Question 9:

(MARTIAN TIME)

Letters with an M in front of it such as My or Md are Martian time, as in Martian Year and Martian Day. Just y and d etc are Earth time.

t = A/T^1 = 2.601973 × 10^10 s

X = 2.601973

T^1 = √(A/B) = 10^3 ms

a. What are the magnitudes of T^-1, T^2 and T^-2?

b. What are the values of A and B?

c. Using A, what are the whole numbers of the Martian years, days, hours, minutes and seconds? (Show the equivalent Earth time).

Answer:

a.

T^-1 = √(B/A) = 10^-3 ks

T^2 = A/B = 10^6 ms²

T^-2 = B/A = 10^-6 ks²

b.

A = tT^1 = X × 10^10 × 10^3 = X × 10^13 ms

B = A/T^2 = X × 10^13 / 10^6 = X × 10^7 ks

To convert the total milliseconds (A) to Martian years (My), Martian days (Md), Martian hours (Mh), Martian minutes (Mm) and Martian seconds (Ms) format we can use the formula below.

Note: 1.88213623601231 and 1.0274912517 are conversion factors, as in 1 Martian Year is 1.88213623601231 Earth Years. 59355048.3388842 is how many seconds in a Martian year and 668.5991 is how many sols (Martian Days) in a Martian year.

Note: we are not using months for this exercise.

Note: a Martian time is given then the equivalent Earth time, and so on.

c.

My – Md/668.5991 = A / (59355048.3388842 × T^1) – Md/668.5991 = 438

y – d/365 = My × 1.8821 – d/365 = 825

Md – Mh/24 = Md/668.5991 × 668.5991 – Mh/24 = 250

d – h/24 = Md × 1.027 – h/24 = 257

Mh – Mm/60 = Mh/24 × 24 – Mm/60 = 6

h – m/60 = Mh × 1.027 – m/60 = 6

Mm – Ms/60 = Mm/60 × 60 – Ms/60 = 45

m – s/60 = Mm × 1.027 – s/60 = 47

Ms – Mcs/100 = Ms/60 × 60 – Mcs/100 = 47

s – cs/100 = Ms × 1.027 – cs/100 = 48

NOTE: obviously we do NOT literally minus the decimal such as d/668.5991 on the calculator, we simply minus the whole number and multiply the decimal by 668.5991, 24 or 60. We do not write or type long numbers. We only have to type the first division below such as My – Md/668.5991 and ‘lift’ the whole number, the rest is done by the calculator.

For example:

Note: you do not need to write the below, it is all done on the calculator.

My – Md/668.5991 = 26019730000000 / (59355048.3388842 × T^1) – Md/668.5991 = 438

y – d/365 = 438.37433762065 × 1.8821 – d/365 = 825

Md – Mh/24 = (438.37433762065 – 438) × 668.5991 – Mh/24 = 250

d – h/24 = 250.28179626251 × 1.027 – h/24 = 257

Mh – Mm/60 = (250.28179626251 – 250) × 24 – Mm/60 = 6

h – m/60 = 6.76311030024476 × 1.027 – m/60 = 6

Mm – Ms/60 = (6.76311030024476 – 6) × 60 – Ms/60 = 45

m – s/60 = 45.7866180146857 × 1.027 – s/60 = 47

Ms – Mcs/100 = (45.7866180146857 – 45) × 60 – Mcs/100 = 47

s – cs/100 = 47.197080881142 × 1.027 – cs/100 = 48

Then insert the whole numbers into the My/Md/Mh/Mm/Ms format:

t = 438 solar years 250 sols 06:45:47

Hand written example: