The Newtonian model of gravity in which the force between two objects is given by GMm/r^2.
3
votes
2answers
630 views
First integral of an equation of motion: $\mu\ddot r=-\frac{k}{r^2}$
I've got an equation of motion (EOM), which is
$
\mu\ddot r=-\frac{k}{r^2}
$
How do I find the first integral of this EOM? I'd appreciate it if someone could show me the steps involved. I should ...
0
votes
3answers
153 views
What was wrong with action a distance?
It is usually said that the idea of fields was introduced (electric and magnetic fields) in electricity and magnetism after Coulomb's law to cure the conceptual problems of action at a distance.
...
1
vote
1answer
99 views
The Value of Newton's Gravitational Constant $G$ within an Atom
Can the value of Newton's Gravitational Constant $G$ be measured within a stably bound atom?
PLEASE NOTE: Since scattering experiments do not involve stably bound systems, their results are not ...
3
votes
1answer
490 views
Combining Proportions to get Newton's Law of Universal Gravitation
I've read a little on the history of Newton's Law of Gravitation and noticed that the formula can be separated into 3 distinct parts that lead to the end result of $F_g = G \frac{m_1 m_2}{r^2}$; the ...
2
votes
2answers
485 views
Why is the center-of-mass of 2 bodies at the focus of their elliptical orbits?
Why is the center-of-mass of 2 bodies (which interact only via Newtonian gravity) located at a focus of each of the elliptical orbits?
I know that when there are no external forces, the center of ...
46
votes
7answers
3k views
Does juggling balls reduce the total weight of the juggler and balls?
A friend offered me a brain teaser to which the solution involves a $195$ pound man juggling two $3$-pound balls to traverse a bridge having a maximum capacity of only $200$ pounds. He explained that ...
3
votes
4answers
572 views
Why does an object thrown parallel to the ground eventually fall down?
Suppose an object is thrown parallel to the ground. The gravity acts downward (ie. perpendicular to the direction of motion of the object). The work done by gravity on that object will be given by :
...
0
votes
1answer
95 views
How to get energy of collision if you know force of gravity of an object($m \rightarrow F=mg$)?
How to get energy of collision if you know force of gravity of an object($m \rightarrow F=mg$)?
You get energy of collision by kinetic energy $E_k= \frac{1}{2}mv^2$, but if you use just force of ...
4
votes
2answers
114 views
What is the mass distribution within the sun?
Jupiter is roughly 1/1000 the total mass of the sun. To get some idea of what effect Jupiter's gravity may have on the sun I'd like to know the approximate mass distribution of the sun. (i.e) the ...
0
votes
2answers
450 views
Newtonian gravity vs. general relativity: exactly how wrong is Newton?
Is there a simple function I can use to describe the difference between simple Newtonian dynamics and the actual observed motion? Or maybe some ratios for common examples of, say, the motion of stars ...
2
votes
3answers
287 views
Does a toy top weigh less when it is spinning?
I am under the understanding that a toy top will weigh less when it is spinning. The Russians made a spinning type transport back in the 70s to lessen its payload over the tundra. Is this an effective ...
0
votes
1answer
167 views
Energy in orbit of satellites around the earth lost?
If the total mechanical energy in a satellite's orbit (assuming circular) is greater when it is closer to the earth, and hence smaller when it is farther from the earth, then we can say that as the ...
0
votes
1answer
148 views
Two moons of Earth?
Hypothetically, suppose there is a situation where the Earth's moon gets neatly sliced into two equal hemispheres, and the force responsible for this slicing also creates a distance between the two ...
2
votes
1answer
306 views
Formula of Gauss' Law of Gravitation
Gauss's law for Gravitation:
$$\int g\cdot \mathrm{d}S=4\pi GM$$
where $g$ is the gravitational field and $S$ is the surface area.
Am I correct?
4
votes
3answers
602 views
Hanging chain in a planet's gravitational field
The curve for a chain hanging between two poles in a uniform gravitational field is known as the catenary.
Is there known an expression for the curve of a hanging chain on a planet of mass $M$ which ...
1
vote
1answer
97 views
Idealized trajectory from sloped surface
I am a GIS programmer implementing a visualization.
I am modeling the idealized trajectory of a particle ejected from a volcanic vent using:
$$\text{distance} = \frac{(v^2 \times ...
0
votes
1answer
57 views
Gravity question [duplicate]
Possible Duplicate:
Don’t heavier objects actually fall faster because they exert their own gravity?
When true: The force pulling the "heavy" object down is greater BUT it also takes more ...
0
votes
6answers
202 views
Relation between field strength and potential?
In terms of gravity and electric fields, I'm not sure what the difference is between field strength and potential is and how they are related? Both using maths and not.
0
votes
1answer
155 views
If 2 charges have the same sign, the coulomb force is positive but repulsive, while with 2 masses the gravitational force is positive but attractive
If you have two point objects both the same positive charge and both of the same mass at a distance $r$ from each other.
The force between them due to gravity is $F_g=\frac{Gmm}{r^2}$ and $F_g$ is ...
13
votes
4answers
495 views
Anti-gravity in an infinite lattice of point masses
Another interesting infinite lattice problem I found while watching a physics documentary.
Imagine an infinite square lattice of point masses, subject to gravity. The masses involved are all $m$ and ...
13
votes
4answers
504 views
Why are so many forces explainable using inverse squares when space is three dimensional?
It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance.
However, since volume is determined by three ...
0
votes
1answer
93 views
Effect on mass of Earth if it stops revolving around Sun
If the object in motion gains mass, will it affect the change in mass of Earth if it stops revolving around Sun, since mass is responsible for gravity how will be the gravitational force change?
19
votes
1answer
705 views
Why does it take so long to get to the ISS?
I don't understand why when first launched Space X's Dragon capsule had to orbit the Earth many times in order to match up with the ISS? Was this purely to match it's speed, or to get closer (as in ...
6
votes
2answers
186 views
Is the gravitational potential of a planet in orbit always equal to minus the squared velocity?
Say a planet (mass $m$) is orbiting a star (mass $M$) in a perfect circle, so it is in circular motion.
$F=ma$ and the gravitational force between two masses $F=\frac{GMm}{r^2}$ so
...
1
vote
5answers
248 views
Electro-gravitation - is it real?
I came across an article claiming that if you charge two plates, one positive and one negative, and fasten them together (assuming they are insulated from each other), they will float in the air. I ...
0
votes
2answers
94 views
Definitions of Lagrange points: $L_4$ and $L_5$
We have the the five Lagrange points (let consider Earth and Sun):
$L_1$ - lie between Sun and Earth;
$L_2$ - beyond the Earth;
$L_3$ - beyond the Sun;
And what's the difference between $L_4$ and ...
2
votes
1answer
88 views
Forces: Worth worrying anything?
I am a general physics student, I had a question in my text-book and according to it two students having gravitational attraction between them = ($6.67\cdot10^-8\ \mathrm{Nm}^2/\mathrm{kg}^2$) is not ...
4
votes
4answers
2k views
How Felix Baumgartner has reached the speed of sound quickly
I have watched Felix Baumgartner freefall; but I wonder how Felix has reached the speed of sound quickly, in a matter of some seconds, then we had no idea of its speed?
Any explanation please.
13
votes
9answers
3k views
Why are orbits elliptical?
Almost all of the orbits of planets and other celestial bodies are elliptical, not circular.
Is this due to gravitational pull by other nearby massive bodies?
If this was the case a two body system ...
2
votes
1answer
123 views
How does one measure Earth's speed of revolution around the sun?
I know that there are several formulae that one can plug numbers into to arrive an estimate of Earth's speed around the sun (Kepler's third law for instance), but I'm wondering how these things are ...
1
vote
3answers
130 views
Dynamics of a Rocket
I am interested in modelling the trajectory of a rocket from the Earth to the Moon by solving a differential equation numerically. Below are some key facts and assumptions I am using. I want to make ...
1
vote
1answer
130 views
How to calculate gravity inside the star?
Gravity must decrease due to less effective mass when going inside the object but also must increase with depth inside the star due to its higher density. Is there a model or formula approximating ...
14
votes
5answers
1k views
Why does the moon face earth with the same side?
I know this is an astronomy question, but no such stackexchange site exists. So here I am, asking about the physics of the solar system.
I know that the rotation period of the moon equals its ...
1
vote
0answers
73 views
Integration question from book “e: The Story of a Number” by Eli Maor [closed]
In the book 'e: The Story of a Number', a derivation of a parachutist problem is given on pg. 109-110. A parachutist jumps from a plane and at $t=0$ opens his chute. At what speed will he reach the ...
3
votes
1answer
112 views
What is the physical meaning of a flux of gravitational field in classics?
I've stumbled upon an answer to a question about square power in Newton's law of gravity. After reading it I got a question whether the flux of gravitational field has actually any physical meaning.
...
6
votes
5answers
290 views
Intuitive explanation of the inverse square power $\frac{1}{r^2}$ in Newton's law of gravity
Is there an intuitive explanation why it is plausible that the gravitational force which acts between two point masses is proportional to the inverse square of the distance $r$ between the masses (and ...
0
votes
2answers
328 views
Does effective potential for a gravitational force have a maximum below $E=0$?
The relevant figure is below (taken from Goldstein's Classical Mechanics). This figure plots the effective potential for a gravitational force. Does the effective potential $V'$ go flat below $E_2=0$? ...
-1
votes
3answers
168 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 ...
2
votes
2answers
200 views
Path to obtain the shortest traveling time
Asume we have a particle sitting at the point A(0,0) in a gravitational field.
(g=9.81) It is going to move along some path to the point B(a,b) Where a>0 and b<0.
What is the curve the particle ...
0
votes
1answer
203 views
Why is a cycloid path the fastest way to roll a ball downward? [duplicate]
Possible Duplicate:
Path to obtain the shortest traveling time
I've been told that if one would want to make a ramp to get a ball from point A to a lower point B (at a certain horizontal ...
4
votes
1answer
105 views
Potential Energy tends to infinity on the N-Body Problem
I need help to solve this problem related with the N-Body problem, i dont understand quite well what I need to define or to express in order to solve it.
We assume a particular solution to the N-Body ...
15
votes
9answers
2k 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.
1
vote
1answer
93 views
Gravity near surface of a large body
The question I want to ask is what point is there in using
$$
F = G {m_1 m_2 \over r^2}
$$
when we don't talk about point masses, but one of the masses is a sphere of radius ...
10
votes
7answers
2k 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?
3
votes
4answers
638 views
Can a balloon float into space? (+orbital velocity)
After watching the recent "space jump" a question arose. Why can a balloon not float into space? Can one be made/designed to do this?
Next, everything in orbit is falling back to earth. It only ...
0
votes
2answers
41 views
How do I know the position of some mass in space (starting at rest) over time when applying earth's gravitational force to it?
I know how to use Newton's law of universal gravitation. But I'm not sure where to go from there.
This is for my understanding while working on a game. I'm not trying to do anything fancy here.
4
votes
2answers
104 views
What was the muzzle velocity of a home made gun launch strait in the air if air time was 8.2sec?
I built a potato gun and wanted to calculate the muzzle velocity. I remember from physics that I could run the numbers by calculating time from launch until landing. After pointing strait into the air ...
1
vote
1answer
410 views
Friction due to air drag at high speeds
I am trying to set up this problem, but I am not sure how to go about doing so. (From University Physics, Young & Freedman):
You throw a baseball straight up. The drag force is proportional to
...
2
votes
1answer
81 views
Mutual Interaction of $N$-Particles in a Cartesian Plane
I am making a simulation of $N$-Particles in a cartesian plane and need help with understanding the basics.
At anytime, in my particle system, I will have $N$ number of particles. I am treating the ...
2
votes
1answer
260 views
Radial fall in a Newtonian gravitational field [duplicate]
Suppose an object of mass $m$ starts at rest at a radial distance $ r_0$ from a perfectly spherical mass $M$ (where $m << M$), $r_0 > R =$ radius of $M$.
Can we analytically determine when ...
