• sophadof
MEDAL and FAN "While you and your young cousin are sitting in the backyard looking up in the night sky, your cousin states, "If the moon were half as big it wouldn't have to move around the earth as fast to stay the same distance away." True OR False? and why? I just need help...
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • chestercat
I got my questions answered at in under 10 minutes. Go to now for free help!
  • matt101
The question sounds tricky but it isn't! The moon is attracted to the Earth because of gravity. Assuming the moon is moving in a perfectly circular path, the force of gravity on the moon by the Earth is also the centripetal force acting on the moon. In other words: \[F_c=F_G\]\[m \omega^2 r=\frac{GMm}{r^2}\] In this equation, the small m is the mass of the moon, while the large M is the mass of the Earth. The angular speed of the moon is ω, and the distance between the moon and the Earth is r. If we rearrange this equation to solve for the angular speed, we can see how the angular speed will change as you manipulate other variables: \[\omega=\sqrt{\frac{GM}{r^3}}\] You can see that the mass of the moon reduces out of the equation completely! In other words, the angular speed of the moon DOES NOT depend on the mass of the moon - it only depends on the mass of the Earth and the distance between the moon and the Earth. Does that make sense?
  • sophadof
Yes it does!! thank you!!(: @matt101

Looking for something else?

Not the answer you are looking for? Search for more explanations.