- #1

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How do you calculate the radius from this information without using a calculator? Trigonometry I am guessing, but I need a better hint.

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- Thread starter johnsholto
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- #1

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How do you calculate the radius from this information without using a calculator? Trigonometry I am guessing, but I need a better hint.

- #2

Simon Bridge

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Place an origin O and draw a circle radius R about it. That's your planet.

The observer is at point A, a distance R+h from O - draw the line OA.

The point B, on the circle, is where the tangent to the circle also goes through point A.

The angle between BA and the tangent to OA (through A) is ##\alpha##.

In your case, h=100m and ##\alpha##=5mrad.

This will give you two right-angle triangles to work your trig on.

You may be able to make an approximation based on h<<R.

- #3

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AB^2 + R^2 = (R+100)^2

AB = (R+100)sinA

But i can't solve the equation without the calculator.

- #4

HallsofIvy

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Why do you need to solve it without a calculator?

- #5

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Alas, I just remembered small angle approximation.

cosA = 1-(A^2/2)

cosA = R/R+100

R ≈ 8000000

I did not enjoy this problem.

- #6

Simon Bridge

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They get easier.

@hallsofivy: I suspect that it's part of the instructions in the

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