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How fast is 0.0000370 times the speed of light?

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It's about one-and-two-fifths times as fast as The Space Shuttle.
In other words, 0.0000370 times the speed of light is 1.43250 times the speed of The Space Shuttle, and the speed of The Space Shuttle is 0.698080 times that amount.
(Orbiter vehicle velocity)
The space shuttle orbits at a speed of 0.000025830 times the speed of light. During liftoff, the space shuttle accelerates to orbital speed in 8.5 minutes, consuming over 1.59 million kg (3.51 million lbs) of propellant in the process.
It's about one-fourth as fast as a Meteor.
In other words, 0.0000370 times the speed of light is 0.260 times the speed of a Meteor, and the speed of a Meteor is 3.80 times that amount.
(formally Meteoroid or meteorite, depending on the context; a.k.a. "shooting star", a.k.a. "falling star")
Small meteoroids enter the Earth's atmosphere at speeds between 0.0000370 times the speed of light and 0.00024 times the speed of light, depending on their size. The fireball effect, known as ablation, ceases once the atmosphere has slowed the meteoroid to a velocity of about 0.00000930 times the speed of light.
It's about one-tenth as fast as a bolt of Lightning.
In other words, 0.0000370 times the speed of light is 0.110 times the speed of a bolt of Lightning, and the speed of a bolt of Lightning is 9.10 times that amount.
(atmospheric electrical discharge)
A bolt of lightning can travel at up to 0.00032 times the speed of light when arcing from the atmosphere to the Earth. An estimated 280 million lightning strikes strikes occur each year.
It's about twelve times as fast as a Bullet (Rifle).
In other words, 0.0000370 times the speed of light is 12.10 times the speed of a Bullet (Rifle), and the speed of a Bullet (Rifle) is 0.0826 times that amount.
(5.56 x 45 mm, a.k.a. 5.56 NATO)
A 5.56 x 45 mm cartridge is fired at a velocity of 0.000003050 times the speed of light. As the NATO rifle cartridge, it is used by the military forces of more than thirty-one countries, including use in the M16 series, M4 Carbine, HK-416, and M249 Squad automatic weapons used by the United States armed forces.
It's about seventeen times as fast as a Jet Fighter.
In other words, the speed of a Jet Fighter is 0.059 times 0.0000370 times the speed of light.
(for Lockheed Martin F-16, a.k.a. Fighting Falcon, a.k.a. Viper) (maximum speed at altitude)
An F-16's maximum speed at altitude is approximately 0.00000220 times the speed of light. The F-16 has a flight ceiling of approximately 15 km (9.32 mi).
It's about thirty times as fast as a Bullet (Handgun).
In other words, 0.0000370 times the speed of light is 28.90 times the speed of a Bullet (Handgun), and the speed of a Bullet (Handgun) is 0.0346 times that amount.
(for .40 Smith & Wesson 135 grain Sierra JHP, VV 3N37 powder, Fed. 100 primer, Remington case) (muzzle velocity)
A 0.40 caliber Smith & Wesson bullet has a muzzle a velocity of 0.000001280 times the speed of light. This type of ammunition has been the standard issue round of the United States Federal Bureau of Investigation (FBI) since 1990.
It's about thirty times as fast as The Speed of Sound.
In other words, 0.0000370 times the speed of light is 32.30 times the speed of The Speed of Sound, and the speed of The Speed of Sound is 0.031 times that amount.
(in dry air at 20°C)
The speed of sound in dry air at 20°C (68°F) is 0.000001140 times the speed of light. Air is a relatively poor acoustic conductor, however, as sound will travel at speeds of between 0.000004990 times the speed of light to 0.00000520 times the speed of light in water, depending on its salinity.