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

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If it was possible to dig a hole that went from one side of the Earth to the other…

...And you jumped in. What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like ...
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1answer
79 views

Center of mass and gravitational force

Say we have a two star system with both stars of equal mass $M$. The center of mass of this system is by definition in the center of the two stars. There is a small asteroid with mass m in orbit ...
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1answer
71 views

Kepler's law of periods question, application [closed]

I'm a year 12 student studying in Sydney Australia. I would like to ask about a physics question which I'm currently troubled on. I have made several attempts of answering the question but no luck. ...
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1answer
31 views

Placatory motion of more than two bodies

Recently in a documentary I heard that Newton's law of gravitation very well explains motion of two bodies such as sun and earth. And when applied to three bodies the answer is chaotic and not stable. ...
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2answers
4k 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 ...
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4answers
583 views

Integrating radial free fall in Newtonian gravity

I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
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1answer
377 views

What if the Earth stops in its orbit and instead falls straight towards the Sun? [closed]

The Earth orbits around the Sun because it has angular momentum. If we stopped the Earth in orbit and then let it fall straight towards the Sun, how long would it take to reach the Sun in seconds? ...
3
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4answers
359 views

Does the law of Universal Gravitation apply to every matter?

If I have a big ball of 20,000,000kg and another of 100g, does it mean that the big ball will pull the small ball towards it?
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5answers
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The Time That 2 Masses Will Collide Due To Newtonian Gravity

My friend and I have been wracking our heads with this one for the past 3 hours... We have 2 point masses, $m$ and $M$ in a perfect world separated by radius r. Starting from rest, they both begin to ...
2
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2answers
110 views

Actual meaning of “Gravitational Potential”?

In a gravitational field, the gravitational force acting on a body (of mass m) at a point x metres away from the attracting body (of mass M) is $\frac{GMm}{x^2}$. Integrating this force from a point ...
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2answers
82 views

Would a black hole created on the surface burrow through the crust?

If scientists created a microscopic black hole with an initial mass of one ton on the surface of the earth, would the gravitational attraction to the center be enough for it to "burrow" until it eats ...
3
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3answers
521 views

Can we apply Schrodinger equation in Newton Gravitational potential and derive the deterministic Newton's gravitation as a special case of it

We know the solutions for wave functions of a an hydrogen atom, and the energy values as given by spectral analysis of radiation emitted by Hydrogen, confirms the possible energy states as predicted ...
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1answer
74 views

Why does a difference in approach to projectile motion yields different results?

A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth, then find the maximum height attained by the ...
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2answers
85 views

Does quasi-static motion imply zero energy dissipation?

When a droplet is deposited on a surface with some surface roughness and subsequently tilted it can stick due to pinning (think of droplets on a window after rain). What I am interested in is ...
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0answers
122 views

Force from a HEMIspherical shell [closed]

I am working on this problem and just trying to figure out what my prof/ TA did in the solution sheet -- but also to make sure I understand what I am doing and some of the mathematics involved. A ...
6
votes
6answers
984 views

Escape velocity from long ladder

The escape velocity of earth is roughly $11 kms^{-1}$. However, what if a long ladder was built extending out of Earth's atmosphere and considerably more. Then if something was to climb up at much ...
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1answer
3k views

String tension in vertical circular motion

Suppose that I have a point mass attached to a massless string and I am rotating it vertically. That means The mass is in uniform circular motion and the path of its motion is vertical circle. How ...
0
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1answer
51 views

Ink in a pen on an artificial satellite

In an artificial satellite, a space traveler tries to fill a pen by dipping it in ink. The amount of ink filled in the pen as compared to the amount of ink filled on the Earth's surface will ...
2
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1answer
62 views

What are the steps and energetic requirements for getting from the HST to the ISS?

There have been several general critiques of the realism some of the physics depicted in the movie "Gravity" notably regarding the the orbital mechanics of the transition from the Hubble Space ...
3
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1answer
889 views

Center of Gravity vs Center of Mass

To calculate the center of gravity of a distribution of mass, can I use gravitational potential (scalar) or must I use gravitational field (vector)? And why, generally, the center of gravity goes ...
6
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1answer
359 views

Proving Kepler's 1st Law without differential equations

Is there a way to show that motion of Earth around the Sun is elliptical (Kepler's 1st law) from Newton's laws without resorting to the use of differential equations of motion?
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2answers
162 views

Vertical uniform circular motion.. can it really be uniform? [closed]

This is the picture in my mind: For centripetal force, I learned that: $T-mg\cos\theta= \frac{mv^2}{r}$ In vertical circular motion, the velocity is naturally going to decrease as kinetic energy ...
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0answers
48 views

How to derive “Anti-Lagrangian” $L_4$ and $L_5$ points

In this paper on co-orbital dynamics the authors discover, numerically, "Anti-Lagrangian" solutions to the restricted 3 body problem. These Anti-Lagrange $L_4$ and $L_5$ points are 120 degrees ahead ...
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3answers
119 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 ...
2
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1answer
387 views

How does Lunar Orbit Injection (LOI) work?

Just what the title states. I read that LOI was used by the Apollo program (and possibly others) to achieve escape velocity. How does it work? Is it merely a matter of centrifugal/centripetal force?
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2answers
162 views

Do heavier objects fall faster? [duplicate]

This question has been asked multiple times here and all over the internet yet I can't find a conclusive answer: Some claim that heavier objects do fall faster: Don't heavier objects actually fall ...
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1answer
329 views

Newton's second law, gravity and buoyancy [closed]

A body of mass $m$ and volume $V$ is immersed into the sea. The body moves under the action of two forces: gravity and buoyancy (Archimedes). Gravity force has a magnitude $mg$, where $g$ is a ...
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1answer
593 views

Gravitational force exerted by a rod on a point mass

I have doubts with the solution of a certain problem. I will give the entire solution below and will lay out my doubts as well. A point mass $m_1$ is separated by a distance $r$ from a long rod of ...
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5answers
699 views

Imagining to speed up the Earth's revolution around the Sun until we feel its motion

If the Earth were revolving around the Sun much faster than it does, let's say 100 or 1000 times faster or whatever big-enough multiple of its actual speed, would we feel it? What sensation would we ...
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2answers
103 views

Does earths gravitational force vary depending on where you are on the planet?

Does the gravitational force acting on a person ever change just by their position on the planet. For instance, at greater altitudes or closer to the equator.
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1answer
137 views

Ball on a slope [closed]

I have a lab report, but I can not write it in a correct way. The lab experiment was about a ball rolling on a slope, I have a height of the slope, the distance, and the time in which the ball spent ...
2
votes
1answer
928 views

Ski Jumper's vertical velocity after $246.5m$ record?

What would be the vertical velocity of this ski jumper (ski flyer), after he first touches down, after he breaks the record with a $246.5m$ jump? What g force would he experience as he slows down? ...
0
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1answer
218 views

Will a free-falling rod (without drag) rotate?

When we consider a bicycle is turning on a flat plane, we know that there is friction, which provide centripetal force on the bicycle. And we know that the bicycle is no longer perpendicular to the ...
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2answers
143 views

Why do orbital speeds decrease further away from the focus?

Why do orbital speeds decrease further away from the focus? A simple question, but I want to make sure I am understanding this correctly: Is it ONLY a function of the gravity well? As in, the ...
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3answers
544 views

Physics Paradox about Newtons Second Law $F=ma$

I randomly thought of this- I'm surprised it took me so long to think of it, and I'm SURE I'm making a simple oversight of something completely trivial, but here it goes. (Im only in high school ...
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2answers
219 views

rotational oblateness

I am trying to compute the amount of oblateness that is caused by planetary rotation. I picture the force of gravity added to the centrifugal force caused by the rotation of the planet as follows: ...
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1answer
187 views

Why do you experience low-gravity outside the Earth (but near it), and experience more gravity on it?

Spacecraft, satellites, etc. They also experience zero gravity, weightlessness, or "micro gravity" when outside Earth, about 20-300+ miles beyond the escape velocity zone("atmosphere"). However, you ...
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2answers
142 views

How does artificial gravity reduction (weightlessness) work on Earth?

Some of us have been to those amusement park/carnival/theme park rides where you enter some capsule/machine, and you will float, etc. There is also some other thing where you go inside a big room ...
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0answers
56 views

origin of cusps in simulated dark matter halos

I keep reading that cusps are one of the most "robust" predictions of N-body simulations of dark matter halos. But any paper I've found on the topic makes it sound like these simulations are ...
7
votes
8answers
10k views

Is gravity a force and if so what is its opposite?

For every force there is an equal force in the opposite direction on another body, correct? So when the Suns gravity acts on Earth where is the opposite and equal force? I also have the same ...
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1answer
803 views

Calculate Mass based on Velocity and Acceleration

I am attempting to design a obstacle avoidance system with the Arduino. My position (for now) is going to be stationary. I will be detecting an incoming object and I want to use the below known ...
15
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10answers
3k 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.
15
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2answers
788 views

Is Newton's universal gravitational constant the inverse of permittivity of mass in vacuum?

Is it possible to consider Newton's universal gravitational constant, $G$, as inverse of vacuum permittivity of mass? $$\epsilon_m=\frac {1}{4\pi G}$$ if so, then vacuum permeability of mass will ...
2
votes
1answer
159 views

How do we know the Earth orbits around the Sun and not the other way around? [duplicate]

I know that describing the trajectory of all planets in the solar system around the Earth is much more complicated than if we take the Sun as the reference point. But besides this, what is the ...
-4
votes
1answer
131 views

Value of of gravity 9.8m/sec^2 and centrifugal force [closed]

I had a doubt regarding centrifugal force on earth is not accounted in any equations as object falling towards earth.eg f=ma.i read questions asked by few about the same and got to a conclusion that ...
1
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1answer
156 views

Determine if an object is in orbit

I am planning on doing a space simulation program with full physics and as part of a hack to avoid too many issues with number precision I was going to switch orbiting objects to a calculated orbit ...
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2answers
230 views

How is the singularity in Newtonian gravity resolved?

In Who's afraid of a Black Hole? at time ~20:38, Michio Kaku makes a claim that $1/r$ when $r=0$ equals $\infty$ and when physicists see the $\infty$ they see a monstrosity. Coincidentally, Newton's ...
0
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2answers
119 views

Under what conditions, will a projectile motion follow a half circle?

What came to my mind is to throw an object far from the earth with a particular speed equal to $$V_{sat}=\sqrt{\frac{G\times M_{central}}{R}}$$like satellites. However, it would follow a full circle.
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1answer
335 views

Details of the new solutions to the three-body problem [closed]

This question is part of this week's Journal Club session. These systems look ridiculously fun to construct. Could someone explain the particulars? What are the various types of solutions, and ...
0
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1answer
56 views

Evaluating $v$ for orbiting a golfball [closed]

The curvature of Mars is such that its surface drops a vertical distance of 2.0 meters for every 3600 meters tangent to the surface. In addition, the gravitational acceleration near its surface ...