Category: Factoid

Factoid Friday – Time Flies

This morning, I awoke to a tweet from astronaut and commander of the International Space Station, Chris Hadfield, saying:

Good Morning, Earth! How did it get to be Friday so soon? Time sure flies at 5 miles per second! (link)

And while I’m sure time does fly while orbiting the Earth 15.7 times a day, there is actually a physical explanation, albeit small, that causes the time on the ISS to slow down: time dilation. So, in my semi-concious stupor, I set about calculating the actual difference in time that Chris Hadfield experiences for his trip on the ISS, and tweeted him back:

@Cmdr_Hadfield At 5 miles per second, your 147 day flight is about 4.5 milliseconds shorter than the time that passes on Earth. (link)

Work

1. The ISS travels at about 5 miles per second (as per Chris’ tweet, the actual value averages 4.7886 miles per second). (cite)

2. Time is dilated when travelling by the gamma factor:

t = \frac{t_0}{\sqrt{1-v^2/c^2}}.

Here, t represents the time passes on Earth, for t_0, the corresponding time that passes on the ISS. So the quantity we are interested in is t - t_0.(cite)

3. Chris Hadfield’s mission on Expedition 35 will last 147 days. (cite)

4. So, plugging in 5 miles per second for ‘v’ (appropriately changed to the same units as ‘c’), and using 147 days for ‘t_0‘ (appropriately changed to seconds), we get:

t = 1.27008000045751×10^7 seconds, or 147 days 0.0045751 seconds. (WolframAlpha)

5. Subtract 147 days, and you’re left with 0.0045751 seconds, or about 4.5 milliseconds. To interpret this as 4.5 milliseconds shorter, we need to remember that the resolution of the Twin Paradox applies the time dilation to the twin that was accelerated, in this case, Chris Hadfield.

This post will invariably attract controversy, so in the interest of staunching the flow of criticisms, please refer to this worked example of time dilation.

Disclaimer

Factoid Fridays are tweet sized factoids with appropriate, but sometimes not peer reviewed, citations. For simplicity, I’ve left out unit conversions (i.e. miles per second to meters per second), so those calculations can be considered an exercise to the reader. If you think there is an error in an assumption or calculation, please contact me.

Factoid Friday – Mosquito Bite

An average mosquito bite takes up 58.6 km of DNA, about 1.5 times the height that Felix Baumgartner fell on his jump from the edge of space.

Work

  1. Mosquitoes take up an average of 5 microlitres of blood per bite. (cite)
  2. About 350 micrograms of DNA can be extracted from 10 ml of blood. (cite)
  3. On average, each DNA base pair (two nucleotides) weighs 615 daltons. (cite)
  4. On average, each DNA base pair contributes 0.34 nanometers to the length of a DNA strand. (cite)
  5. Felix Baumgartner’s free fall was estimated to be 39 kilometres. (cite)

An average mosquito will consume about 5 ul of blood, equivalent to  (5 ul / 10 ml * 350 ug = 0.175 ug) 0.175 ug of DNA. Out of the 0.175 ug of DNA from a mosquito bite, there are (.175 ug / 615 daltons * 1 base pair = 1.714*10^14 base pairs) 1.7*10^14 base pairs of DNA. Each of the DNA base pairs contributes 0.34 nm to the length of a DNA strand, so there are (1.714*10^14 base pairs * 0.34 nm = 58.3 km) 58.3 km worth of DNA in a mosquito bite. Felix Baumgartner fell an estimated 39 kilometres, so the length of DNA in a mosquito bite is (58.3 km / 39 km  = 1.4948 times ) 1.5 times the height that Baumgartner fell. For a quick check of my math, see WolframAlpha. (cite)

Disclaimer

Factoid Fridays are tweet sized factoids with appropriate, but sometimes not peer reviewed, citations. For simplicity, I’ve left out unit conversions (i.e. micrograms to daltons), so those calculations can be considered an exercise to the reader. If you think there is an error in an assumption or calculation, please contact me.