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Math Help - Radius of Earth

  1. #16
    MHF Contributor
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    Hi purplec16,

    The horizon makes a 90 degree angle with the Earth's centre.
    This is because the astronaut's line of sight makes a tangent with the planet
    (if you balance a perfectly round ball on a table, it's centre is directly above the point of contact or tangency).

    The triangle has the same sides and angles,
    so the trigonometry works exactly as skeeter originally outlined.

    Sin(65.8^o)=\frac{opposite}{hypotenuse}=\frac{R}{R  +380}

    (R+380)Sin(65.8^o)=R

    RSin(65.8^o)+380Sin(65.8^o)=R

    380Sin(65.8^o)=R-RSin(65.8^o)=R[1-Sin(65.8^o)]

    R=\frac{380Sin(65.8^o)}{1-Sin(65.8^o)}
    Attached Thumbnails Attached Thumbnails Radius of Earth-spacelab3.jpg  
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  2. #17
    Member purplec16's Avatar
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    Sorry Skeeter, my mistake 380 miles is correct
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  3. #18
    Member purplec16's Avatar
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    Thank you so much, I get it now and I completely understand, Thank you Skeeter and Archie
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