Will there be a last man on the moon?

I was born in 1990. Mankind first stepped on the moon on July 20th 1969. We did it again in November of the same year, again in February and July of 1971, and in April and December of the following year.

In total there have been 12 men to have set foot on another celestial body. I have never known a day where I have not been sharing the Earth with a lunar astronaut. But today 8 of those 12 heroes have passed away. The 4 remaining, Buzz Aldrin, David Scott, Charles Duke and Harrison Schmitt are aged 89, 87, 83 and 84 respectively.

We haven’t been back to the moon since 1972. NASA have a target to get another human there with the Artemis mission by 2024, but is this already too late?

So my question to you is Is it likely that we will see another human on the moon before all our lunar astronauts go extinct? or will it soon be the day of the last man on the moon?

We can use statistics to help us infer the odds.

Firstly let’s take mortality predictions from the US social security actuarial life table of 2016.

data = read.table('life_exp.txt',header=TRUE)

You can download the data here.

Next we calculate the probability that an astronaut will die within n years, given their age. This is given by,

P(death in N years | current age) =
P(death in year N | age in year N) \times P(alive in year N-1 | current age) + P(death in year N-1 | current age)

pdeadn = function(startyr = 2019, endyr = 2020, birthyr){
  age = startyr - birthyr
  nyrs = endyr-startyr+1 #add one because you count the first year as 2016
  cat('number of years:', nyrs, '\n')
  
  pdead=c()
  pdead[1] = data$pdeath_male[which(data$age == age)]
  for(i in 2:nyrs){
    age = age+1
    pdead[i] = (1.0 - pdead[i - 1])*data$pdeath_male[which(data$age == age)] + pdead[i-1]
  }
  
  cat('final age:', age,'\n')
  return(pdead)
}

We apply this to our 4 alive astronauts, who were born in 1930, 1932, 1936 and 1935, to get the probability of their deaths up until 2040.

startyr = 2019 #start at current year since we know they are alive
endyr   = 2040
birthyr = c(1930, 1932, 1936, 1935)
pdead   = sapply(birthyr, function(x) pdeadn(startyr=startyr, endyr=endyr, birthyr=x)) #probability of death

Assuming that the deaths of any of the astronauts are independent events, the probability that all the lunar astronauts are dead is given by the multiplication rule,

P(all astronauts dead) = P(Aldrin dead) \times P(Scott dead) \times P(Duke dead) \times P(Schmitt dead)

Applying this we can obtain the following plot of the probability that all astronauts are dead as a function of time,

yrs      = seq(2019, 2040)
pdeadall = apply(pdead, 1, prod)
plot(yrs, pdeadall, ty = 'l', tck = 0.02, xlab = 'year', ylab = 'P(all lunar astronauts dead)', xlim = c(2019, 2040))
axis(side = 3, tck = 0.02, labels = FALSE)
axis(side = 4, tck = 0.02, labels = FALSE)
abline(v = 2024, lty = 'dashed', col = 'orange', lwd = 3)

0000d7

The orange line shows the goal launch date of NASA’s Artemis program to get the first woman and next man on the moon. From this we can see that there is a 12% probability that all the Apollo Astronauts will not see the next landing on the moon. However, experience shows that space launches are never delivered on time. The following plot shows the predicted launch date of NASA’s Hubble Space Telescope as a function of time.

hubble_launch_date

Hubble launched in 1990, 2.3 times the original scheduled launch time. If the Artemis program faces similar delays, we won’t see a moon landing until 2031, by which case the probability that we will go back on progress, and that I will see a day where no man has stepped on the moon will have increased to 78%, and by 2034 (the set goal of the Chinese to land on the moon) almost certainly (93%) this will be the case 😦

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