Transcript Satellite Motion

Satellite Motion
Low Orbit

A container falls off the space station while in low
earth orbit. It will move
A) straight down toward Earth.
B) curving slowly down toward Earth.
C) in the same orbit as the space station.
D) ever farther away due to lower mass.
E) rapidly away into space.
Short Period


An object in space would go
in a straight line without
another force.
Gravity supplies a force to
hold objects in circular orbits.

In low orbit the period is
related to the gravitational
acceleration.
mv 2
mg 
RE
 2RE 
v 
  gRE
 T 
2
4

RE
T2 
g
2
2
no gravity
gravity
Low Earth orbit period: T < 90 min.
Geosynchronous Orbit

In higher orbits, the
gravitational force is
significantly less than on the
surface.
• Use the force of universal
gravitation.
• Fgrav = G M m / r2

The height for a satellite with
a 24 hr period can be found.
GMm mv 2

2
r
r
 2r  GM
v2  
 
r
 T 
2
GMT
r3 
4 2
2
radius: r = 4.22 x 107 m
altitude is r - 6400 km = 36,000 km
Free Fall

The net force of an object in
circular orbit matches the
centripetal acceleration.


This is the same for a freely
falling object.
Velocity does not change the
force or acceleration.
v
Fnet
a
a=g
Fnet = mg
v
Earth
Weightlessness

Objects in free fall exert no normal force.
• Fnet = -ma = -mg + FN
• If a = g, FN = 0

The same is true in orbit.
• Fnet = mar = Fgrav + FN
• If ar = Fgrav/m , FN = 0

Objects in orbit are weightless.
Spin the Station

A spinning station in orbit has
a centripetal acceleration of its
own.
• Acceleration is on the inside
pointing inward.

There is a corresponding
centripetal force for object on
the inside wall.
Satellite
F
a
Station Gravity

The centripetal force is like
an elevator accelerating
upward.
• Fnet = mar = FN
Satellite

The net force must be due to
a normal force.
• Experience as weight
W  mar  mrw 2
F
a
• If rw2 = g then it matches
earth’s gravity.
next