Taking R = 6400 km and a uniform Earth: At what height is g a sixteenth of its surface value?
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Taking and a uniform Earth:
- At what height is a sixteenth of its surface value?
- At what depth is times its surface value?
- At what height is smaller than at the surface?
Need a reminder? The key ideaShow
At a planet's surface . At a height : . At a depth in a uniform planet: . A spinning planet's equator needs of it for the circular motion.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. (a) , so .
Step 2. (b) .
Step 3. (c) , so .
Answer: (a) . (b) . (c) .
Check. For (c), the shortcut gives . Nearly the same: is small next to .
Watch out. In (a), the height is , not .
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