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

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112 views

Largest size of a low gravity, Earth-like planet with Volcanoes and Earthquakes?

Provided that the Solar System consists only of Sol, a planet, and the planet's moon.... How large can my planet be so that it has low enough gravity that teenage human girls trained for jumping, are ...
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1answer
160 views

Clearing up confusion about orbital mechanics

When I see an orbital mechanics problem, I recall the following things from my "toolbox": Angular momentum is conserved for a body orbiting a planet, since the torque due to gravity is 0. Kinetic ...
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1answer
29 views

Can the gravitational constant be directly measured?

The value of the gravitational constant $G$ is $6.67384\times 10^-11 {\rm m}^3{\rm kg}^{-1}{\rm s}^{-2}$. This value is used in the formula to calculate the attractive force between two objects with ...
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0answers
33 views

Perturbations of planetary Orbits

I have, for years, been an Astronomy and physics nerd. For the first while, I was a total astronomy nerd. Then I slowly transitioned into physics and have been, for less than a year, a physics nerd. ...
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4answers
174 views

What exactly is the mass of a body? What determines it?

The term "mass" is very common. But what does it depend on? How is it known?
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1answer
36 views

Could you give boundary conditions to the gravitational potential given the density distribution?

We´re doing a project that's all about solving differential equations with separation of variables. We´re trying to find the gravitational potential given the density distribution (that has azimuthal ...
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2answers
114 views

Newton's Principia: Astronomical prerequisites?

I am planning to read the Principia but I currently have no knowledge about Astronomy. What astronomy prerequisites do I need to understand the Principia? I would prefer older books (or "treatises"), ...
0
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2answers
64 views

$N>2$ gravitating masses can never reach equilibrium [closed]

If you have $N>2$ point masses, each attracted to each other by the force of gravity, how could you go about showing that they will never reach equilibrium?
5
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2answers
380 views

Before Einstein came up with General Relativity, were there serious reasons to doubt Newton's theory?

Before Einstein came up with General Relativity, was there any serious reason to doubt Newton's theory (and its various developments)? I only know about the discrepancy in Mercury's orbit, which may ...
2
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2answers
34 views

Does the microgravity environment in highly elliptical orbits differ from circular orbits?

I think everyone understands the microgravity environment broadcast from the ISS. But the ISS stays in a fairly circular orbit, the acceleration of gravity should be fairly uniform, the altitude and ...
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5answers
2k views

In circular motion, with a constant distance, why does the mass of the orbitting object have no effect on its revolution at all?

Using Newton's universal equation and some circular motion equation, the orbiting object's mass cancels out. But can someone please explain why this is without using pure algebra?
3
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1answer
42 views

Tidal tails of galaxies after collision

When there is a collision of 2 disc shaped galaxies, there is a tail formation created from both the galaxies. I read here that this was due to tidal forces, but I couldn't figure out how this ...
1
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1answer
59 views

Why doesn't an airplane simply go up in the air and stay there?

To get where a plane wants to go for example if I wanted to go from California to Japan, why can't an airplane simply stay up in the sky and let the earth rotate underneath it? Is it the ...
0
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3answers
90 views

How high could i jump if I weighed only half as much? [closed]

E.g. I weigh 150 lbs I had a thrust device that lifted 75 pounds. How high could I jump? What if that thrust lifted 2/3 of my weight (100 lbs)? Obviously, I cant fly, but I guarantee if I weighed ...
4
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1answer
3k views

Is acceleration due to gravity constant?

I was taught in school that acceleration due to gravity is constant. But recently, when I checked Physics textbook, I noted that $$F = \dfrac{G \cdot m_1 \cdot m_2}{r^2} $$ So, as the body falls ...
11
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6answers
2k views

The square in the Newton's law of universal gravitation is really a square?

When I was in the university (in the late 90s, circa 1995) I was told there had been research investigating the $2$ (the square of distance) in the Newton's law of universal gravitation. ...
0
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2answers
39 views

Centre of Mass and tangential velocity star and planet

We have two objects - one massive star, and one planet which has a considerably smaller, but non-negligible mass, in a circular orbit about a common centre of mass. Using equation $F$=$GMm$/$r^2$ ...
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2answers
120 views

Why is the potential energy for a body raised up by a height negative?

I tried deriving the potential energy of a body when raised at a height $h$ above the earths surface, using the formula: $$PE = -W_\text{conservative}$$ where $W_\text{conservative}$ is the work ...
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3answers
257 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 ...
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4answers
154 views

Gravitational force of a ring [closed]

Given a ring with mass $m_1$, radius $R$ and a point mass $m_2$ with distance $x$ regarding the center of the ring. How can I calculate the gravitational force of this ring ? At first glance I'd say ...
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1answer
30 views

What is total force in this context?

One site said the total forces is the sum of the vectors. My homework question is "A skydiver of mass 90 kg is falling with a terminal speed of 60 ms-1. What does that mean? What is the total force ...
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1answer
55 views

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: ...
0
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1answer
46 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 ...
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2answers
213 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
41 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
629 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
141 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
114 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 ...
81
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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 ...
22
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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
59 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
152 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
125 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
83 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
90 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
87 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 ...
2
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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
45 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 ...
2
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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
votes
3answers
233 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
77 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
114 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 ...
0
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1answer
52 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
794 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 ...
0
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3answers
711 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
43 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
50 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 ...