Difference between revisions of "File:Space is BIG.jpg"
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By this equation, we get that the angular size of a pin is: | By this equation, we get that the angular size of a pin is: | ||
inverse tangent(0.0590551 inches/36 inches) = | inverse tangent(0.0590551 inches / 36 inches) = θ<sub>pin</sub> | ||
:Where a pin head is 1.5 mm = 0.06 in wide | :Where a pin head is 1.5 mm = 0.06 in. wide | ||
θ_pin = 0.094° = 338 arcsec | θ_pin = 0.094° = 338 arcsec | ||
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==Calculate distance for pinhead-sized Death Star== | ==Calculate distance for pinhead-sized Death Star== | ||
(1) D = ( | (1) D = (θ<sub>pin</sub> * d) / 206,265 arcsec | ||
d = D * 206,265 / | d = D * 206,265 / θ<sub>pin</sub> | ||
d = 120 km * 206,265 / 338 arcsec | d = 120 km * 206,265 / 338 arcsec | ||
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==Calculate size at Moon's distance from Earth== | ==Calculate size at Moon's distance from Earth== | ||
(1) D = ( | (1) D = (θ<sub>Death Star</sub> x d) / 206,265 arcsec | ||
θ<sub>Death Star</sub> = D x 206,265 arcsec / d | |||
θ<sub>Death Star</sub> = 120 km x 206,265 arcsec / 385,000 km | |||
θ<sub>Death Star</sub> = 64 arcseconds = 1 arcminute | |||
---- | ---- | ||
==Calculate distance to appear as large as the Moon== | ==Calculate distance to appear as large as the Moon== | ||
(1) D = ( | (1) D = (θ<sub>Moon</sub> x d) / 206,265 arcsec | ||
d = 120 km * 206,265 arcsec / 1860 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. | d = 13,307 km = 8,264 mi, which is roughly the distance of a direct flight from New York to Hyderabad, India. | ||
Revision as of 01:03, 24 September 2016
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) = θpin
- 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 = (θpin * d) / 206,265 arcsec
d = D * 206,265 / θpin
d = 120 km * 206,265 / 338 arcsec
d = 73,152 km
Calculate size at Moon's distance from Earth
(1) D = (θDeath Star x d) / 206,265 arcsec
θDeath Star = D x 206,265 arcsec / d
θDeath Star = 120 km x 206,265 arcsec / 385,000 km
θDeath Star = 64 arcseconds = 1 arcminute
Calculate distance to appear as large as the Moon
(1) D = (θMoon x 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
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:49, 26 August 2016 |  | 1,420 × 699 (99 KB) | Kabutton (talk | contribs) |
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