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Phys111 lecture13

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Samantha Bambalan

1) Newton's universal law of gravitation states that every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. 2) Orbital motion, like the moon orbiting the Earth, is in a state of constant free fall under the force of gravity. 3) For a satellite or moon to maintain a stable, circular orbit around a planet, it requires a precise centripetal acceleration provided by the planet's gravitational pull.

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Newtons Universal Law of Physics 100 Chapt 10 Gravitation
Very fast horizontal toss t = 0s t = 1s x= 8km 5m t = 2s x=16km t = 3s x=24km 20m 45m V=8km/s
Orbital motion is free fall VV == 46 km/s V = 8km/10km/km/s CEilirpctuilcaarl OOrrbbiitt!
Centripetal acceleration a = v2/r for a circular orbit (v = 8km/s = 8x103m/s) a = (8 x103 m/s)2 6.4 x 106 m = 64 x106 m2/s2 6.4 x 106 m = 10 m/s2 Toward Earths center = g
Artificial satellite a v a = v2/r = g
Moon-earth v a=v2/r
Is the Moon in free-fall around the Earth? r=3.84x105km v a = v2/r what is v? v = dist/time = 2pr 28d = 2x3.14x 3.84x108 m 28dx(24h/d)x3.6x103s = 24 x 108 m 2.4x106s = 1.0 x 103 m/s
Moons centripetal acceleration amoon = v2/r; v = 1.0 x103 m/s) amoon= (1.0 x103 m/s)2 1.0x106 m2/s2 3.84 108 m = x 3.84 x 108 m = 2.7 x 10-3 m/s2 損 1 3600 g Toward Earths center
Newtons dreams Hmmmmm The Moon is in free-fall around the Earth Its acceleration is only 1/3600 g (accel at the Earths surface)
Distances The moon is 60x further from the Earths center than objects on (near) the Earths surface r=3.84x108m = 60 x 6.4x106 m = 60 x RE 1 60 1 ( ) 3600 2= RE = 6.4x106m
Newtons big idea The force of gravity gets weaker as distance squared The moon is 60x further from the Earths center than objects on (near) the Earths surface The strength of Earths gravity near the Moon is (1/60)2 t=1/3600 times weaker
Gravity gets weaker as 1/dist2
Universal law of gravity m r M F 袖 m F 袖 M F 袖 1 r2 combine: F 袖 mM Proportionality constant: Newtons Constant r2 F = G mM r2
Universal Universal: applies to all objects!!!
What is G? W= G mME R2 E W W= m GME R2 E W= m g g= GME R2 E
Force of gravity between ordinary-sized objects 80kg 60kg 1m F = G mM r2 F = 6.7x10-11Nm2/kg2 60 kg 80kg (1m)2 F = 6.7x60x80x10-11N F = 32160.x10-11 N = 3.2x10-7 N 損 30x109 times bigger! Boys weight = mg = 80kg x 10m/s2 = 800 N
Measuring gravity force between ordinary-sized objects is very hard
Moons gravity causes tides
So does the Suns Half Moon New Moon Full Moon
Measuring Weight N mg
Weightlessness N =mg N >mg N <mg N =0
Weightlessness means N =0 compensating upward
Weightlessness in action
Floating is space is really free-falling in space
What is g on the moon? W= G mMM R2 M W= m GMM R2 M W= m gM gM= GMM R2 M W RM=1.7 x 106m m MM
gM on the Moon g = GMM R2 M 6.7x10-11Nm2/kg2 x 7.4x1022Kg (1.7x106m)2 = gM = 1.7 m/s2 1/6 x gEarth
summary Obey the law!
Phys111 lecture13

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Phys111 lecture13