00:01
We've been told that we can describe the position of the satellite explorer 7 by an ellipse.
00:09
And the equation of the ellipse is x squared over a squared.
00:14
And we're told that a is 4 ,465.
00:18
So i have that squared, plus y squared over b squared.
00:24
And b is 4 ,462.
00:28
A and b are very similar to each other.
00:30
So this is almost a circle, but not quite.
00:34
And the earth is at one of the two focal points.
00:37
So it's not a perfectly round orbit.
00:40
Earth is offset to the focal point, and we have a very, very tiny deviation from a circle into an ellipse.
00:50
So we want to graph both this ellipse and the earth on a graph and see where this satellite is above the surface of the earth.
01:00
Now, to do that, i need to find where the focal point is because that's where the center of the earth is.
01:06
So if you recall, we can find the focal point by this equation.
01:11
A squared equals b squared plus c squared, where a and b, a is the larger of these two numbers, b is the smaller one, and c is the distance from the center to each of the fosite.
01:25
So a squared, that's going to be 4 ,465 squared.
01:31
Equals b squared, 4 ,462 squared plus c squared.
01:38
If i solve that, i get c squared equals 26 ,781, or c equals approximately 164 miles.
01:50
So if that's where c is, then i can find the equation that shows where the edge of the earth is.
01:58
Because the earth we're going to say is a circle.
02:00
It's not 100 % a circle, but it's close enough for what we're talking about.
02:04
We're going to treat it like a circle.
02:08
It doesn't tell me which focus to put the earth at.
02:15
So i'm just going to pick one, x minus 164.
02:21
And the focal point is along the major axis.
02:23
I'm not moving up and down...