Question

The angle subtended by moon at a point on earth is 0.31’. If the distance of moon
from earth is 
8 3.34 10 m , find the diameter of the moon.

Answer 1

Answer:

3.46 × 10^6 metre

Explanation:

Solution…..here, thita =0 degree 31 minute= 31/60×π/180 radian

r= 3.34×10^8 metre

Diametre of moon, l = D=?

Now we find diametre of moon by this formula

lthita = l/ r

l = r × thita

Here we assume that diametre of moon is equal to L

D=( 3.34×10^8) × 31 / 60 × π / 180

D = 3.46 × 10^6 metre

Answer 2

$The \: formula \: for \: angular \: size \: is:$

$δ = 2 \: arcsim \: ( \frac{d}{2D} )$

$δ \:  is \: the \: angular \: size,  \: d \:  is \: the \: diameter \: of \: the \: object \: (in \: this \: case \: the \: Moon), \: and \:  D \: is \: the \: distance.$

$d=2Dsin( \frac{δ}{2} )$

$We \: know \: that:$

$δ=31′≈0.5167 \: degree$

$D = 3.34 \times {10}^{8}$

$If \: we \: plug \: in \: the \: values:$

$d≈2.334 \times {10}^{8} \times sin( \frac{0.5167 \: degree)}{2}$

$d≈6.68 \times {10}^{8} \times sin(0.2583 \: degree)$

$d≈6.68 \times 10 {}^{8} \times 0.0045$

$d≈3011846 \: m≈3011.846 \: km$

$So, \: the \: diameter \: will \: be \: approximately \: 3000 km.$