How Far Does the Moon Fall Toward Earth in One Second?

AI Thread Summary
The discussion focuses on calculating how far the Moon falls toward Earth in one second, given its center-to-center distance of 384,400 km and an orbital speed of 1024 m/s. The user seeks assistance with the appropriate equations to determine the vertical distance the Moon falls below its tangent line due to gravity. They mention the need for centripetal acceleration in the calculations and reference a geometry problem involving a tangent line and an angle theta. A diagram has been provided to aid in visualizing the problem. The conversation emphasizes the importance of understanding the relationship between orbital motion and gravitational effects.
eunhye732
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The center-to-center distance between Earth and Moon is 384400 km. The Moon completes an orbit in 27.3 days.
(b) If gravity were switched off, the Moon would move along a straight line tangent to its orbit, as described by Newton's first law. In its actual orbit in 1.00 s, how far does the Moon fall below the tangent line and toward the Earth?

part (a) was asking for the Moon's orbital speed which was 1024 m/s. for part (b) my question is I don't know what equation to use to solve for this. All i know is that I need to use centripetal acceleration but when?
thanks and i hope you can help~!
 
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The second part is a geometry problem.
Consider a circle with a tagent line drawn at one point. Now after 1.0 s, the moon (under gravity) moves through an angle of theta. I truly think this needs a diagram, so I've attached one now. We want to solve for y.

http://img400.imageshack.us/img400/503/745636345ew.gif
 
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