Newton

1
Newtons Universal Gravitation
Every particle in the universe is attracted to
every other particle by a force that is directly
proportional to the masses and inversely
proportional to the square of the distance
between them
Fd2 is a constant m1m2
value G!
F ? m1m2 d2
G 6.67 X 10-11 Nm2/kg2
2
F Gm1m2 d2
for an object and the earth
Fw GmMe re2
since Fw mg, then
g GMe r2
where r is the distance from the center of the
earth!
What is the weight of a 12 N object that is
raised to a height of Rearth above the surface of
the earth?
F2Re (1/4)FRe 3 N
F a 1/r2
3
Newtons Shell Theorem- What would be the weight
of a 5.00 kg groundhog that burrows down a
distance of r/2 toward the center of the earth?
Why isnt it simply 4mg ?
The Shell Theorem states that when inside a
sphere, the mass used is the mass that is
inside the shell upon which the point is
located.
4
Ve (4/3)pRe3 Vs (4/3)pRs3
Re
Rs
Ve Re3 Vs (½Re) 3
Vs ?Ve so Ms ?Me
Rs (½)Re
The 5.0 kg groundhog would only weigh 24 N-- So
what would it weigh at the center of the earth?
5
At what point between the earth and the moon will
a capsule experience 0 net gravitational pull?
Fe
Fm
GMem GMmm re2 rm2
?F 0 Fe - Fm
Rm / Re (7.36 X 1022) / (5.96 X 1024)
.111
About 210,000 mi from earth and 26,000 mi from
the moon!
6
Keplers Laws of Planetary Motion
1) Planets orbit in ellipses with the sun at one
focus
2) Planets move so that they sweep out equal
areas in equal times
v2
v1
v1gtv2
7
3) For all planets, the square of the period (T2)
is proportional to the mean distance from the sun
cubed (r3)
T12 T22 r13 r23
A similar result is produced when relating the
period to the length of the semi-major axis (a)
M mass of the body orbited!
T12 T22 a13 a23
T2 4p2 a3 GM
8
What is the period of Pluto about the sun (msun
1.99 e 30 kg), the most eccentric of orbiting
planets, if its mass is 1.21 e 22 kg and its
semi-major axis measures 5.91 e 12 m?
Compute the mass of the sun from the period and
radius of the Earths orbit (1.50 X 1011 m).
At what height above the surface of the earth
should a satellite be placed so that it is in
geosynchronous orbit about the earth?
(Geosynchronous orbit requires that the satellite
stays above the same point on the earth at all
times).