[time-nuts] Re: gravity fields affect time keeping?

[Tom Van Baak]

Kevin,

That moon link is making the rounds through the 'net. It's an 
interesting topic what to do with SI units and UTC timekeeping for Mars 
and Moon.

 > I’m curious about what type of clocks are affected by local gravity, 
and how much.

1. The obvious example is pendulum clocks since they are directly 
related to g. Period T = 2pi sqrt(L/g) so a 1 ppm change in g is a 5e-7 
change in frequency. This is why you have to recalibrate a good pendulum 
clock if you move it up or down a few floors (g depends on elevation). 
The same is true if you move it north or south (g depends on latitude). 
The very best pendulum clocks are also affected by tides (local g 
changes due to sun and moon).

2. OCXO are also sensitive to acceleration, including g, the 
acceleration of gravity. Check the 2g-turnover spec on the datasheet. 
It's not uncommon to see 1e-10 or 1e-9, which means its frequency 
changes by 1 ppb if you rotate (literally, turn over) the oscillator. 
This is why you want to place your best quartz frequency standards on a 
very solid table or rack or floor, without vibration, and especially do 
not tilt them, not even by a millimeter.

3. The best atomic clocks and all optical clocks are good enough that 
relativistic effects appear (both velocity and gravity). The frequency 
changes by 1.1e-16 per meter change in elevation. This is why you can 
demonstrate gravitational time dilation using portable cesium clocks and 
a mountain. Go up one km, stay for a day, and the clock comes back 10 ns 
ahead (older) compared to the clock you left at home.

 > Clocks on Earth and the Moon naturally tick at different speeds

The UTC timescale is based on the SI second defined at sea level on 
planet earth. Cesium clocks tick at a different rate depending on the 
mass and radius of the planet. So compared to a clock freely floating in 
space far far away from any mass, a clock at the surface of the earth 
runs 6.95e-10 slower, which is about 60 us per day, and a clock on the 
surface of the moon runs 3.13e-11 slower, which is about 2.7 us/day. The 
difference is about 57 us/day, as the article mentions.

/tvb


On 1/30/2023 12:34 PM, Kevin Rowett via time-nuts wrote:

>  From an article about moon time keeping:https://www.nature.com/articles/d41586-023-00185-z <https://www.nature.com/articles/d41586-023-00185-z>
>
> The author says
>
>
> “...Clocks on Earth and the Moon naturally tick at different speeds, because of the differing gravitational fields of the two bodies. …”
>
> I’m curious about what type of clocks are affected by local gravity, and how much.
>
> Anyone familiar enough to go into detail?
>
> KR
>