# Time Dilation Math

Praise ye the LORD. Praise God in his sanctuary: praise him in the firmament of his power.

(Psalms 150:1) KJV

We can calculate a distance to the firmament with the question: If GPS clocks are faster by 38,640 ns per day at an orbital radius of 26,541 km, what’s the orbital radius when the clocks are faster by 1,000 years?

At an orbital radius of 26,541 km above the center of the earth time passes faster on GPS satellites by 38,640 nanoseconds per day.

– GPS Time Dilation

The first part of the math is to calculate how many times 38,640 nanoseconds are in 1,000 years to get the factor by which we have to multiply the orbital radius.

#### Convert GPS deviation to seconds

• 38,640 nanoseconds per day
• 1 nanosecond = 1.00E-09 second
• GPS time dilation in seconds = 3.86E-04 seconds

#### Seconds per day

• 60 seconds x 60 minutes x 24 hours = 86,4000 seconds

#### Seconds per 1,000 years (millennium)

• 1,000 years x 365 days = 365,000 days
• 86,400 seconds per day
• Seconds/Millennium = 86,400 x 365,000 = 3.15E+10

#### Orbital radius multiplication factor

• Seconds/Millennium / GPS deviation
• 3.15E+10 / 3.86E-04 = 8.16E+13

#### Orbital Radius (km)

• 26,541.00 x 8.16E+13 = 2.17E+18

#### Orbital radius (AU)

• AU in km = 1.5E+08
• 2.17E+19 / 1.5E+08 = 1.45E+10

#### Orbital radius (light years)

• Light Year in AU = 63241
• 1.45E+10 / 63241 = 2.29E+05

## Table of Calculations

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