Wheather Satellites

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 1, Section 1.4

See attachment.

[Math Tutor]

Start by getting Earth's circle into standard form. Group and complete the square:

[tex]x^2 + 2x + y^2 + 4y = 4091[/tex]

[tex](x^2 + 2x + 1) + (y^2 + 4y + 4) = 4091 + 1 + 4[/tex]

[tex](x + 1)^2 + (y + 2)^2 = 4096[/tex]

So on this map Earth has center [tex](-1, -2)[/tex] and radius [tex]\sqrt{4096} = 64[/tex].

The satellite orbits [tex]0.6[/tex] unit above the surface with the same center, so its radius is just

[tex]r = 64 + 0.6 = 64.6[/tex]

The center doesn't change, only the radius does. That gives

[tex](x + 1)^2 + (y + 2)^2 = (64.6)^2[/tex]

[tex](x + 1)^2 + (y + 2)^2 = 4173.16[/tex]

The main trap here is adding [tex]0.6[/tex] to the [tex]4096[/tex] instead of to the radius. You have to take the square root first, add the height, then square again.

[nycmath]

Math Tutor,

This question tossed me into bewilderment. I thank you for your clear explanation.