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

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What's my $dM$? 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: ...
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1answer
43 views

How to find an equation for $x$ in terms of $t$ for a particle falling under gravity with resistance given by $mkv^2$? [closed]

Okay so I have determine the velocity $v$ and displacement $x$ as functions of $t$ for a particle falling under gravity with resistance given by $mkv^2$. I have set up the equation of motion divided ...
12
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2answers
203 views

Is it possible to prove that planets should be approximately spherical using the calculus of variations?

Is it possible to use the Lagrangian formalism involving physical terms to answer the question of why all planets are approximately spherical? Lets assume that a planet is 'born' when lots of ...
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0answers
39 views

Explaining why planets are round [duplicate]

is it possible to prove that planets (and/or stars) are always round (elliptical if you consider the spin)? Is there a set of equation that demonstrate that fluids (after all, molten rocks "floating" ...
11
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1answer
609 views

Apollo and orbital mechanics: orbital decay if the Trans Earth Injection (TEI) burn had failed

I'm reading Jim Lovell (Apollo 8 and 13) and Jeffrey Kluger's book Apollo 13, which is a fantastic read about a long past era I only have kindergarten memories of. On page 54 there is a paragraph that ...
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1answer
111 views

Calculating the first cosmic velocity / velocity for a circular orbit

Today in class we calculated first cosmic velocity using this equation $$G\frac{mM}{(R+h)^2}=\frac{mV^2}{R+h},$$ where $m$ = mass of the body, $M$ = mass of the Earth, $R$ = radius of the Earth, $h$ = ...
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2answers
86 views

How to solve the inverse square law equation of motion

From $$m\boldsymbol{\ddot{r}}=\boldsymbol{\hat{r}} f(r)$$ I can get $$r''-r \theta '^2=-\frac{k}{m r^2}$$ $$2 r' \theta '+r \theta ''=0$$ Now it seems that all the books tells me the method to solve ...
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6answers
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Could we send a man safely to the Moon in a rocket without knowledge of general relativity?

I'm wondering if it's possible to send a man to the Moon using equations consistent with Newtonian gravity and without the elaborate tools of Einstein gravity. Are the predictions made by Newtonian ...
21
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10answers
6k views

Why do space crafts take off with rockets instead of just ascending like an aircraft until they reach space?

I guess it's not a very educated question, but I never quite understood why spacecrafts have to shoot up and can't just reach space by simply continuing an upwards ascent like an airplane.
2
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2answers
56 views

The mass/energy of an $H$-atom and the gravitational force between it and another particle of mass $m$

The gravitational force between an $H$-atom and another particle of mass $m$ will be given by Newton's law: $$F=\frac{GMm}{r^2}$$ The question is, what is $M$ here? I thought the answer would be ...
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2answers
141 views

Collision of two satellites

In a theoretical situation in which two identical satellites travelling around the Earth in opposite directions collided head on so that there velocities relative to the earth both became 0, would ...
0
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1answer
103 views

What is the Jacobian matrix of Newton's law of gravity? [closed]

I am trying to come up with the gradient of a vector (Jacobian matrix) for Newton's Law of Gravity. In other words, the differential gravitational field in 3-dimension. Here's the initial Law. ...
3
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1answer
46 views

Discrepancy between integrating over a continuous mass and intuition

Looking at the first problem on the page, Physics LAB: Advanced Gravitational Forces, and I have a little confusion: I totally follow and agree with the solution presented, but I'm wondering why I ...
2
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2answers
76 views

In this particular problem: Is the mass of the system the mass of the person?

I am doing this problem: The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N. What is the magnitude of the acceleration? This is how I solved ...
0
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1answer
86 views

Find the center of gravity of a system with three spheres [closed]

Three spheres are put on a table. The first sphere, whose mass is 1 kg is 20 cm away from the second whose mass is 2 kg and the third sphere is 100 cm away from the first sphere and has a mass of 5 ...
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4answers
81 views

Is the mathematics in my answer valid? (C is the right answer) [closed]

I have a good understanding of the concepts at hand, but I'm not so good at the mathematics part. I know the answer already (C), but would like to understand the mathematical way of determining it. ...
2
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1answer
66 views

Wouldn't dark matter throw off the calculation of Earth's 'light' mass and estimates of its composition?

The Cavendish experiment first determined the mass of the Earth and (arguably) the gravitational constant. However, given the ubiquitous nature of dark matter, it seems reasonable that at least some ...
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2answers
102 views

General Relativity view of Newton's apple

If one considers the free fall of an object of mass $m$ from a hight $h$ in the Earth's gravitational field (neglecting air friction) from the point of view of GR, what would be the main corrections ...
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1answer
43 views

Create a star system fit to conic equation

For simulation purposes, I'm trying to create a binary star system. If I have a conic equation such as $ax^2 + by^2 = c$, and the masses of two stars, how would I find the $x$- and $y$- velocity ...
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0answers
21 views

Orbits of binary pulsars. How to calculate? [duplicate]

If I may ask: How can the orbits of binary pulsar stars, with similar mass, be calculated from Kepler's laws? Considering that both large central masses must be located at their mutual foci. Also, how ...
4
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3answers
231 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 ...
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4answers
2k views

Escape velocity from Earth

We know the escape velocity from the Earth is 11.2km/s. Isn't it the velocity required to escape from earth if we go normal to the surface of earth? i.e while we derive the formula for the escape ...
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2answers
70 views

Can $F=ma$ be used to calculate ground reaction force of someone walking/running?

Can Newton's second law of motion $F=ma$ be used to calculate ground reaction force of someone walking/running?
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3answers
92 views

Why does weight affect acceleration with gravity

I'm sure this question has been asked before, but my question is different, because it can't be answered with some formulae. My question is, why do heavier objects decelerate faster when moving away ...
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1answer
47 views

Where do we get the terms involving $\Phi$ in parentheses come from in the static weak field metric?

I am confused about the static weak field metric. As written in Hartle, it reads \begin{equation} ds^2 =-\left(1+\frac{2\Phi(x^i)}{c^2}\right)(cdt)^2 +\left(1-\frac{2\Phi(x^i)}{c^2}\right)(dx^2+dy^2 ...
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4answers
773 views

Gravity force between two objects with different mass

We know thanks to Newton that: $$F=G\frac{m_1\cdot m_2}{r^2}$$ Where $G$ is the Gravitational Constant that is about $6.673\cdot10^{-11}$ $m_1$ and $m_2$ are the masses of two different objects ...
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3answers
403 views

Forces on a ball thrown upwards

When a ball is thrown up in upward direction, it is said that force is in downward direction. Why we don't we consider the force given to the ball to throw up in the upward direction? Is there is no ...
0
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1answer
42 views

Decreased velocity away from gravity

Say I have a particle ($G$), which has the mass of the earth (hypothetically), and I have a second particle ($P$) moving away from $G$, in a line that is not parallel to the earth. Would this line ...
0
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1answer
48 views

The stronger the gravity, the faster an object will fall? [closed]

On a planet with gravitation ten times stronger than that of Earth's, will an object fall faster? Let's suppose that there are two planets; Roddo and Earth, respectively. Roddo has ten times the ...
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2answers
114 views

Units in gravitational $N$ body simulations

I am trying to write a code in Python to simulate $N$ bodies interacting through gravity. In particular I am trying to see whether a system of particles with random initial positions and zero velocity ...
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2answers
45 views

How did the planets (in the Solar System) start to revolve around the sun if they were attracted towards the Sun via the gravitational force? [duplicate]

The planets in the Solar System revolve around the Sun in almost circular paths called orbits. The Sun pulls the planets with the gravitational force,but the planets do not get drawn to the Sun but ...
22
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3answers
3k views

Why does the Moon face Earth with the same side?

I know that the rotation period of the moon equals its revolution period. It's just so astonishing that these 2 values have such a small difference. I mean, what is the probability of these 2 values ...
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0answers
22 views

Why does the Moon not rotate about its axis, relative to Earth's rotation [duplicate]

One of the common features of the Moon is the fact that only one face of the Moon is ever visible from Earth, regardless of how much of its orbit the moon has made about the Earth. This would imply ...
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3answers
157 views

Does the Earth revolve around the Sun?

I am aware of this Phys.SE question: Why do we say that the earth moves around the sun? but I don't think this is a duplicate. In a binary star system, where the masses of the 2 stars are not so ...
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1answer
74 views

Do we need Escape Velocity [duplicate]

This may seem silly a lot but I really need some clarification on the necessity of escape velocity for a rocket leaving the Earth's gravity. A stone thrown vertically upwards reaches to a certain ...
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2answers
68 views

Does the gravitational force of a massive, spherical body draw only towards its center of gravity, and to no other area?

Consider the premise that at the center of Earth (for example) an object would be weightless because of the relatively even distribution of mass surrounding it, and the resulting gravitational pull on ...
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2answers
71 views

Orbital Velocity Question

I have a satellite in a stable trajectory around Earth, of a Mass $m$. I know that its velocity is: $$ v = \sqrt{mG/r}\, $$ But now it begins accelerating directly against the gravity vector (i.e. ...
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1answer
64 views

How do you calculate density if you also account for gravity?

Consider this. I have an Earth-sized quantity of water that I throw into space. Naturally, it will assume the shape of a ball. Now hear me out. Density's definition generally assumes that it will ...
3
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1answer
94 views

How did special relativity change physicists views on the two prominent inverse square laws (ie Newton grav and Coulomb's law)?

On page 107 in Hartle's Gravity -- An introduction to Einstein's General Relativity, he says the following With the success of special relativity it became apparent that the Newtonian theory of ...
5
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4answers
150 views

How would swimming in low gravity work?

Sorry I know very little of actual physics, I'm not looking for hard and fast numbers just a general idea of how the mechanics would work. For the sake of argument, say you were on a planet or moon ...
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2answers
103 views

Would it be possible to make a space elevator only in the atmosphere?

I wonder if with current day technology we could make a "floating platform" which hangs from a satellite by a space elevator. This could allow a "launch process" involving floating a balloon to the ...
1
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1answer
47 views

Can small chunks of cosmic matter revolve around artificial satellites in space?

I have always studied that where there is a body with mass, there is gravitational pull. So can small chunks (or dust) of cosmic matter revolve around artificial satellites in space? Or rather are ...
1
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0answers
173 views

How the Moon causes the tides?

I am considering the following question but I con't quite figure it out... I have looked up differential gravity but I cannot derive the equation for the effect on earth, and I haven't found any ...
2
votes
1answer
45 views

Computing the gravitational force on a planet in a particular system [closed]

I have a system of four planets moving in a 2D plane. I'm trying to write some code (C++) to find the positions of these planets at time t=3. I'm probably going to attempt this via a leapfrog ...
2
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1answer
182 views

If a bullet is fired vertically upwards, when it comes back does it fall to the same spot?

What I'm basically asking is that if a body is projected with sufficiently high velocity so that it doesn't escape from the earth's gravitational field but reaches an appreciable height with respect ...
1
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2answers
105 views

Problem with an exercise: position and velocity of a thrown sphere with non uniform acceleration

You stand at the earth's surface, have an object, for example a sphere, of mass $ m_1 $ and throw it with a velocity $ v_1 $ into the atmosphere, perpendicular to the surface. Let $g$ at the surface ...
0
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5answers
389 views

If you are on Earth, are your mass and weight the same?

I was wondering how mass and weight are different so I Googled it. I found that mass is constant no matter where you are because it is the amount of matter in an object and weight changes because it's ...
6
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2answers
216 views

Will an object falling into Earth's orbit start spinning?

Assume an object falls towards Earth (I've drawn a hyperbolic orbit, but this would apply to any orbit). The object starts at $A$, and at this point it is not rotating i.e. an observer on the object ...
0
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1answer
110 views

Prove that orbits are conic sections

How does one prove that an orbit of a satellite around a planet of significantly greater mass than the satellite is a conic section (i.e. an ellipse, circle, hyperbola, or parabola)? Also, there is ...