00:01
So for this problem, we are given that the length of, we're trying to find the length of the major axis of the orbit of uranus.
00:08
We're given its orbital period of 84 years.
00:12
So the first thing that we can recognize is that we're going to use kepler's third law, obviously, which is t squared over a cube is equal to a constant value.
00:23
Another way of writing this is that t squared is proportional to.
00:30
A cube.
00:32
Yeah, i didn't write that proportionality symbol, right? but you get the gist of it.
00:37
So the thing that would make this k value 1 is what we're interested in.
00:42
And to do that, we need to get everything into the right units.
00:45
So the units for t need to be in years.
00:49
The units for a, need to be in au or astronomical units.
00:54
The units for any masses need to be in solar units, which is equal to the mass of the sun, which is 1 .99 times 10 to the power 30...