00:01
In this question we are given the orbital period for comet hyakutake and we are asked to find the semi -major axis of its orbit and then compare it to a couple of other distances.
00:17
So the relationship we need between the orbital period of a body in an elliptical orbit is t equals 2 pi times a, the semi -major axis to the three -halves power divided by the square root of the gravitational constant g times the mass of the star that the body is orbiting.
00:45
So we need to rearrange this to solve for our semi -major axis a.
00:56
So we'll start by squaring both sides and we're going to get a equals g ms t squared over 4 pi squared.
01:19
So clearly a was going to be equal to the cube root of g times the mass of the star, in this case the sun, times t squared divided by 4 pi squared.
01:38
Swell.
01:42
Now we need the period of the comet in seconds and we'll end up finding a in terms of meters.
01:52
So this period in seconds we will take our 30 ,000 years and multiply by 365 days per year multiplied by 86 ,400 seconds in one day.
02:19
It's from a pop song from i think the late aughts.
02:28
And we get 9 .4608 times 10 to the 11th seconds.
02:38
And i like to keep some extra decimal places when i'm doing my calculation and then round at the end.
02:46
So now we're able to calculate the semi -major axis for this comet's orbit...