Why don’t we fly off the Earth into space?

Our Earth is a planet (one of eight in our Solar System) circulating our Sun (a star). We are standing on the densest of the eight planets, meaning the Earth has the greatest mass per unit volume of any planet. At its core, the Earth is about 89% iron. That much iron in this big a planet produces a bunch of gravitational force. It is that gravitational force attracting us to the Earth’s core that causes us to stick to the surface. So, the simple answer is: We don’t fly into space because the attractive force of gravity won’t let us?

What is gravity?

I thought you might ask that. To understand gravity, we have to go back to a fellow by the name of Isaac Newton who lived in England, was born on Christmas Day 1642 and liked to observe apples. One day, Isaac watched one fall from an apple tree in the garden. He wondered why that apple fell directly down, perpendicular to the ground, as if it were headed to the center of the Earth. Newton was a focused lad and that apple’s descent really got to him. On July 5, 1687, Isaac Newton published, in three volumes, his “Mathematical Principles of Natural Philosophy,” referred to as the “Principia” and considered by many to be one of the most important books ever written. Included in this revered tome is Newton’s Law of Universal Gravitation, “gravity” for short. According to Newton, gravity is the force that attracts a point mass (the Earth) to another point mass (me standing on the Earth), and it does this attracting by an amount of energy (or directional force) proportional to the product of the two masses and inversely proportional to the square of the distance between them. Isaac’s equation can be presented like this:

F=G(m1m2/rr)

In this formula, F is the measure of the gravitational and directional attractive force between the two objects (the bigger mass pulling the small mass toward itself), G is the gravitational constant (a fixed and experimentally verified fudge-factor number that makes the equation work), m1 is the first mass (the Earth), m2 is the second mass (me) and r is the distance between me and the center of the Earth. Put them all together, stir briskly and you find that there is a very strong gravitational force (F) pulling me toward the center of the Earth and holding me on the surface of our planet because I can’t move through dirt and rock.

How much gravitational force is holding you down?

Trick question – I like it. To do the exact calculation of gravitational force (F) for me where I am sitting typing right now, to the center of the Earth, would require me to know how far that is, plus my mass and the mass of the planet and the big G (gravitational constant), and then to do a bunch of number crunching, making sure I got the units right. That would be a lot of work. But, there’s a short cut – that’s the “trick” part of your question.

Okay, smartie, what’s the short cut?

Me. How much I weigh. My weight is what’s holding me down. Take away my weight, make me lighter that a feather, and I’d float away like Dorothy and Toto to “somewhere over the rainbow . . . where troubles melt like lemon drops.” So, for a small object (me) relative to a very large object (the Earth), the Newtonian equation can be simplified to calculate a gravitational field vector (g) pulling on me. This little “g” has been determined to be about 9.8 meters per second square, on average, for everywhere on the surface of the Earth. Now, the longer equation of Sir Isaac (they made him a Knight) can be tweaked and simplified to F=mg, where m is my mass and g is the 9.8 number. But wait, W=mg, where W is my weight. The equations are the same. So, for me right here, the gravity equation can be simplified to F=W. It’s true. My weight is a close approximation of the force of gravity on me right here, right now, today.

What if you wanted to lose weight?

I’d go to Mars.

Why?

Mars is a smaller and less dense planet. When you do the equations with the smaller mass of the planet Mars, I’d tip the bathroom scale at a much lower number. Drop me on Mars with my Earth muscles and I’d be able to jump higher and lift more than any old Martian. I’d be a Superman – assuming they had some air to breathe. There may be some downsides.

Maybe you should stay here, eat less and exercise more?

I guess you’re right, but it still sounds like fun, going to Mars. I can see myself now in the Martian Olympics, getting ready for the long jump. I get set, the gun fires, I sprint to the line, jump into the air, stretch my legs, arms flailing. It’s . . .

. . . time for lunch. Can you help in the kitchen? You only get a half sandwich.

I wonder if Sir Isaac was treated like this?

You’re not a Knight yet.

Details,

Grandpa Jim