File:Space is BIG.jpg
Original file (1,420 × 699 pixels, file size: 99 KB, MIME type: image/jpeg)
Calculations
(1) Small-Angle Formula: D = θ d / 206,265 arcseconds, where the number of arcseconds in a circle divided by 2π = 206,265
D = linear size of an object
θ = angular size of the object, in arcseconds
1° = 60 arcminutes = 3600 arcseconds
d = distance to the object
Angular size of a pinhead
θ_Moon = 0.5°, which is roughly the size of a dime held at arm's length:
(2) 0.5° = inverse tangent(x / 36 inches)
x = 0.314 inches
By this equation, we get that the angular size of a pin is:
inverse tangent(0.0590551 inches/36 inches) = θ_pin
- Where a pin head is 1.5 mm = 0.06 in wide
θ_pin = 0.094° = 338 arcsec
Calculate distance for pinhead-sized Death Star
(1) D = (θ_pin * d) / 206,265 arcsec
d = D * 206,265 / θ_pin
d = 120 km * 206,265 / 338 arcsec
d = 73,152 km
Calculate size at Moon's distance from Earth
(1) D = (θ_Death_Star * d) / 206,265 arcsec
θ_Death_Star = D * 206,265 arcsec / d
θ_Death_Star = 120 km * 206,265 arcsec / 385,000 km
θ_Death_Star = 64 arcseconds = 1 arcminute
Calculate distance to appear as large as the Moon
(1) D = (θ_Moon * d) / 206,265 arcsec
d = 120 km * 206,265 arcsec / 1860 arcsec
d = 13,307 km = 8,264 mi, which is roughly the distance of a direct flight from New York to Hyderabad, India.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 15:49, 26 August 2016 | 1,420 × 699 (99 KB) | Kabutton (talk | contribs) |
You cannot overwrite this file.
File usage
The following page uses this file: