Gravitaional attraction between two objects

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SUMMARY

The gravitational attraction between two objects, specifically the Earth and the Moon, increases by a factor of 6 when the mass of the Earth is doubled and the mass of the Moon is tripled. This conclusion is derived from the gravitational force formula F = G*m1*m2/r^2, where G is the gravitational constant. By substituting the new masses into the equation, the new force F' can be expressed as F' = 6*F, confirming the factor of increase. This analysis clarifies the relationship between mass and gravitational force.

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  • Understanding of Newton's Law of Universal Gravitation
  • Familiarity with gravitational constant (G = 6.67×10−11 N·(m/kg)²)
  • Basic algebra for manipulating equations
  • Knowledge of mass units (kilograms) and distance units (meters)
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  • Learn about gravitational potential energy and its calculations
  • Explore the effects of varying distances on gravitational attraction
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Students studying physics, educators teaching gravitational concepts, and anyone interested in understanding the fundamentals of gravitational attraction and its mathematical representation.

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Homework Statement


If the mass of the Earth were twice as big, and the mass of the moon were three times bigger, by what factor would the gravitational attraction between the two be multiplied?


Homework Equations


0f36df929ac9d711a8ba8c5658c3bfee.png



The Attempt at a Solution


Ive used this formula and failed twice to get the correct answer. please help.
 
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EliteCodexer said:

Homework Statement


If the mass of the Earth were twice as big, and the mass of the moon were three times bigger, by what factor would the gravitational attraction between the two be multiplied?


Homework Equations


0f36df929ac9d711a8ba8c5658c3bfee.png



The Attempt at a Solution


Ive used this formula and failed twice to get the correct answer. please help.
Show us what you did.

Chet
 
6.67×10−11 N·(m/kg)2 x [(1.194438 x 10 ^19) x (2.204301927 x 10^14)/147765666409]

Mass of earth: 5.97219 × 10^24 kg
Mass of moon: 7.34767309 × 10^22 kg
Distance between centers of masses: 384,403 km
 
Rather than put all the numbers in, just note that F depends on the product of the masses. So if one mass doubles and the other triples, you can replace m1 with 2xm1 and m2 with 3xm2. Write both equations (the original one and the one with the new masses) side by side, and the answer should be obvious...
 
nope. still not getting it.
 
So, in the original equation, you have

F = G*m1*m2/r^2

In the new equation, you have

F' = G *(2xm1)*(3xm2)/r^2 = 6*G*m1*m2/r^2 = 6*F

So the force is increased by a factor of 6. Does that make sense?

(Apologies for the badly formatted equations, I'm useless with this stuff... will have to learn).
 
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OOOHHHH. wow. Yeah i get it now. Sorry it took me so long. I thinking way to much into it. Thank you!
 
Naz93 said:
So, in the original equation, you have

F = G*m1*m2/r^2

In the new equation, you have

F' = G *(2xm1)*(3xm2)/r^2 = 6*G*m1*m2/r^2 = 6*F

So the force is increased by a factor of 6. Does that make sense?

(Apologies for the badly formatted equations, I'm useless with this stuff... will have to learn).

Please check your PMs. It is against the PF rules to do other students' homework for them.
 

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