Gravitaional attraction between two objects

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The gravitational attraction between the Earth and the Moon increases by a factor of 6 if the Earth's mass is doubled and the Moon's mass is tripled. The calculation is based on the gravitational force equation, F = G*m1*m2/r^2, where the new force F' becomes 6 times the original force F. The discussion highlights the importance of understanding how mass changes affect gravitational attraction. The user initially struggled with the calculations but eventually grasped the concept after clarification. The thread emphasizes the need for independent problem-solving in homework contexts.
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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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