of the Moon is between 29′20″ and 34′6″. The fact that the intervals overlap (the former interval is contained in the latter) is a coincidence, and has implications for the types of solar eclipses that can be observed from Earth. Gravitational acceleration While not constant but varying depending on latitude and altitude, the numerical value of the acceleration caused by Earth's gravity on the surface lies between 9.74 and 9.87 m/s2, which is quite close to 10. This means that as a result of Newton's second law, the weight of a kilogram of mass on Earth's surface corresponds roughly to 10 newtons of force exerted on an object. This is related to the aforementioned coincidence that the square of pi is close to 10. One of the early definitions of the meter was the length of a pendulum whose half swing had a period equal to one second. Since the period of the full swing of a pendulum is approximated by the equation below, algebra shows that if this definition was maintained, gravitational acceleration measured in meters per second per second would be exactly equal to π2. The upper limit of gravity on Earth's surface (9.87 m/s2) is equal to π2 m/s2 to four significant figures. It is approximately 0.6% greater than standard gravity (9.80665 m/s2). Rydberg constant The Rydberg constant, when multiplied by the speed of light and expressed as a frequency, is close to : This is also approximately the ratio between one meter and one foot: 1 m/ft = 1m/(0.3048m). US customary to metric conversions As discovered by Randall Munroe, a cubic mile is close to cubic kilometers (within 0.5%). This means that a sphere with radius n kilometers has almost exactly the same volume as a cube with sides length n miles. The ratio of a mile to a kilometre is approximately the Golden ratio. As a consequence, a Fibonacci number of miles is approximately the next Fibonacci number of kilometres. The ratio of a mile to a kilometre is also very close to (within 0.006%). That is, where m is the number of miles, k is the number of kilometres and e is Euler's number. A density of one ounce per cubic foot is very close to one kilogram per cubic metre: 1 oz/ft3 = 1 oz × 0.028349523125 kg/oz / (1 ft × 0.3048 m/ft)3 ≈ 1.0012 kg/m3. The ratio between one troy ounce