Imagining astronomical quantities
How can we grasp the cosmic dimensions of celestial space at the terrestrial scales of our Earthbound existence?
Let 1 mm represent 1 million km; then 1 m represents 1 billion km. With this length scaling of 1:10¹², the Sun has a diameter of 1.4 mm, making it the size of a grain of sand with a mass of 2 mg, and the Earth has a diameter of 0.013 mm, less than the width of a human hair.
Our scale-model of the Solar System has the following dimensions of distance out from the model Sun:
Imagine – a grain of sand that pulls other matter into its orbit from as far away as 15 km.
An actual grain of sand does indeed have a gravitational pull, following the law of universal gravitation that applies to all objects with mass. The 2-mg grain that models our Sun exerts an acceleration due to its gravity with the same length scaling of 1:10¹², explaining its vanishingly small pull even on adjacent matter, undetectable amongst other forces such as Earth’s gravity.