Question

Find the distance of moon from earth
if the parallax angle as measured from
2 places at distance of 6.4 x 10^6 m on
earth 57 mins of an are
on​

Answer 1

Answer:

As the distance of star increases, the parallax angle decreases, and great degree of accuracy is required for its measurement. Keeping in view the practical limitation in measuring the parallax angle, the maximum distance of a star we can measure by parallax method is limited to 100 light year.

Answer 2

Answer:

The distance of the moon from the earth is $3.86 \times 10^{8} m$

Explanation:

Given distance between two places on earth,  $b=6.4 \times 10^{6} m$

The parallax angle, $\theta= 57 arc minutes$

In arc seconds, $\theta= \frac{57}{60} arc sec$

The parallax angle in radians, $\theta= \frac{57}{60}\times \frac{\pi }{180} rad$

Parallax angle is given by the ratio of distance between two viewpoints to the distance of the object from th view points, as shown in the figure, i.e., $\theta=\frac{b}{D}$

Therefore, the distance of moon from the earth is

$D=\frac{b}{\theta}$

$=\frac{6.4 \times 10^{6} }{ \frac{57}{60}\times \frac{\pi }{180} }$

$=\frac{6.4 \times 10^{6}\times 60\times 180 }{{57}\times {\pi } }$

$=\frac{6.4 \times 10^{6}\times 60\times 180 }{{57}\times {3.14 } }$

$=\frac{115.2 \times 10^{8} }{29.83 } }$

$=3.86 \times 10^{8} m$

Henceforth, the distance of the moon from the earth is $3.86 \times 10^{8} m$