WEBVTT

00:00:03.530 --> 00:00:06.830
Now the little prince wants to
know how fast this little body

00:00:06.830 --> 00:00:08.010
is going around.

00:00:08.010 --> 00:00:11.410
And well, we can just do f
equals ma analysis again,

00:00:11.410 --> 00:00:14.520
but use a different option
here for the description

00:00:14.520 --> 00:00:16.219
of the circle of motion.

00:00:16.219 --> 00:00:21.620
So we are going
to get minus Gm m1

00:00:21.620 --> 00:00:27.985
over r squared equals
minus mv squared over r.

00:00:27.985 --> 00:00:34.440
And here one r cancels,
and this m cancels.

00:00:34.440 --> 00:00:37.130
And that goes to plus.

00:00:37.130 --> 00:00:47.750
If we solve this for v,
we get v equals Gm1 over r

00:00:47.750 --> 00:00:50.130
and the square root of that.

00:00:50.130 --> 00:00:54.170
And so now the little
prince knows how fast

00:00:54.170 --> 00:00:57.590
this object is going,
given the radius here

00:00:57.590 --> 00:01:02.280
that we've calculated over
there with Kepler's laws.