Question

find the distance of moon from earth if the parallax angle as measured from 2 places at a distance of 6.4 × 10 power 6 m on the earth is 57 minutes of an arc.​

Answer 1

The distance of the moon from the earth is 3.9×10^8m.

Given:

The parallax angle as measured from 2 places at a distance of 6.4 × 10 power 6 m on the earth is 57 minutes of an arc.

To Find:

The distance of the moon from earth.

Solution:

To find the distance of the moon from the earth we will follow the following steps:

As we know the relation between arc, parallax angle and the distance of the moon from the earth is given by,

$parallax \: angle(x) = \frac{arc}{radius} = \frac{distance \: on \: earth}{distance \: on \: moon \: and \: earth}$

$Parallax \: angle = \frac{arc}{radius} = \frac{57}{60} \times \frac{\pi}{180} = 0.0165$

57 arc minutes means an arc of 57 in 60 seconds.

π/180 is multiplied to convert degrees into radians.

π = 3.14

Now,

$distance \: on \: moon \: and \: earth \: = \frac{distance \: on \: earth}{parallax \: angle(x)}$

Putting values in the above equation we get,

$distance \: on \: moon \: and \: earth \: = \frac{6.4 \times {10}^{6} }{0.0165} = 3878 \times {10}^{5} m = 3.9 \times {10}^{8} m$

Henceforth, the distance of the moon from the earth is 3.9×10^8m.

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