Difference between revisions of "File:Space is BIG.jpg"
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=Calculations= | |||
(1) Small-Angle Formula: | |||
D = θ d / 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: | |||
(3) inverse tangent(0.0590551 inches/36 inches) = θ_pin | |||
θ_pin = 0.094° = 338 arcsec | |||
---- | |||
==Calculate distance for pinhead-sized Death Star== | |||
(1) D = (θ_pin * d) / 206,265 | |||
d = D * 206,265 / θ_pin | |||
d = 120 km*206,265/338 | |||
d = 73,152 km | |||
---- | |||
==Calculate size at Moon's distance from Earth== | |||
(1) D = (θ_Death_Star * d) / 206,265 | |||
θ_Death_Star = D * 206,265 / d | |||
θ_Death_Star = 120 km * 206,265 / 385,000 km | |||
θ_Death_Star = 64 arcseconds = 1 arcminute |
Revision as of 15:36, 26 August 2016
Calculations
(1) Small-Angle Formula: D = θ d / 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:
(3) inverse tangent(0.0590551 inches/36 inches) = θ_pin
θ_pin = 0.094° = 338 arcsec
Calculate distance for pinhead-sized Death Star
(1) D = (θ_pin * d) / 206,265
d = D * 206,265 / θ_pin
d = 120 km*206,265/338
d = 73,152 km
Calculate size at Moon's distance from Earth
(1) D = (θ_Death_Star * d) / 206,265
θ_Death_Star = D * 206,265 / d
θ_Death_Star = 120 km * 206,265 / 385,000 km
θ_Death_Star = 64 arcseconds = 1 arcminute
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 15:49, 26 August 2016 | 1,420 × 699 (99 KB) | Kabutton (talk | contribs) |
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