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Thread: Weather Satellites

  1. #1
    Senior Member harpazo's Avatar
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    Weather Satellites

    Earth is represented on a map of a portion of the solar system so that its surface is a circle with equation x^2 + y^2 + 2x + 4y - 4091 = 0. A weather satellite circles 0.6 unit above Earth with the center of its circular orbit at the center of Earth. Find the equation for the orbit of the satellite on this map.

    Seeking the first-two steps.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Weather Satellites

    Put the given circle representing the surface of the Earth into the form:

    $\displaystyle (x-h)^2+(y-k)^2=r^2$

    Then the trajectory of the satellite will be:

    $\displaystyle (x-h)^2+(y-k)^2=\left(r+\frac{3}{5}\right)^2$
    Last edited by MarkFL; Nov 25th 2018 at 09:56 AM.
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  3. #3
    Senior Member harpazo's Avatar
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    Re: Weather Satellites

    Quote Originally Posted by MarkFL View Post
    Put the given circle representing the surface of the Earth into the form:

    $\displaystyle (x-h)^2+(y-k)^2=r^2$

    Then the trajectory of the satellite will be:

    $\displaystyle (x-h)^2+(y-k)^2=\left(r+\frac{3}{5}\right)^2$
    x^2 + 2x + y^2 + 4y - 4091 = 0

    x^2 + 2x + y^2 + 2y = 4091

    x^2 +2x + 1 + y^2 + 4y + 4 = 4091 + 1 + 4

    (x + 1)^2 + (y + 2)^2 = 4096

    (x + 1)^2 + (y + 2)^2 = 64

    So, r = 64.

    The equation I seek is

    (x + 1)^2 + (y + 2)^2 = (64 + 3/5)
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    Re: Weather Satellites

    Quote Originally Posted by harpazo View Post
    x^2 + 2x + y^2 + 4y - 4091 = 0

    x^2 + 2x + y^2 + 2y = 4091

    x^2 +2x + 1 + y^2 + 4y + 4 = 4091 + 1 + 4

    (x + 1)^2 + (y + 2)^2 = 4096

    (x + 1)^2 + (y + 2)^2 = 64 …. this should be 64^2

    So, r = 64.

    The equation I seek is

    (x + 1)^2 + (y + 2)^2 = (64 + 3/5)^2

    Now evaluate the RHS.
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  5. #5
    Senior Member harpazo's Avatar
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    Re: Weather Satellites

    Quote Originally Posted by Debsta View Post
    Now evaluate the RHS.
    RHS = (323/5)^2

    RHS = (104,329)/5

    Final Answer: (x + 1)^2 + (y + 2)^2 = (104,329)/5
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    Re: Weather Satellites

    Quote Originally Posted by harpazo View Post
    RHS = (323/5)^2

    RHS = (104,329)/5

    Final Answer: (x + 1)^2 + (y + 2)^2 = (104,329)/5

    RHS should be on 25 not 5.
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  7. #7
    Senior Member harpazo's Avatar
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    Re: Weather Satellites

    Quote Originally Posted by Debsta View Post
    RHS should be on 25 not 5.
    Yes, you are right. I forgot to square 5.

    RHS = (323/5)^2

    RHS = (104,329)/25

    Final Answer: (x + 1)^2 + (y + 2)^2 = (104,329)/25

    Correct?
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