm}{d^2}.$$ Could someone walk me through this?
2
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1answer
189 views

Integrals and Legendre Polynomials

I was told by a professor that this equality: $$\frac{1}{2\pi}\int_0^{2\pi}\frac{1}{|r-r(\varphi)|}d\varphi = \frac{1}{r}\sum_0^{\infty} \bigl(\frac{a}{r}\bigr)^n{|P_n(0)|}^2$$ ( where: $a$ is the ...
2
votes
2answers
1k views

Weight versus gravitational force [duplicate]

What is the difference between weight and gravitational force? I am a beginner who want to study physics properly.
1
vote
3answers
13k views

If mass is added to a toy car does it affect its speed making it faster

If mass is added to a toy car (29.7g) and dropped down a wooden ramp would it affect its speed making it go faster? I know friction comes in to play to, so if you could give me an answer or an ...
4
votes
3answers
2k views

Acceleration of an object dropped inside an accelerating elevator

A stone is released from an elevator going up with acceleration of $g/2$. What is the acceleration of the stone just after the release? The answer is $g$. Shouldn't the stone carry the acceleration ...
0
votes
1answer
151 views

Martian space elevator from the vulcano Olympus Mon to the moon Phobos?

In my fascinating imagination, I am seeing a space elevator from the vulcano Olympus Mon to the moon Phobos. Phobos also seems to keep spaceships - while a smaller shuttle attaches itself to the ...
0
votes
2answers
616 views

Gravitational field strength inside the Earth [duplicate]

please could someone give me a relatively straight forward answer why the gravitational field strength follows a straight line (linear) relationship with distance from the center of the Earth but when ...
1
vote
2answers
78 views

Centrifuge speed of an object higher than a stationary orbit

In the question At what altitude above equator do gravitational and centrifugal forces cancel each other?, I asked how high a tower on the equator has to be such that at its top, gravitational and ...
0
votes
2answers
133 views

At what altitude above equator do gravitational and centrifugal forces cancel each other? [closed]

How high has to be a tower at equator to get on its peak the same - but of course inverted sing - value of gravitational and centrifugal forces?