# Question 5: Forward.

Question 5:

(FORWARD)

t = A/T^1 = 3.66519142918809 × 10^7 s

X = 3.66519142918809

T^2 = A/B = 10^18 ns²

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

b. What are the values of A and B?

c. Using B, what are the whole numbers of the years, days, hours, minutes and seconds?

d. Check that the remainder months add up to the remainder days.

a.

T^1 = √(A/B) = 10^9 ns

T^-1 = √(B/A) = 10^-9 Gs

T^-2 = B/A = 10^-18 Gs²

b.

A = tT^1 = X × 10^7 × 10^9 = X × 10^16 ns

B = A/T^2 = X × 10^16 / 10^18 = X × 10^-2 Gs

To convert the total gigaseconds (B) to years (y), months (M), days (d), hours (h), minutes (m) and seconds (s) format we can use the formula below.

Because there is no obvious consensus on precisely how many days are in month, that is 28 – 31, therefore, when we are using months, in order to get the months and days to match and corroborate we must state that we are using 31 days in a month, therefore, we are using conversion factor of 365/31 months in a year. However, you could use a different whole number (a number without a decimal) for the conversion factor (or the amount of days in a month) such as 365/30 = 73/6.

c.

y – M/(365/31) = B / (31536000 × T^-1) – M/(365/31) = 1

M – d/31 = M/(365/31) × (365/31) – d/31 = 1

d – h/24 = d/31 × 31 – h/24 = 28

h – m/60 = h/24 × 24 – m/60 = 5

m – s/60 = m/60 × 60 – s/60 = 5

s – cs/100 = s/60 × 60 – cs/100 = 14

NOTE: obviously we do NOT literally minus the decimal such as s/60 on the calculator, we simply minus the whole number and multiply the decimal by (365/31), 31, 24 or 60. We do not write or type long numbers. We only have to type the first division below such as y – M/(365/31) 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.

y – M/(365/31) = 0.03665191429188 / (31536000 × T^-1) – M/(365/31) = 1

M – d/31 = (1.16222457800231 -1) × (364/31) – d/31 = 1

d – h/24 = (1.91006357970465 – 1) × 31 – h/24 = 28

h – m/60 = (28.211970970844 – 28) × 24 – m/60 = 5

m – s/60 = (5.08730330025062 -5) × 60 – s/60 = 5

s – cs/100 = (5.23819801503748 – 5) × 60 – cs/100 = 14

Then insert the whole numbers into the y/M/d/h/m/s format:

t = 1 year 1 month 28 days 05:05:14

d.

y – d/365 = B / (31536000 × T^-1) – d/365 = 1

d – h/24 = d/365 × 365 – h/24 = 59

h – m/60 = h/24 × 24 – m/60 = 5

m – s/60 = m/60 × 60 – s/60 = 5

s – cs/100 = s/60 × 60 – cs/100 = 14

For example:

d = m × 31 + d

d = 1 × 31 + 28 = 59

NOTE: obviously we do NOT literally minus the decimal such as s/60 on the calculator, we simply minus the whole number and multiply the decimal by (365/31), 31, 24 or 60. We do not write or type long numbers. We only have to type the first division below such as y – M/(365/31) 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.

y – d/365= 0.03665191429188 / (31536000 × T^-1) – d/365 = 1

d – h/24 = (1.16222457800231 – 1) × 365 – h/24 = 59

h – m/60 = (59.2119709708438 – 59) × 24 – m/60 = 5

m – s/60 = (5.08730330025054 -5) × 60 – s/60 = 5

s – cs/100 = (5.23819801503237 – 5) × 60 – cs/100 = 14

Then insert the whole numbers into the y/d/h/m/s format:

t = 1 year 59 days 05:05:14

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