Gravitaional attraction between two objects

[EliteCodexer]

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

The Attempt at a Solution

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

 

[Chestermiller]

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

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

 

[EliteCodexer]

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

 

[Naz93]

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...

 

[EliteCodexer]

nope. still not getting it.

 

[Naz93]

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).

 

[EliteCodexer]

OOOHHHH. wow. Yeah i get it now. Sorry it took me so long. I thinking way to much into it. Thank you!

 

[berkeman]

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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