00:01
All right, so let's say we have a satellite in a geosynchronous orbit around saturn, and saturn, we're told, takes about 10 .7 hours to undergo a complete rotation, and also the mass of saturn, it'll help to know, is 5 .68 times 10 to the 26th kilograms.
00:20
So from this information, we want to find the altitude of the satellite.
00:25
So we can use kepler's third law, which says that the orbital period squared, in the appropriate units times g times m over four pi squared is equal to our orbital distance cute and it'll also help to know the radius of saturn because our orbital distance reflects the distance above the surface plus the orbital radius so we can write this as about 5 .82 times 10 to the 7 meters approximately so anyway if we plug in our numbers what will have a 6 .67 for g times 10 to the negative 11th cubic meters per kilogram per second squared times t squared now we got to convert 10 .7 hours to seconds so 10 .7 times 3 ,600 because that's how many seconds we have in an hour so that comes out to 38 ,000 520 seconds.
01:34
That's our orbital period.
01:36
This is divided by 4 pi squared.
01:39
This is going to equal our orbital distance cubed.
01:45
So if we multiply all those numbers together, sorry, missing the mass of saturn...