## Measuring space and time

### From PhysicsEd

Space and time, whether in everyday life or in Special or General Relativity, are described in numbers.

Time is measured in terms of Earth's rotation on its axis, that is how long on average it takes for the Sun to return to the same position east-west in the sky. We divide that day by 24 to get an hour, and the hour by 60 to get a minute, and the minute by 60 to get a second. In physics keeping time precisely requires instruments that measure it to a small fraction of a second. The GPS device in your cell phone or maybe in your car depends on measuring time to within a few billionths of a second! The fundamental unit of a second is the scale by which we measure time in physics and astronomy. Oddly, we use the factors of 60 even though it makes the math hard. Where does that come from? It is perhaps because there are about 360 days in a year that we divide a circle into 360 degrees, and from that choose to measure time in multiples of 60 seconds to get minutes, 60 minutes to get hours, and 24 hours to get a day. Making things more complicated, we will see that time slows down where gravity is stronger, and that it depends on how fast you are moving with respect to the clock you read.

We keep our civil time relative to the Earth's position in space at some instant in the past. You can find a time here on Earth more precisely from the National Institute of Standards in the US that is set by the oscillations of an atomic master clock, but even that is not precise enough for some uses.

What about length or distance, and mass? The English system where a mile is 5,280 feet, a yard 36 inches, a pound 16 ounces, and a gallon 256 Tablespoons, is complicated.

So most of the world except the United States, including physicists, use metric units that for quantities other than time are based on multiples of 10.

 Table￼


A simple exercise:

How many millimeters (mm) are in one kilometer (km) ?

Answer: Since 1000 millimeters (mm) = 1 meter (m), and 1000 meters are in a kilometer (km),

$1000 \times 1000 = 1,000,000 = 10^6$

In this class we will measure distances in meters, but it helps to have a sense of how far that is. A meter is just over one yard, about 40 inches. A kilometer is 1000 meters, about 0.6 miles. Occasionally you will see road signs in kilometers in the US, but elsewhere in the world that's all you will see. How fast is 100 km/hr? Take a look at the speedometer in your car and you'll see the second set of metric numbers on it for most cars now. The speed of 100 km/hr is about 60 miles/hour. The speed of light is about 300,000 = 105 km/s, 3×108 m/s, 186,000 miles/s, or 1 foot per nanosecond (a billionth of a second).

To measure mass, that is how much matter there is in something, we use a kilogram. Near Earth the force of gravity on a kilogram of stuff is about 2.2 pounds. When you go to the grocery and buy 10 lbs of potatoes, you are getting about 5 kg of matter. Because it is easy to do, we usually "weigh" something, that is find the force of gravity on it, to find its mass. However, in physics we measure force in a different unit called a Newton which we will discuss later.