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I weigh myself on scale at sea level, a weigh myself at 20,000 feet above sea level. Do I weigh the same, based on gravitational pull?

If I knew this, I wouldn't ask question, because I would have enougb factors in the equation, to solve. If I was a physicists.
1 vote
1 answer
78 views

How to set up differential equation for gravitational system?

Consider the following system Here, two immovable objects with mass $M$ are positioned $2d$ distance apart (in an empty universe). Meanwhile, an object of mass $m$ is placed somewhere above them on ...
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1 vote
2 answers
37 views

Proof for equal eccentricity in a binary star system

What is the proof that the orbits of two stars orbiting around a common center of mass have equal eccentricities? You can use: $m_1r_1 = m_2r_2,$ then say that $r_1= a(1+e_1)$, $r_2=a(1-e_2)$ and from ...
1 vote
0 answers
26 views

Did Newton derive Titius-Bode Law of the planets in his Principia? [closed]

In college I was taught that no one knows why the planetary orbits conform to the Titius-Bode Law. Recently I read that Newton HAD figured that out in his Principia. Right Now I can’t even find a ...
1 vote
0 answers
30 views

Work needed to orbit earth

In school I have always been told that it's better to launch spacecrafts from around the equator to utilize earth's rotation. Now, when wanting to theoretically put a large object with a lot of mass ...
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1 vote
0 answers
46 views

Moon, Earth and the Sun [closed]

How to prove that the geometric locus of the points where the attractive forces of the Sun and the Moon are of equal intensity is a sphere of radius $ r = \frac{R \sqrt{Mm}}{M-m } $, where $M$ is ...
0 votes
0 answers
33 views

Chain sliding off a pivot

Imagine a one-dimensional infinitely thin chain with linear mass density $\rho$ that is hanging on a pivot such that half of the chain is to the left and half is to the right. If both sides are ...
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1 vote
0 answers
26 views

Escape velocity for particle on pole of a rotating, spherical planet?

I got a book called "Problems and Solutions in Mechanics" and decided to try some problems. Here is problem 1008 Consider a rotating spherical planet. The velocity of a point on its equator ...
2 votes
0 answers
53 views

Solving the inverse square law differential equation without components

Is there any way to solve Newton's law differential equation for a satellite in orbit, both for position and velocity. The solution for both for position and velocity might be able to be written in ...
1 vote
0 answers
22 views

Centre of Gravity of Earth-Moon Elevator [closed]

Suppose you have a cylindrical elevator that resembles a rod of mass $m$, cross-sectional area $A$ and uniform density $\rho$, with a length $L$ spanning the distance between the Earth and the Moon. ...
0 votes
0 answers
41 views

Why is it important to release energy as quickly as possible to perform a vertical jump?

Let's assume that we create this mechanism, where we must decide if the actuating cylinders are double-acting hydraulic or pneumatic with a spring inside. the goal is for the mechanism to suddenly ...
1 vote
1 answer
84 views

Why is the gravitational potential of a uniform disc not symmetric about its center?

Consider a uniform, infinitely thin disc of surface mass density $\sigma$ and radius $R$ placed in the $xy$-plane with its center as the origin. The gravitational potential at a point on the axis of ...
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0 votes
1 answer
39 views

Is tidal energy an infinite source of energy?

As tidal waves are caused due to gravitational force which acts infinitely until the presence of mass (the Moon) which make me think of an infinite source of energy. So what's wrong in here?
0 votes
1 answer
45 views

Derive Sun's trajectory from movement of two planets in a 2D plane

Consider a solar system with 1 sun and two planets revolving around the sun in a 2D Euclidean space. While time continues, the sun moves forward, while the two planets revolve around the sun (move up ...
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0 votes
1 answer
59 views

How do the planets stay in their orbit? [duplicate]

The Sun has a strong gravity. The planets also have gravity. So they attract each other. But then why dont they go and mix up with the Sun? If it is the orbit of the planets or a pre-existing motion ...
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0 votes
1 answer
89 views

From my reference frame, why does the Earth need a huge kinetic energy [$0.5M_E(11200)^2=3.75*10^{32}$ joules] to escape me? [closed]

I wake up screaming into the void, when I see the Earth almost touching me but going away from me at 11.2 $km/s$. After waiting forever, the Earth comes to a stop at infinity. I don't remember what ...
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0 votes
1 answer
68 views

Free falling elevator - A person would "levitate"? [duplicate]

If an elevator goes into free fall, assuming there's no friction or anything like that, would it actually float? From what I understand, this would only happen if the elevator falls with an ...
1 vote
1 answer
51 views

Car on hill centripetal force

One of the exercises in my textbook (Giancoli) deals with a car going up the slope of a hill and then decending into a valley. Curvature/radius is $R$ in both situation, and I'm supposed to answer the ...
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1 vote
1 answer
108 views

Vertical movement of an object with gravitational acceleration not constant

I don't know how to start, but i will give you some context: Let's say that we have a body that we want to vertically propel at a distance of $h_f=10$ km of it's original spot considering that the ...
0 votes
2 answers
33 views

Equilibrium of differential mass element of a homogeneous rod hanging from ceiling

I was solving a question that asked me to find the change in length of a rod when it is hung from the ceiling. When I saw the solution, they took some differential elements and said that a force due ...
1 vote
1 answer
48 views

Why is gravity positive in this scenario? [closed]

I am working on some simple tasks ahead of my exam in physics. But I can't wrap my head around this one... I understand that the speed on the top of the rise has to be smaller than the start speed - ...
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2 votes
2 answers
64 views

Why does the energy for a circular orbit not lie in the pit of the effective potential?

According to the well-known graph of the effective potential, it is clear that the body enters orbit only starting with some energy and at this energy the orbit goes round. In an experiment in the ...
0 votes
2 answers
78 views

Is the topic of gravitational potential energy convoluted and unnecesary? [closed]

If we throw an object upwards from the surface of the Earth, we do some work on it to give it kinetic energy. Now as it travels up, Gravity of the Earth does negative work on it till it loses all the ...
1 vote
3 answers
106 views

Deriving energy for elliptical orbit

So I wanted to derive the total energy for an elliptical orbit, $E = -GmM/2a,$ and while I was doing it, I ran into this hurdle. So at the closest point to the focus, the orbiting object is at a ...
2 votes
5 answers
113 views

Does horizontal acceleration affect gravity?

If we apply 1G horizontally in some object, will this constant force equal to G affect the time of falling? If the force does not affect gravity, why gravity is prioritized over this force if both are ...
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0 votes
1 answer
36 views

Why don't we feel centripetal force as we move from the outside of orbit to the inside?

In a debate with a flat earth friend and need help to make sure I understand this correctly. He points out that the part of earth that is on the outside of its orbit is traveling faster than the ...
4 votes
5 answers
337 views

Orbital motions

Suppose two satellites are moving in circular orbits around the earth and then crash into one another. My Question is this, how do we know that the bodies move in an elliptical orbit after the crash? ...
0 votes
0 answers
51 views

Equation for position and velocity of a body falling in a gravitational field [duplicate]

I have tried asking this question on many forums and have so far failed to get a clear answer. Here is the problem. A body with a negligible mass is falling from a distance $R_1$ in a gravitational ...
1 vote
3 answers
65 views

Is Earth's surface gravity termed $g$ derived from Newton's universal law of gravity?

Trying to apply the basic Newton law $F = m a$ to a falling apple and a paper clip I encountered a problem I consider a beginner's: The fact that all objects are subject to the same acceleration ...
1 vote
2 answers
59 views

Why is it proclaimed for astronauts to be "falling"?

My physics teacher explained that the reason why it looks like astronauts are floating is because they are "falling". However, the way I think of it is that the outwards inertial force of ...
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0 votes
1 answer
81 views

What is the force of gravity on two particles? [closed]

Suppose that I have a system of two particles. They have the same mass $m$. At the origin O is something with a very large mass $M$ which is attracting the two particles. The first particle has ...
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0 votes
1 answer
49 views

How is the potential energy of a satellite/planet in orbit derived?

Recall that for a Hookian spring: $F(r) = -kr$ (force vector and radius vector point in opposite directions, hence the negative sign) Since negative work is a positive change in potential energy, $$U(...
0 votes
2 answers
69 views

Orbital height without the gravitational constant and the mass of either object [closed]

Is it possible to calculate the orbital height of an object using only the orbital period T = 93min, radius of the Earth R = 6378km and the gravitational acceleration at the surface of the Earth g = 9,...
0 votes
1 answer
60 views

Newtonian Gravity from curved space?

Imagine you have the arc-length of a curve, in spherical, coordinates: $$ s = \int_{\mathcal C}{d\tau \; \sqrt{f(r)^2 \left (\frac{dr}{d \tau} \right )^2 + r^2 \left (\frac{d \theta}{d \tau} \right )^...
0 votes
0 answers
76 views

Solution to two-body problem in orbital mechanics for $r(t)$ and $\theta(t)$, rather than $r(\theta)$?

I have written a simple numerical integration code to calculate the orbits of two planetary bodies orbiting a star, in order to calculate the transit-timing variation for one body due to the ...
0 votes
1 answer
29 views

Force calculation to jump [closed]

I was trying to calculate the force required for a person to jump. Initially, it looks a very easy question, but it quickly became tough as I worked on it. First of all, let us assume that person or ...
0 votes
1 answer
29 views

Body free fall calculation of the time durance as a direct derivation by time (non-relativistic)

Let's assume a body in free fall during 16 meters without resistance and I'd like to directly calculate the time of this fall. Sure, one could painfully calculate: $v^2 = 16 m·9.81 \frac{m}{s^2}$ $v = ...
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0 votes
0 answers
46 views

How does this trick work in solving the 2-body central force equation of orbit?

I am working on understanding the derivation of Kepler orbits via section 8.5 of John R. Taylor's classical mechanics textbook, and one small detail has been tripping me up. The equation being solved ...
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1 vote
1 answer
73 views

Escape Velocity from orbit

I am a bit confused about the escape velocity formula. I know that escape velocity is $$ V_\text{escape} = \sqrt{\frac{2GM}{R_e}} .$$ My question is does this equation change when for example I want ...
  • 23
0 votes
1 answer
21 views

Experiment to find the Center of Gravity under non-uniform $g$-field

When asked about how to find the center of gravity (CG) for a system, the answer normally goes like "suspend the system at different points and see how the vertical lines pass through. The CG is ...
0 votes
2 answers
77 views

What is the weight of a body during free fall?

Is it '0' or is it equal to the product of the mass of the body and acceleration due to gravity? Please explain in relation to weightlessness of body in freefall.
1 vote
2 answers
111 views

Questions regarding an Olympiad problem for perturbational solutions of the three-body problem

This theoretical problem on the International Physics Olympiad talks about the three-body problem with respect to LISA. In one of their solutions to the problem: Consider the case $M=m$. If $\mu$ is ...
4 votes
3 answers
392 views

Work done by the force of gravity

My question is very similiar to this one: Work done by gravity on falling object does not seem to equal change in mechanical energy As I've understood it, work is only done on an object if the object ...
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-1 votes
2 answers
113 views

Equivalence of Center of Inertia and Center of mass [duplicate]

Why does center of gravity and center of mass correspond to the same point on the body only when gravitational field applied can be assumed to be constant? Reference: IE Irodov, Fundamental laws of ...
-4 votes
2 answers
68 views

Why $cG = 0.02 \rm N$? [closed]

The unit of their product is Newton and its value is precisely (up to their uncertainty) equal to 1/50. And I know! It is tempting to re-think that they might not be constant, but their product must. ...
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0 votes
0 answers
42 views

Path reconstruction from accelerometer and gyroscope data

I found a dataset here whose columns are attitude.roll, attitude.pitch, attitude.yaw gravity.x, gravity.y, gravity.z rotationRate.x, rotationRate.y, rotationRate.z acceleration.x, acceleration.y, ...
4 votes
1 answer
142 views

Foundational considerations in definition of Newtonian Spacetime

My doubt comes from lecture 08 on Theoritische Mechanik by Frederic Schuller. He gives definition of Newtonian Space time as followg: A Newtonian Spacetime is a quintuple of structures $(M,\mathcal{O}...
0 votes
1 answer
64 views

Kepler's Two-Body Problem Choice of Sign

I have been going over the solution to Kepler's problem and there is a subtlety I am missing. The notes I am following (my own notes from a while ago in fact...) get to the following expression $$ \...
0 votes
1 answer
46 views

Why do particles of an interstellar cloud reach the center simultaneously?

A spherical cloud in interstellar space is made of point matter particles. The cloud's mass is evenly distributed with density $\rho$. The particles start to attract one another (due to gravitational ...
0 votes
2 answers
91 views

Uncomputability of the $n$-body problem

The gravitational $n$-body problem is well known to be uncomputable; one can not find a general algorithm that works in all cases that can predict the trajectories of $n$n-bodies. However, in contrast ...
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