# What is the angular diameter of the earth viewed from the moon? What about the earth viewed from the sun?

Apr 24, 2016

From Moon at 384000 km from the Earth,, Earth's angular diameter is ${2.02}^{o}$, nearly. From the Sun at 1 AU from the Earth, it is 17.7", nearly.

#### Explanation:

Let P be the point of contact of the tangent from an observer O on Moon's surface to the Earth centered at E and $\alpha$ be the Earth's angular diameter,

In $\triangle E P O$, right angled at P, OE = 384000-1737= 382263 km, EP = radius of the Earth = 6738 km and

sin $\frac{\alpha}{2}$= (EP)(/EO)=6738/382263=0.01763.

$\alpha = {2.02}^{o}$, nearly.
Really, this is angular chord. The length of the contact chord is little short of Earth's diameter. So, the angular diameter is a little more than ${2.02}^{o}$..

From the Sun instead, EO = 149597871-696342 = 148901529 and
sin (alpha/2) = (EP)/(EO) = 6378/148901529 = 0.0000428

$\alpha = {0.00491}^{o} = 17.7$".. .