Galileo’s Astronomy and Newton’s Gravitation#
Example 1: the moon is moving right along!#
The Question:
How fast is the Moon traveling, using modern parameters?
The Answer:
The Moon’s actual distance from the center of the earth used by Newton was \(D_M=1,031,400,000\) ft and the period is roughly 30 days, actually 27.3 days, or \(2..36 \times 10^{6}\) seconds (I asked Mr Google). The more modern value for this distances is \(1,261,000,000\) ft, or \(1.26\) billion feet or… \(1.26 \times 10^9\) feet.
So the speed is the distance around divided by the time to go around:
\[
\begin{align*}
v_M &= \frac{
\end{align*}
\]
That’s about 2287 mph. Moving right along, that thing is. You’ll next be asked to do the same thing for a familiar orbiting object.