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

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Condition on $U_{eff}$ for a mass to get trapped in orbit around a heavier mass

this question is now solved, and I have already edited the wikipedia page The wikipedia page on Effective Gravitational Potential states that $$U_{eff} \leq E$$ is a condition for a free mass getting ...
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1answer
41 views

$N>2$ gravitating masses can never reach equilibrium

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?
2
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2answers
19 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
1k 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?
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1answer
47 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 ...
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3answers
54 views

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

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
254 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 ...
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0answers
18 views

What is the particle distribution in Saturn's Ring System?

In watching the scientifically scream-inducing film 'Interstellar', there was a shot of the spacecraft moving through the Rings of Saturn. In this shot, and in every graphical representation of the ...
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0answers
21 views

How to find the nature of an orbit knowing 2 altitudes and the time interval? [on hold]

A body was observed at an altitude of $366 km$ and then at $633 km$, after $12.5$ minutes. Angular separation between the 2 measurements is 45 degrees: find nature of orbit and true anomalies at 2 ...
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2answers
25 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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4answers
86 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
24 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
37 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: ...
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1answer
38 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 ...
1
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0answers
37 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" ...
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0answers
50 views

What is the general proof of Earths “True gravity”?

What is the proof that while calculating gravity, the experiment was not affect by the following factors: Earths Centripetal Force Moons Gravity Centripetal Force due to Sun Earths Rotational ...
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2answers
133 views

Kepler's Laws to Determine Radius of Circular Orbit

"In nonrelativistic limit of general relativity there is a correction to the Newtonian gravitational potential energy $−h/r^3$ with $h = αL^2/(mc)^2$, where c is the speed of light, α = GMm and L is ...
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1answer
28 views

Change of value of $g$ due to rotation [closed]

A body stretches a spring by a particular length at the earth's surface at the equator. At height $3x$ kilometre above the South Pole it will stretch the same spring by the same length. Assume the ...
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1answer
22 views

Question on Gravitation and Time Period [closed]

The time period of revolution of satellite is $T$. The kinetic energy of the satellite is proportional to A) $T$ B) $T^2$ C) $T^3$ D) $T^{-2/3}$
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2answers
54 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 ...
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2answers
125 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 ...
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1answer
72 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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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 ...
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1answer
73 views

What is the Jacobian matrix of Newton's law of gravity? [on hold]

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. ...
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2answers
46 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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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 ...
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1answer
63 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 ...
0
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0answers
18 views

How to Model Differential Gravitational Field from Vectors?

The tides are caused by differences in the gravitational field of the moon on the near side and far side of the earth. If I set this gravitational field as a vector field using Newton's Law of ...
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4answers
77 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
votes
1answer
52 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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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 ...
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2answers
49 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
61 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 ...
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2answers
89 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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0answers
29 views

Using Kepler's law to calculate time to Mars [closed]

Suppose a mangalyan is sent to mars by launching it into a transfer orbit eom around the sun. It leaves the earth at E and meets mars at M. If semi-major axis of Earth's orbit is $a_e$ and that of ...
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1answer
45 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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0answers
41 views

What force acts on a coin that has been tossed when it is half way to the top? and what force acts on it when it is at the top?

This is a homework question and it appears to be a misleading question. I think that the answer is gravity for both of them. The only alternative answer I have is kinetic energy half way up and ...
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3answers
85 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 ...
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1answer
39 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 ...
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1answer
33 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 ...
3
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1answer
31 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 ...
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0answers
20 views

Why does the Moon not rotate about its axis, relative to Earth's rotation [duplicate]

One of the common features of the Moon is the fact that only one face of the Moon is ever visible from Earth, regardless of how much of its orbit the moon has made about the Earth. This would imply ...
0
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1answer
45 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 ...
-2
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2answers
29 views

How did the planets (in the Solar System) start to revolve around the sun if they were attracted towards the Sun via the gravitational force? [duplicate]

The planets in the Solar System revolve around the Sun in almost circular paths called orbits. The Sun pulls the planets with the gravitational force,but the planets do not get drawn to the Sun but ...
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3answers
62 views
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3answers
114 views

Does the Earth revolve around the Sun?

I am aware of this Phys.SE question: Why do we say that the earth moves around the sun? but I don't think this is a duplicate. In a binary star system, where the masses of the 2 stars are not so ...
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1answer
49 views

Do we need Escape Velocity [duplicate]

This may seem silly a lot but I really need some clarification on the necessity of escape velocity for a rocket leaving the Earth's gravity. A stone thrown vertically upwards reaches to a certain ...
1
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2answers
53 views

Does the gravitational force of a massive, spherical body draw only towards its center of gravity, and to no other area?

Consider the premise that at the center of Earth (for example) an object would be weightless because of the relatively even distribution of mass surrounding it, and the resulting gravitational pull on ...
0
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2answers
67 views

Orbital Velocity Question

I have a satellite in a stable trajectory around Earth, of a Mass $m$. I know that its velocity is: $$ v = \sqrt{mG/r}\, $$ But now it begins accelerating directly against the gravity vector (i.e. ...
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1answer
54 views

How do you calculate density if you also account for gravity?

Consider this. I have an Earth-sized quantity of water that I throw into space. Naturally, it will assume the shape of a ball. Now hear me out. Density's definition generally assumes that it will ...