The Physics of Superheroes: Spectacular Second Edition by James Kakalios Page B

for the gravitational force on Superman are the same thing! Comparing the two expressions for Superman’s weight = (Mass 1) × g and the force of gravity = (Mass 1) × [(G × Mass 2) /(distance) 2 ] , since the forces are the same and Superman’s Mass 1 = 100kg is the same, then the quantities multiplying Mass 1 must be the same; that is, the acceleration due to gravity g is equal to (G × Mass 2)/d 2 . Substituting the mass of the Earth for Mass 2 and the radius of the Earth for d in this expression gives us g = 10 meter/sec 2 = 32 feet/sec 2 .
    The beauty of Newton’s formula for gravity is that it tells us why the acceleration due to gravity has the value it does. For the same object on the surface of the moon, which has both a smaller mass and radius, the acceleration due to gravity is calculated to be only 5.3 feet/sec 2 —about one sixth as large as on Earth.
    This is the true meaning of the story of Isaac Newton and the apple. It certainly wasn’t the case that in 1665 Newton saw an apple fall from a tree and suddenly realized that gravity existed, nor did he see an apple fall and immediately write down F = G (m1 × m2)/ (d) 2 . Rather, Newton’s brilliant insight in the seventeenth century was that the exact same force that pulled the apple toward the Earth pulled the moon toward the Earth, thereby connecting the terrestrial with the celestial. In order for the moon to stay in a circular orbit around the Earth, a force has to pull on it in order to constantly change its direction, keeping it in a closed orbit.
    Remember Newton’s second law of F = ma : If there’s no force, there’s no change in the motion. When you tie a string to a bucket and swing it in a horizontal circle, you must continually pull on the string. If the tension in the string doesn’t change, then the bucket stays in uniform circular motion. The tension in the string is not acting in the direction that the bucket is moving; consequently, it can only change its direction but not its speed. The moment you let go of the string, the bucket will fly away from you.
    Back to the case of the moon. If there were no gravity, no force acting on it, then the moon would travel in a straight line right past the Earth. If there were gravity but the moon were stationary, then it would be pulled down and crash into our planet. The moon’s distance from the Earth and its speed are such that they exactly balance the gravitational pull, so that it remains in a stable circular orbit. The moon does not fly away from us, because it is pulled by the Earth’s gravity, causing it to “fall” toward the Earth, while its speed is great enough to keep the moon from being pulled any closer to us. The same force that causes the moon to “fall” in a circular orbit around the Earth, and causes the Earth to “fall” in an elliptical orbit around the sun, causes the apple to fall toward the Earth from the tree. And that same gravitational force causes Superman to slow in his ascent once he leaps, until he reaches the top of a tall skyscraper. Once we know that in order to make such a powerful leap, his body had to be adapted to an environment where the acceleration due to gravity is fifteen times greater than on Earth, that same gravitational force informs us about Krypton’s geology.
    One consequence of Newton’s law of gravitation—which states that as the distance between two objects increases, the gravitational pull between them becomes weaker by the square of their separation—is that all planets are round. A sphere has a volume that grows with the cube of the radius of the orb, while its surface area increases with the square of the radius. This combination of the square of the radius for the surface area with the inverse square of the gravitational force leads to a sphere being the only stable form that a large gravitational mass can maintain. In fact, to address the astrophysical question of what distinguishes a very large asteroid from a very small