ok, tarkus, try this...
We know that the Moon and the Sun appear the same relative size from Earth, hence a Solar Eclipse when the Moon passes between the Earth and Sun. So let's test out the trigonometry on that using an online calculator (while using the calculator perhaps you could answer Jason's long standing question...):
SunSize: 1,392,000 km diameter
Distance from Earth: 152,000,000 km (at aphelion)
http://sizecalc.com/#distance=152000000kilometers&physical-size=1392000kilometers&perceived-size-units=degreesApparent size = 0.525 degreesMoonSize: 3474 km diameter
Distance from Earth: 384,400 km
http://sizecalc.com/#distance=384400kilometers&perceived-size=0.517805degrees&physical-size-units=kilometersApparent size = 0.518 degreesThe two numbers match to a hundredth of a degree, so
we have proved that you can measure relative size of astronomical objects using trigonometry, do you agree?
So let's turn to the NASA animation:
MoonSize: 3,474 km diameter
Distance from DSCOVR: 1,520,830 - 384,400 = 1,136,430 km
http://sizecalc.com/#distance=1136430kilometers&physical-size=3474kilometers&perceived-size-units=degrees0.17515 degreesEarthSize: 12,742 km diameter
Distance from DSCOVR: 1,520,830 km
http://sizecalc.com/#distance=1520830kilometers&perceived-size=0.48004degrees&physical-size-units=kilometers0.48004 degreesCompare relative sizes:
Moon/Earth size ratio (using trigonometry) = 0.17515 / 0.48004 = 0.365 =
36.5%Moon/Earth size ratio (pixel sizes from animation) = 164 pixels / 448 pixels = 0.366 =
36.6%Therefore, animation is totally consistent with our calculations. The relative Moon and Earth sizes are exactly what we would expect.
If you want to further prove to yourself that relative size calculations can work at any distance, no matter whether close or astronomical then let's link those two items up.
All you need to do is go outside with a 67mm tennis ball (or other similar sized spherical object). Place it on a fence post or table edge, and then step back 7.4 metres. My crystal ball predicts that if you line up the tennis ball with the Moon you will get a Tennis Eclipse...
(Here's the crystal ball by the way:
http://sizecalc.com/#physical-size=67millimeters&perceived-size=0.518degrees&distance-units=meters)
Move further back and Moon will become visible from behind the tennis ball (and thus LARGER in relative terms compared to the tennis ball). Move further forward and Moon will be totally hidden by the tennis ball (and the Moon will become smaller in comparison to the tennis ball).
After doing this please come back and confirm that you now understand how distance from observer determines relative object sizes and that it applies at all distances, and that the NASA animation is totally correct.