Question

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

Answer 1

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 EPO`, right angled at P, OE = 384000-1737= 382263 km, EP = radius of the Earth = 6738 km and

sin `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`".. .