00:01
All right, everyone, so what we have here is a rocket that's initially in circular orbit around the earth.
00:06
And what we're asked to solve for is to determine the time that's needed for the rocket to travel from the inner orbit at a to the outer elliptical orbit at a prime.
00:14
So the way that we're going to solve this problem is by utilizing our knowledge of orbital mechanics and the knowledge of periapsis and apoapsis and also the conservation of angular momentum.
00:26
So let's go ahead and solve this problem.
00:29
What we first need to determine is that d velocity at periapsis, so a.
00:37
So to move from a to a prime, the rocket we know has to follow this elliptical orbit with rp, which is equal to 8 times 10 to the 6th plus the radius of the earth, which is equal to 14 .4 times 10 to the 6 meters.
00:57
And our apoplepsis, which is equal to 19 times 10 to the 6th, plus the radius of the earth, which is equal to 25 .4 times 10 to the 6 meters.
01:08
We can determine the speed at a for the elliptical orbit by saying that ra is equal to rp all over 2gme all over rpbp squared minus 1.
01:24
What we can do is isolate bp, which is the velocity at periapsis, which is also at a.
01:30
So we know that bp equals va, which is equal to the square root of 2 times g m -e r -a all over r -p times the quantity r -p plus r -a...