Relating Gravitational Field Strength and Mass

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Discussion Overview

The discussion revolves around the relationship between gravitational field strength (g) and mass (m), exploring the proportionality and dependencies involved in gravitational interactions. Participants examine the implications of mass and distance on gravitational strength, as well as the constants involved in the equations governing these relationships.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant proposes that g ∝ m could be correct, suggesting that a larger mass results in a stronger gravitational force.
  • Another participant questions the dependence of radius (r) on mass (m), indicating that the relationship may not be straightforward if considering two planets of the same composition.
  • A participant expresses confusion about the proportionality relationship for g in relation to m, considering whether it should be g ∝ m/r² or include the gravitational constant G, suggesting g ∝ Gm/r² might be more accurate.
  • One participant notes that the relationship between mass and gravity is defined by the gravitational constant, which was established through experimentation and historical context regarding Newton's and Einstein's contributions.
  • Another participant introduces a proportionality involving volume (m ∝ r³) and gravitational acceleration (g ∝ m/r²), suggesting a relationship where increased mass leads to increased gravitational acceleration.
  • A participant shares a separate question about determining the orbital period of an asteroid, expressing uncertainty about the application of Kepler's constant and the calculations involved.

Areas of Agreement / Disagreement

Participants express various viewpoints regarding the relationship between gravitational field strength and mass, with no consensus reached on the correct proportionality. The discussion includes multiple competing views and uncertainties about the dependencies involved.

Contextual Notes

Participants highlight the need for consistent notation and clarify the relationships between mass, radius, and gravitational strength, indicating that assumptions about these relationships may vary based on context.

taetae
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I know the formula for calculating field strength is g= GM/r2 , however if I'm trying to show the proportionality relationship between just g and m, would g ∝ m be correct, since a larger mass equals a stronger force of gravity and vice versa?
 
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Hello tae2, :welcome:

What about the dependence of ##r## on m (c.q. vice versa) ? Think two planets of the same composition ...

PS do use consistent notation: don't change capital M for lower case m if it is not the intention to designate another variable
 
BvU said:
Hello tae2, :welcome:

What about the dependence of ##r## on m (c.q. vice versa) ? Think two planets of the same composition ...

PS do use consistent notation: don't change capital M for lower case m if it is not the intention to designate another variable

Yup, that's where I got confused haha. The mass of the object needs to be divided by the square of it's radius. The question I'm stuck on asks for me to write a proportionality relationship for g relating to m, would g∝ m/r2 be more accurate then? Or should the constant of proportionality, G, be included as well, making it g∝ Gm/r2?

(Taking a class online is so frustrating when you don't quite understand something, I feel like I'm teaching myself!)
 
Last edited:
I'm also confused by what your teacher is asking. The relation between mass and gravity is the gravitational constant. It's just a constant proportion. It came about by experimentation. Newton understood the concept that two objects pulled each other and that that force was relative to the distance. He had a problem with that he needed a force of certain units and his equations had a completely different unit, so he added the G and gave it a unit. Later on once we had more precise measurements of mass and force, we were able to discover the value of this constant.

Of course then Einstein came along.
 
Exercise means gravitational acceleration at the surface, I would venture.

With ##m\propto r^3## and ##g \propto m/r^2## I would say: 8 times heavier, then twice the gravitational acceleration... but I agree that an online answer is a gamble

taetae said:
I feel like I'm teaching myself)
isn't so bad at all ! :smile:
 
Thank you for the help! I hope it's ok to sneak one other question into here (I went through and did all the rest of the questions but this is the only other one I'm confused with). I just want to check whether or not I did it correctly.
It's about determining the orbital period of an asteroid (in Earth years) that has the average radius of orbit as 2.77 AU. It says to use the value of Kepler's constant "expressed in the units of yr2/AU3" and the formula T2=Cr3. So, if my understanding is correct, to find the value of Kepler's constant you would do:
C=T2/r3
C=12/13 = 1yr2/AU3

And then to calculate the orbital period:
T=√Cr3
T=√(1yr2/AU3)(2.77)3

I feel like this doesn't look right...I'm pretty sure I didn't input the correct value for C but I'm unsure how to otherwise get it..
 

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