The Earth and Moon are separated by about 4.0 10^6 m. Suppose Mars is [{MathJax fullWidth='false' 2.9 \times 10^{11} }] m from Earth and forms a right triangle with Earth and the Moon. Assume a pupil diameter of 6 mm and the wavelength is 550 nm. Determine the following. a. angular separation of Earth and Moon as seen from Mars b. angular resolution of the eye c. Could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope?

a) α=7.9x10^-4 rad

b) θ=1.12x10^-4 rad

c) The Earth and the Moon cannot be seen without a telescope.

Explanation:

In this exercise we will use the concepts of angular resolution, which depends on both the wavelength of the rays and the diameter of the eye or lens on the meter. Its unit of measure is the radian. The attached image shows the solution step by step.

fgravity=10x10=100n case 1

fgravity=30x20=600n case 2

6 times more

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