There are a few different ways you can keep time:
Use the rotation of the Earth. This is a sundial or measuring the position of the stars to track the passage of time. Due to natural variations in the Earth’s orbit, this method is not super accurate, and varies widely over the year and across different latitudes.
Similarly, you could use the orbit of the Moon, however that requires the Moon be visible in the sky, and generally is very hard to get precision closer than a day, and, without telescopes, closer than around a week.
Another option is to use the burn rate of a candle, incense, or similar objects. The accuracy of this depends on how perfectly you can make the devices. The more variation you have, the less accuracy you get.
You can measure the rate at which objects are fall through a hole. The two most common methods here are sand hourglasses and water clocks.
The other major version of a gravitation clock is a to use a pendulum, such as in a grandfather’s clock. This works as it turns out that a pendulum swings with a consistent period based on its length, so you can measure the swings to track time. This was later improved by using electromagnet to help keep the pendulum swinging and also to track the swings better.
Much more recently, it was discovered that a quartz crystal will vibrate at a specific frequency when an electric current is applied. Measuring these vibrations allow for fairly accurate timekeeping, so long as you can apply electricity. This method is much better than prior methods as it doesn’t require any large moving parts and isn’t suspectable to most motion. Overall, this is probably the most common time keeping method used today, found in almost all watches, computers, and clocks. Even if other methods could be used, these devices will normally use a quartz oscillator for some internal timekeeping, such as a computer’s clock cycle.
Even more recently, only discovered in 1879 and starting widespread usage in the 1960s, are atomic clocks. This uses caesium-133 which happens to have an atomic transition between energy states at an extremely accurate frequency when exposed to microwave radiation and can be easily measured. A full scale atomic clock measures time to a precision of 9 billionths of a second and an accuracy of about 15 decimal points, many orders of magnitude better than quartz crystal clocks.
From those, there are a few derived methods. That is, these methods only work *because* one of the previous methods was used, typically a quartz crystal or atomic clock:
The electric grid uses AC power that cycles back and forth in flow direction on a regular basis. Most of the world uses either 50hz or 60hz AC. The precision of this depends on how well the electric grid maintains its power load and supply, though in most developed nations, it will be within a few cycles per day on average.
Many major nations broadcast a radio signal that specifies the exact time according to their standard on a regular basis. In the US, this occurs at least every second using the official atomic clock. Any device can listen for this signal to detect the current time, and is how many self-setting clocks work. If you need more precision than the second, you need to use a local version, such as a quartz crystal, and adjust your tracking when you get the signal.
GPS, and similar systems, work by broadcasting the time, based on an atomic clock on the satellite, and a satellite identifier. As such, you can listen for the GPS signal to grab the time to an extremely high precision, but, again, only with intermittent data, around a second. Tracking at higher precision requires a local time keeping that gets adjusted. Due to the prevalence of GPS systems, this has started to heavily take over from the dedicated radio signal for self-setting clocks.
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