Astronomy pluto travels in a path that is not circular...

ASTRONOMY Pluto travels in a path that is not circular. Pluto's farthest distance from the Sun is 4539 million miles, and its closest distance is 2756 million miles. Write an equation that can be solved to find the minimum and maximum distances from the Sun to Pluto.

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Transcript

00:01 So we're given the apollon and the perihelion for pluto, the distance from the sun.

00:09 And we have the maximum distance as 7 .4, the minimum 4 .4.

00:15 And we know that the perihelion occurred in 1989, and the next one is in 2237, which means that the period is the difference between those two numbers.

00:28 Now, t is in time after 2000.

00:31 So we need to write that model.

00:34 So i have, first of all, the 2237.

00:39 We're starting our time at t of 0.

00:43 And we know that the low is at 4 .4 billion kilometers, high is at 7 .4.

00:50 So that distance is 3.

00:52 So our amplitude, we know, is going to be 1 .5.

00:55 And the middle of the graph is 1 .5 higher than 4 .4 or 1 .5 lower than 7 .4.

01:03 So there's our vertical shift.

01:06 Our period, we know, is 248.

01:09 And that coefficient for that trig function is 2 pi divided by the period, which will round to this value.

01:17 So let's write the model.