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

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2answers
798 views

Can the mass of an orbiting object and the object being orbited be determined by the distance and orbit velocity alone? [duplicate]

This question is the inverse of: "Could an object orbit while moving at twice the speed, but at the same distance, if it had half the mass?" I'm curious about the nature of orbits, but am not well ...
1
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2answers
250 views

What's the weight of the earth?

What's the weight of the earth? That is, what's the weight of the earth in the gravitational field of the sun? I imagine it's either $0$, because there's no net fall toward the sun, so the downward ...
8
votes
2answers
386 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: ...
17
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2answers
1k 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 ...
0
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1answer
632 views

Gravitational Field from Irregular Object

How does one calculate the gravitational field of an irregularly shaped object? I was thinking specifically of the gravitational field due to a human, and tried to see if modeling a human as an ...
-1
votes
1answer
108 views

Expressing a force in components [closed]

If there is an object on some ramp, how do I express its weight in terms of vectors orthogonal and parallel to the ramp surface? For example, if the object has a weight $\vec W=m\vec g$, then how do ...
9
votes
1answer
451 views

What are common methods for calculating the time dependency of elliptical orbit?

After playing a game called "Kerbal Space Program" I got interested in orbital mechanics and started messing with simplified calculations to determine $\Delta v$ requirements. In which I compared two ...
3
votes
4answers
374 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?
11
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3answers
559 views

Can we disprove Artificial Gravity (like in the movies) with a thought experiment?

Suppose you have a Device that creates an 'artificial gravity' (AG) inside a Box, with these properties: the system does not use inertial forces (like centrifugal force) or a huge mass to create AG ...
0
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0answers
171 views

Does the earth really move round the sun? [duplicate]

Is there really any empirical proof that the earth moves round the sun? I've read simple explanations using mass-gravity relation. But then some questions remain, is gravity a function of mass alone? ...
2
votes
2answers
272 views

Bertrand's theorem

I found in Goldstein's Classical Mechanics that the condition for closed orbits is given by $\frac{d^2 V_{eff}}{dr^2}>0$.(bertrand's theorem). Can somebody explain to me, how this inequality is ...
-1
votes
2answers
723 views

Two balls falling one above the other [closed]

Two balls, first with the mass $m_1$ and the second with the mass $m_2$ are falling from the heigh $h$. Suppose all the collisions are perfectly elastic and do not consider the size of the balls. $m_1 ...
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5answers
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What happens with the force of gravity when the distance between two objects is 0?

so I had my first approximation to the gravity equation \begin{equation} F=GmM/r^2 \end{equation} and some questions arose that my teacher couldnt respond: if r approximates to 0 with mM being ...
0
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0answers
84 views

What is the equation for Lin-Shu density wave theory?

Lin-Shu density wave theory is a (very good) theory to explain the spiral arm structure of spiral galaxies. Where can I find the equations that underlie this theory? I've seen its computer ...
1
vote
1answer
200 views

History of Newtons law of gravitation

I have some questions about the history of Newtons law of universal gravitation. Did Newton discover his three laws of motion before he discovered the universal law of gravitation? I know two ...
-3
votes
2answers
14k views

Why two balls of different mass dropped from the same height falls the ground at the same time? [duplicate]

When two balls of different masses, thrown from equal height they reaches the ground at the same time. Can anyone explain this in terms of laws of Physics(or with mathematical equations)?
1
vote
1answer
396 views

Calculate magnitude of force acting on some area by falling object

I have simple question: is it possible to calculate magnitude of force acting on some area by falling object? Let's say I have an object with mass $5\text{ kg}$. I drop that object in height 1 ...
-1
votes
1answer
453 views

Newtons Cannon ball problem [closed]

Let's I have a Newton's Cannon ball of 15 kg and want to fire so it will round the earth and back to me. My query is which law can evaluate the speed that cannon ball will revolve round the sun ...
2
votes
1answer
177 views

Understanding Kepler's problem

I wanted to know a few things about elliptical motion, that I do not understand so far. Let's imagine that we have an attractive gravitational two body problem where both bodies carry out elliptical ...
3
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2answers
386 views

Finite velocity at infinite distance

If an object were launched exactly at escape velocity it would have zero velocity at infinity. But what if we launch an identical objects at greater than escape velocity? Apparently it will have a ...
-1
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3answers
267 views

Forces involved in a climbing jet aircraft

I have a problem with which I need help. The question is: A jet aircraft is climbing at an angle of 45° above the horizontal and is accelerating at 4.5m/s2. What is the total force that the cockpit ...
6
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0answers
191 views

Derivation of Universal Variables

Does anyone know of link to the derivation of the Universal Variables? This is in regards to Kepler's equations. The Wikipedia link didn't have enough information for me, and the Colorado page ...
11
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3answers
518 views

No closed orbits for a Newtonian gravitational field in 4 spatial dimensions

We are supposed to show that orbits in 4D are not closed. Therefore I derived a Lagrangian in hyperspherical coordinates $$L=\frac{m}{2}(\dot{r}^2+\sin^2(\gamma)(\sin^2(\theta)r^2 \dot{\phi}^2+r^2 ...
3
votes
3answers
762 views

How you feel in outer space vs. orbit?

I understand that when someone is in low earth orbit, the "pull" of their inertia is equal to the pull of gravity. However, the force of gravity is still acting on them. However, if they are in outer ...
0
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1answer
168 views

Question about weightlessness

Let us consider +Y as upward and -Y axis as downward. So the acceleration that works these objects is always $-g$. For the first picture, if the lift is going upward with acceleration $a$, then ...
2
votes
2answers
644 views

How to calculate air resistance of penny dropped from Empire State Building?

If a penny is dropped from the Empire State Building, then its speed, without taking air resistance into consideration, is $\sqrt{\left(32\frac{\textrm{ft}}{\textrm{s}^2}\right)(1454\textrm{ ...
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votes
4answers
11k views

Terminal velocity of all falling objects is same?

Ideally 2 objects of different mass and weight will hit the floor at same time because they face same gravitational pull and accelerate. Will the terminal velocity of both objects be same also? and ...
3
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1answer
95 views

Why doesn't this equation for orbital motion change with position in the orbit?

The question and answer are on pg.8-10 of this PDF: At first, I went through it, thinking nothing of it. But then, I wondered: "What if we picked a final state in which the space junk was NOT at ...
11
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2answers
432 views

How large can planets or moons appear?

In many artistic impressions or movies there are pictures or scenes where the sky is filled with an enormous moon (as seen from a planet) or vice versa. I wonder if there is an upper limit to the ...
2
votes
1answer
156 views

Acceleration due to gravity?

I was looking into orbitals and found something I haven't been able to understand. http://www.math.ubc.ca/~cass/courses/m309-01a/hunter/satelliteOrbits.html There is a part on the page which states ...
4
votes
2answers
414 views

Why are some jenga pieces easier to remove than others?

Jenga is a game place with wooden blocks stacked on top of one another in an alternating pattern. Players take turns removing blocks from any layer and placing them on top. As the game progresses ...
0
votes
1answer
115 views

Vector cross product of $\mathbf{r}$ and $\ddot{\mathbf{r}}$ in polar coordinates

I'm struggling with the following question: Question 6 A planet of mass $m$ moves under the gravitational attraction of a central star of mass $M$. The equation of motion of the planet is ...
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3answers
802 views

Is it possible to whirl a point mass (attacted to a string) around in a horizontal circular motion *above* my hand?

I'm studying circular motion and centripetal force in college currently and there is a very simple question but confuses me (our teacher doesn't know how to explain either :/), so I hope we can sort ...
3
votes
4answers
970 views

Potential energy sign conventions

Almost every book on physics that I read have some weird and non-clear explanations regarding the potential energy. Ok, I do understand that if we integrate a force over some path, we'll get a ...
2
votes
1answer
98 views

Falling through the ground [duplicate]

I do not know much about physics but I know that according to Newtons third law of motion when we walk we are pushing the ground down but the ground is pushing us up. What force is making the ground ...
6
votes
1answer
218 views

How reliant is the Solar System on being exactly the way it is?

We know that all objects with mass exert forces on all other objects of mass such that $$ F = \frac{GMm}{R^2}.$$ And as others have discussed the planets do interfere with each other ...
1
vote
1answer
178 views

Defining the star as the ellipse focus rather than the barycenter, what does the other focus do? [duplicate]

There are a lot of images and animations on the internet depicting two bodies orbiting around their common barycenter. The barycenter is defined as the (let's say right) focus of the ellipse. If we ...
3
votes
4answers
3k views

Why is potential energy negative when orbiting in a gravitational field?

I had to do a problem, and part of it was to find the mechanical energy of satellite orbiting around mars, and I had all of the information I needed. I thought the total mechanical energy would be the ...
0
votes
2answers
126 views

Constant of gravity in earth fixed coordinate system

I have this problem: If the constant of gravity is measured to be $g_0$ in an earth fixed coordinate system, what is the difference $g-g_0$ where $g$ is the real constant of gravity as ...
7
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4answers
1k 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 ...
3
votes
1answer
1k views

Pendulum in an elevator

Suppose we have a pendulum tied to the ceiling of an elevator which is at rest. The pendulum is oscillating with a time period $T$, and it has an angular amplitude, say $\beta$. Now at some time ...
0
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2answers
205 views

Escape velocity to intersection of two gravitational fields

Find the minimal velocity needed for a meteorite of mass $m$ to get to earth from the moon. Hint: the distance between the center of earth and the center of moon is $\approx 60 R_E$, and the ...
1
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1answer
1k views

Gravitational potential energy of mass between two planets

Suppose I want to launch a rocket from earth to some point $O$ between the center of earth and the center of moon (on a straight line connecting their centers), where the gravitational force of the ...
3
votes
1answer
176 views

Tension of rope in the gravitational field of earth

Two balls of mass $m$ each one are connected with mass-less rope with the same length as the radius of earth. The system is in free fall. Prove that the tension of the rope when the nearest (to ...
3
votes
2answers
139 views

Orbits within a $-\vec{r}$ field

Let's say that we have a cold dark matter theory, so we imagine weakly interacting particles. Now, let's say that one of those dark-matter particles has a rare interaction while traveling through the ...
1
vote
2answers
2k views

The potential and the intensity of the gravitational field in the axis of a circular plate

Calculate the potential and the intensity of the gravitational field at a distance $x> 0$ in the axis of thin homogeneous circular plate of radius $a$ and mass $M$. Could anybody describe how to ...
2
votes
1answer
292 views

Understanding Kepler's $2^{nd}$ law in terms of angular momentum conservation

A) Explain how Kepler's $2^{nd}$ law - "The radius vector from the Sun to a planet sweeps out equal areas in equal time intervals" - can be understood in terms of angular momentum conservation. I ...
0
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1answer
341 views

Change in speed of a satellite

Suppose there's some satellite orbiting the earth in circular motion. Suppose there's an asteroid that hits the satellite in the same direction as the instant velocity vector of the satellite. The ...
4
votes
2answers
512 views

Is Earth's orbit around the sun affected by the ~8 minutes light delay?

Gravitational change occurs at the speed of light. As a consequence, we experience on Earth the gravitational attraction of the sun based on its position relative to us ~8 minutes ago. How does this ...
0
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2answers
218 views

How to calculate time for ball to reach plane while considering mass, gravity and wind resistance?

The scenario that I'm having is such that a ball of radius $15mm$ is thrown from a location point $\vec{p}=(2, 5, 2)$ in a direction of $\vec{d}=(3, 0, 4)$. The initial velocity is $30m/s$. There were ...