Gravity Revisited: Earth-Moon & Earth-Sun Comparisons

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Discussion Overview

The discussion revolves around the gravitational interactions between the Earth and the Moon compared to those between the Earth and the Sun, particularly in hypothetical scenarios where these bodies are not in orbit. Participants explore the implications of Newton's Law of Gravity, the nature of gravitational forces, and the concept of acceleration in relation to mass.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the acceleration of the Earth and the Moon towards each other compared to the Earth and the Sun, suggesting that if both pairs are at the same distance, the gravitational force would differ due to their masses.
  • Another participant states that while the gravitational forces are the same, the accelerations must differ due to the different masses involved, referencing F=ma.
  • A later reply emphasizes that for equilibrium, the forces must be equal, leading to different accelerations and thus different velocities for the two bodies.
  • Some participants challenge the idea that two objects of different masses fall at different times, referencing Galileo's experiments and suggesting that they would land simultaneously in the absence of friction.
  • One participant introduces the notion that Newtonian physics may be fundamentally flawed, proposing that multiple gravitational forces need to be vector summed when considering interactions among three bodies (Earth, Moon, Sun).
  • Another participant argues that the time to impact for two different masses is less than the time for a lighter mass, even if the difference is negligible, and questions the implications of this claim.
  • Some participants discuss the universality of free fall and how it relates to the frame of reference, suggesting that the accelerations are relative to the center of mass of the two bodies involved.
  • There are references to empirical observations supporting the universality of free fall, while also noting that from a mathematical perspective, it may not hold true under certain conditions.

Areas of Agreement / Disagreement

Participants express differing views on the nature of gravitational interactions, the implications of Newton's laws, and the outcomes of hypothetical scenarios. There is no consensus on whether different masses fall at different rates or on the validity of Newtonian physics in these contexts.

Contextual Notes

Limitations include assumptions about the absence of other celestial bodies and the neglect of orbital dynamics. The discussion also highlights the complexity of gravitational interactions in multi-body systems and the potential discrepancies in interpretations of Newtonian mechanics.

  • #31
Yes, I agree with Morberticus and Dave. You're basically saying the same thing I said in post #17. I don't even think the OP was even considering anything more than a two body problem. Using more than two bodies only serves to complicate the understanding of the universality of free fall and the equivalence principle. The EP has not been mentioned in this thread. But I think it is important to bring it up because the UFF and EP go hand in hand. I will use the following illustration:

uff_ep.gif


The dot located between m1 and m2 is the CoM. Notice that it is in the center an equal distance from m1 and m2. This tells us that the mass of m1 and m2 are equal. I cannot do animation here so you'll have to visualize the following.
Lets increase the mass of m2. Two things will happen. 1)The increase in inertial mass of m2 will cause the CoM to move to a position closer to m2. 2)The increase in gravitational mass of m2 will cause the relative acceleration of m1 and m2 toward each other to increase. Now, the equivalence principle tells us that gravitational mass is proportionally equal to inertial mass. So the shorter distance that m2 has to travel to reach the CoM (as a result of the increase in inertial mass of m2) exactly offsets the increase in acceleration (as a result of the increase in gravitational mass of m2). So the acceleration of m2 relative to the CoM remains constant, and the time that it takes to reach the CoM decreases. The only way to change the acceleration of m2 relative to CoM is to change the mass of m1.
 
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  • #32
Hello all.

I have a question.
Has any of the above discussion been experimentally verified?
Not saying it's wrong. Just want to know.
 
  • #33
Pallidin, I deleted part of my first paragraph in post #31 because I felt some parts of it may be incorrect. However, I have a high degree of confidence with the post as it is now. Please be more specific with your question. There have been lots of experimental tests for the UFF and EP.
 
  • #34
TurtleMeister said:
There have been lots of experimental tests for the UFF and EP.

Would you be willing to be more specific as to the sources?
 
  • #35
I think http://www.npl.washington.edu/eotwash/" has some of the most recent tests of the EP. Right off hand, I don't have a recent source for the UFF.
 
Last edited by a moderator:
  • #36
OK, good read.
But, I understand that this has not been endorsed by the NSF, DOE or NASA.
Am I missing something there?
 

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