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1)
Energy = Power * Time
Units: 1 Joule = 1 Watt * 1 second (One day has 24*60*60 s = 86400 seconds)
2)
M
3
would ‘experience’ no netgravitational force if F
grav 31
= F
grav 32
. According to
Newton’s universal law of gravity we can express the gravitational forces in terms of the
masses of the three objects and we find:
G·M
1
·M
3
/ x
2
= G·M
2
·M
3
/ y
2
b
x
2
/y
2
= M
1
/M
2
(M
3
and G cancel on both sides)
With y = d
12
– x we can write x = sqrt(M
1
/M
2
)·(d
12
– x) , (‘sqrt’ = ‘square root’)
or: x = c·d / (1+c)
, with c = sqrt(M
1
/M
2
).
3)
F
grav
= mg
4)
F
grav by sun
/ F
grav by moon
= [G·M
sun
· m / R
2
sunearth
] / [G·M
moon
· m / R
2
moonearth
]
= M
sun
· R
2
moonearth
/ (M
moon
· R
2
sunearth
)
5)
The escape velocity is the speed at which the kinetic energy is eqal to the gravitational
potential energy U
g
=  G M·m / R, where M and m are the masses of the planet and the
projectile, respectively. R is the radius of the planet if the projectile is launched from the
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 Spring '08
 ROGERS
 Physics, Energy, Force, Power

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