INTRO: Measuring Change
The name planets means wandering stars; since ancient times,
people realized that these lights moved through the sky in a way
that was different from the other stars.
Every night, a given planet would have moved slightly. By keeping
records, people were able to trace the orbit, or trajectory, followed
by a planet. Kepler showed that this was an ellipse.
Because a planet had a new position each night, it was possible to
take the quotient of the change in position over change in time to
estimate velocity.
d
~
x
dt
≈
~
x(today) −
~
x(yesterday)
today − yesterday
=
∆
~
x
∆t
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