Satellite Motion
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Satellite Motion - General Physcis - Lecture Slides, Slides of Physics
Satellite Motion, Low Orbit, Short Period, Geosynchronous Orbit, Testing Models, Kepler’S Work, Kepler’S First Law, Orbital Speed, Kepler’S Second Law, Orbital Period are key points in this lecture. All important points and concepts related to physics are introduces and some explained in this course.
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2012/2013
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Satellite Motion
Low Orbit ^ A container falls off the space station while in lowearth orbit. It will moveA) 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.
Geosynchronous Orbit ^ In higher orbits, thegravitational force issignificantly less than on thesurface.
-^ Use the force of universalgravitation.•^ Fgrav
= G M
m^ /^
(^2) r
^ The height for a satellite witha 24 hr period can be found.
(^22) 3
2 2
2
GMT^
r
GMr
r T
v
mvr
GMmr^
radius:
r^ = 4.22 x 10
7 m
altitude is
r^ - 6400 km = 36,000 km
Testing Models ^ Geocentric
(or
Ptolemaic
) means the Earth is at the
center and motionless. Heliocentric
(or
Copernican
) means the Sun is at the
center and motionless. Scholars wanted to differentiate models bycomparing the predictions with precise observations. This originated the modern
scientific method
.
Kepler’s First Law ^ The orbit of a planet is an ellipse with the sun at onefocus.
A path connecting the two foci to theellipse always has the same length.
Orbital Speed ^ The centripetal force is due to gravity.
-^ GMm
(^2) / r =
(^2) mv / r
(^2) • v
=^ GM
/ r
^ Larger radius orbit means slower speed. ^ Within an ellipse larger distance also gives slowerspeed.
Orbital Period ^ An ellipse is described bytwo axes.
-^ Long – semimajor (
a )
-^ Short – semiminor (
b )
^ The area is
ab
(becomes
(^2) r for a circle).
^ The speed is related to theperiod in a circular orbit.
(^2) • v =^ GM
/ r
-^ (
r / T )
2 =^ GM
/ r (^2) • T = 4
23 r/GM
^ Larger radius orbit meanslonger period. ^ Within an ellipse, a largersemimajor axis also gives alonger period.
b a
Kepler’s Third Law ^ The square of a planet’s period is proportional to thecube of the length of the orbit’s semimajor axis.
•^ T
23 / a
= constant
-^ The constant is the same for all objects orbiting the Sun
semimajor axis
:^ a
direction of orbitThe time for one orbitis one period:
T next