Is this calculus correct, or do the decimals points have to be converted ?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks so much , cause I'm stuck

The gravitational constant is 6.673 * 10 to the -11th power.

The radius of the moon is 1737400 meters.

Its mass (which is independent of gravity) is 7.35 * 10 to the 22nd power kg.

Now, given that F=ma and F=GmM/r squared, we can set

a = GM/r squared.

So:

a = (6.67300f * (Math.Pow(10, -11)) * 7.36f * Math.Pow(10, 22))/(1737400f*1737400f)

Running this I get a = 1.62704402190015.

Now, since F (the force of gravity) = ma, then for the same object, F1/F2 = ma1/ma2. This means that the ratio of the forces is equal to the ratio of accelerations since the m cancels out: F1/F2 = a1/a2.

Finally, we take acceleration on the earth, which is roughly 9.8m/s/s. Dividing our calculated value for a by that, we get:

1.62704402190015 / 9.8 = 6.02319

And there it is, our 1:6 ratio.

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