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

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Square Cube Law?

I've heard about something called the square cube law. What is it? All I know of it is that it has something to do with mass of large objects and their gravitational influence.
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1answer
54 views

How the gravitational constant $G$ is determined?

We know the gravitational constant is $G=6.67545 \times 10^{-11} m^3 kg^{-1} s^{-2}$. But how this value is determined at first?
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1answer
74 views

Throwing an object in the air [closed]

Studying formulas about velocity and acceleration I came up with a question: if I throw an object in the air with a velocity $v_0$ (suppose i throw it vertically) in how much time its final velocity ...
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1answer
48 views

Finding at a distance from the Earth speed of satellite [closed]

A satellite at 8000 km from Earth where gravity is 6.4 m/s^2. What is the velocity of satellite? I don't the formula to find speed of satellite.
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5answers
358 views

Infinities in Newtons law of gravity (for point particles)

Newtons law of gravity for two particles of mass $m_1$ and $m_2$ is: $G\frac{m_1.m_2}{r^2}$. Supposing that the particles are point particles then gravitional attraction will bring them closer ...
7
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1answer
483 views

Gravitational force from spherical shell

Say we have a point mass $\mu$ located at $(0,0,R)$ and a spherical shell (not considering it's volume!) of radius $R$ located in the origin. So we have a particle standing right on top of the sphere ...
4
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1answer
32 views

Galaxy velocity curve

When deriving the relation between velocity of a star and its distance $r$ from the center of the galaxy, one assumes that the masses outside $r$ have no contribution and those inside $r$ give a force ...
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2answers
112 views

Why does earth have a minimum orbital period?

Using the equation for Kepler's constant for Earth $K$: $$K = \frac{GM}{4\pi^2}$$ $$K = 1.01 \times 10^{13} \;\rm m^3/s^2$$ Finding time ($r = 6.4 \times 10^{6} \;\rm m$ (radius of Earth)): $$K = ...
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0answers
95 views

Application of trigonometry to the slingshot effect/gravity assist

I have been trying to understand the formula $$v_f^{2}=v_i^{2}+2V(V(1-\cos\beta)+v_i(\cos(\alpha-\beta)-\cos\alpha))$$ as it relates to Fig. 2 on page 5 of this exposition: ...
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1answer
54 views

Help for orbits of planets

Suppose that an asteroid) that moves at a velocity $v$ passes near to a planet: now I know that the gravity force of the planet will curve the trajectory of the asteroid so I tried to make a draw of ...
7
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1answer
97 views

Is $4 \pi G$ the true most fundamental gravitational constant? [closed]

Newton's law of gravitation is: $$F = G m_1 m_2 \frac{1}{r^2}$$ It looks simple and natural. But that's only in 3 dimensions. Let's look what happens in $n$ dimensions: $$n=2 : F = 2 G m_1 m_2 ...
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402 views

Derivation of Kepler's laws

How can analytically be derived the Kepler's laws? I found some extremely synthetic equations which from the Newton's laws (in particular $\mathbf{F} = m \mathbf{a}$) tried to obtain the Kepler's ...
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0answers
20 views

Relation between Earth's rotation-gravity and moving object on Earth [duplicate]

This might be silly question. It's about the rotation of the Earth and the objects moving on it. If I jump into the air, why did I also move with the Earth though I am in the air? I am supposed to be ...
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4answers
228 views

Why Newton's law of universal gravitation is a valid law? What causes any two bodies in the universe attract each other with a force?

Why Newton's law of universal gravitation is a valid law? What causes any two bodies in the universe attract each other with a force? What causes a larger body in space to have a gravitational pull on ...
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0answers
87 views

Only gravitation and Newton's $2^{\mathrm{nd}}$ law needed to derive Kepler's laws?

It is known that Kepler's laws of planetary motion can be derived from Newton's laws of motion and his law of universal gravitation. However, are all of Newton's laws of motion necessary? According ...
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1answer
67 views

Tension in string and gravitational force on bob relative strength

When calculating time period of simple pendulum (an approximation of SHM at small amplitudes) we take gravitational force greater than tension in string and resolve gravitational force in two ...
2
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3answers
67 views

Question about (complex) motion of Moon

In an ideal situation, we can use a simple formula to determine the velocity at which a body revolves around a massive body at a particular distance. I was wondering if there is an intuitive way to ...
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0answers
50 views

Why doesn"t centrifugal force throw us off the earth? [duplicate]

I was drawing a diagram and trying to resolve all the forces. It seems to me that because of gravity, centrifugal force will produce a sort of "dragging" motion along the surface of the earth. The ...
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1answer
102 views

Tidal force of Sun?

As I understand, satellites and the Moon orbiting Earth are in free fall. Isn't the same true for Earth orbiting the Sun? My question is then: How can the Sun's gravity affect tides? Aren't the ...
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2answers
113 views

How do you know which way to choose the limits of an integral?

I am reading http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S4 In the beginning of equation 13.18, in which Mr. Feynman calculates the potential energy of an object outside a spherical shell, ...
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4answers
100 views

What would the gravity be like if Earth and the moon were touching?

What would the gravity be like if Earth and the moon were touching? Assuming the moon keeps its form and doesn't collapse on its own weight, would the area between it and the Earth (point B) have ...
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3answers
1k views

Rocky Planet in the center of System [duplicate]

We all know that mostly stars are at the center of planetary systems, but is it possible that instead of star there was a rocky planet in the center with stars (and other planets and moons) orbiting ...
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1answer
104 views

Tangential and radial acceleration in projectile motion

I'm currently learing kinematics, specifically projectile motion and as an example in my textbook is a bullet fired at some angle. I understand the derivation of formulas to describe that motion and ...
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2answers
76 views

Do I need to take weight of the rocket into account when calculating escape velocity?

Here there is the old problem. I know from the old problem that the work $W_v$ that I need to make a rocket fast enough to reach the escape velocity is $$W_v= G \frac{mM}{r}$$ therefore because ...
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1answer
125 views

Why does acceleration seem not to be the gradient of gravitational potential?

Consider a spherically symmetric distribution of density $\rho(r)$. We can define the mass enclosed within each radius $r$ using $\frac{dM(r)}{dr} = 4\pi r^2 \rho(r)$, with the condition that $M(r=0) ...
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3answers
614 views

Gravitational doubt [duplicate]

If we can shield a charge from electrical forces by putting it inside a hollow conductor. Can we shield a body from gravitational influence of nearby matter by putting it inside a hollow sphere or by ...
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1answer
53 views

Balancing stick on hand - inverted pendulum motion

How do I calculate the velocity and acceleration of a stick that is vertically on my hand? How fast and far do I need to move my hand from side to side to keep balancing the stick? Assuming that we ...
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1answer
50 views

How to find the force of the compression at the core of a planet?

For example the core of the planet Jupiter, how to find out the magnitude of the force that compresses its core? and can that be thought of as the total force that holds the planet together?
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1answer
59 views

In a universe that is expanding at a constant rate, do objects that are attracted to each other feel a force opposite to their attraction?

In this article, the authors make the claim (pg 44) that "Expansion by itself—that is, a coasting expansion neither accelerating nor decelerating—produces no force." I'm having a hard time convincing ...
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4answers
582 views

Why are people weightless whilst in orbit around the Earth? ISS? Satellites? [duplicate]

Had physics for 2 years now on highschool, but there is a thing I am wondering about. You know the in the height above the earth surface around where the satellites are (Or the ISS), I've calculated ...
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1answer
48 views

Two equations for $y$ in projectile motions

I have two equations on my equation sheet: $$y=v_o t \sin \theta - \frac{1}{2} g t^2.$$ And then another: $$y_{\max} = \frac{v_o^2 \sin 2 \theta }{2g}.$$ I understand that the first one is an ...
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2answers
234 views

Why do we orbit around the sun instead of one the other stars?

I am still very new to many physics theories, however while sat in class today, a thought came to mind that I have not been able to answer from simple googling. What is so specific about our sun ...
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1answer
86 views

Could an orbiting mass generate power?

If an heavy object (e.g. 10 tons) orbiting around Earth at 370 miles high, is connected with a cable back to Earth, we assumed either Earth is going to pull the mass or vice versa (or it will fall ...
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1answer
52 views

It is a numerical [closed]

If the densities of the moon and the earth are related by $\rho_m / \rho_e =3/5$, and if $g_m /g_e = 1/6$, then what is $R_m /R_e$? ($g=$ acceleration due to gravity and $R=$ Radius)
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1answer
102 views

Calculate analytically the time until two spheres meet due to gravitation [duplicate]

Imagine you have two homogeneous spheres with the same diameter of $d=0.1 m$. They have the same mass $m = 1 kg$. The distance between the centers of mass is $r= 1 m$. Their electrical charge shall be ...
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0answers
80 views

Force of gravity in the event horizon [closed]

I recently posted a question about black holes and gravity (this) and I discovered the Schwarzschild radius: $r_s=\frac{2GM}{c^2}$. I thought with a friend of mine about the actual force (in Newtons) ...
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2answers
46 views

Velocity required for orbit of satellite

I am very confused about orbital velocity for satellite launched from earth. It is states that: $$ v=\sqrt{\frac{GM}{r}} $$ Some says that it is equal to 8000 m/s and some say 3.1 km/s. Please remove ...
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3answers
85 views

What is an intuitive explanation using forces for the equatorial bulge?

The earth is not a sphere, because it bulges at the equator. I tried fiddling with centripetal force equations and gravity, but I couldn't derive why this bulge occurs. Is there (a) a ...
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3answers
86 views

Would an Object Near a Pre-Blackhole Star Experience the Same Gravity as Post-Blackhole?

My question was inspired by this question, which got me thinking. According to Newton's Law of Gravitation, $$F = G\frac{m_1m_2}{r^2},$$ the gravity of an object is inversely proportional to the ...
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2answers
335 views

Does the mass of a star change as it collapses into a black hole?

I know (I think!) that when a really big star collapses on itself it creates a black hole. My question: When a star collapses, is the mass equal to the mass of the star when it's not a black hole? Or ...
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3answers
216 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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2answers
288 views

Loop-the-loop question [closed]

Problem: The marble rolls down the track and around a loop-the-loop of radius R. The marble has mass $m$ and radius $r$. What minimum height $h$ must the track have for the marble to make it around ...
4
votes
3answers
155 views

Does gravity cause Archimedes' principle and how?

Why do lighter objects float and denser sink? I understand this from the perspective that if the object can displace the equal mass of water it will float, but I wonder from the perspective of ...
0
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3answers
32 views

Gravitional force

Does the gravitation of Earth have a limit? when a body projected vertically with $v=11km/s$ (escape velocity) from Earth's surface does this means that it does not return back to Earth?
3
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3answers
131 views

Why aren't there more natural satellites orbiting the Earth than just the Moon?

Considering that there's a lot of debris in space and that impacts fling out rocks into space all the time, why do we only have one large natural satellite - the Moon? Shouldn't there be all kinds of ...
2
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1answer
73 views

A zero gravitational potential and non zero gravitational field

Give an example of a situation in which there is a non-zero gravitational field and a zero gravitational potential at the same point? $$dV=-\vec E\cdot d\vec r.$$ The above equation implies that ...
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0answers
36 views

Dependence of Force as a function of Distance? [duplicate]

Why is the strength of a field (i.e. gravitational or electric) inversely correlated to the square of the radius? It is clear to me why the further you get a way from a field, the field's enacted ...
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4answers
121 views

Gravity and acceleration

I've imagined this little scenario to help me conceptualize things. Let's say we have a doughnut-shaped object with a hole whose diameter is greater than that of a sphere. Let's say that the sphere ...
0
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1answer
58 views

Calculating Gravitational Attraction Involving Massless Objects

Using the formula $F=G\frac{m_1m_2}{d^2}$ where $m_1$and $m_2$ are the masses of two objects, $G$ is the gravitational constant, and $d$ is the distance between the objects, it is possible to ...
2
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2answers
114 views

Potential and kinetic energy on spherical surface

A small particle of mass $m$ is atop of a semi-sphere as shown in the figure. A little push was given to the particle. Prove that the particle will leave the spherical surface at a height of ...