http://www.ck12.org Chapter 9. Newton’s Universal Law of Gravity
FIGURE 9.12
can and poke a hole in the side of the can, small enough so your finger can easily cover it, but large enough so water
can easily flow out. Fill the can with water, holding your finger over the hole to prevent the water from flowing out.
Now, hold the can at arm’s length and remove your finger for a moment to convince yourself the water will freely
flow. Then release the can. As soon as the can is in free fall the water will stop flowing out. The apparent weight of
the water is zero—there is no normal force on the water and there is no apparent water pressure. The can and water,
however, still have a force of gravity acting on them, because that is, of course, the force causing the can to fall in
the first place!
http://demonstrations.wolfram.com/ConditionForFreeFallAroundEarth/
Illustrative Example 2
Ageosynchronoussatellite is one which remains above a fixed point on the Earth’s surface in its revolution about
the planet. What distanceRsfrom the surface of the earth must a satellite be placed in order to achieve such an orbit?
Answer:
First, we must ask ourselves, what periodTmust a satellite have in order to remain positioned over the same point
on the Earth’s surface?
Since the satellite appears fixed in space as seen from the surface of the Earth, it must have a period of revolution
equal to the period of rotation of the Earth, that isTe= 1 .00 days→ 24. 0 h→ 86 , 400 s.
Again,G= 6. 67 × 10 −^11 N∗m
2
kg^2 andme=^5.^97 ×^10
(^24) kg
Recall,T^2 =^4 π
2
Gmer
(^3) orr (^3) =Gme
4 π^2 Te
2
r^3 =
Gme
4 π^2
Te^2 →r=
3
√
( 6. 67 × 10 −^11 )( 5. 97 × 1024 )
4 π^2( 86 , 400 )^2 = 42 , 226 , 910 →
r= 4. 22 × 107 m→ 4. 22 × 104 kmBut this result is measured from the center of the Earth, not the surface of the Earth. Thus,