Gravity!

Sr. Isaac Newton

Tell the story, that Sr. Isaac Newton, while he was hit by an apple falling from its tree he had an epiphany that gave birth to his theory of gravity, and the laws of motion. Well, there’s no solid evidence about this story, although it was well known that Sr. Newton was obsessed with the moon’s motion around Earth, and the effect of a falling apple did put some insight that leads to the discovery of its mathematical model describing how gravity’s influence on an object decreases in an inverse square proportion to the distance to that object. This means that two physical bodies will attract each other with a force that gets stronger the closer they are from each other.

I learned about Sir Isaac Newton in my school years, but I guess in the class you don’t fully appreciate the dimension of his work and in general what these laws represent, and with time this subject is practically forgotten. This is a lost opportunity to learn in a more close and tangible way about the journey that culminated in one of the greatest (if not the greatest), work on physics, Newton’s Principia Mathematica.

It was during this work where Sr. Newton introduced the now well-recognized laws of motion (first law – Law of inertia, second law – Law of motion and third law – Law of reciprocal actions), and the most interesting gravitation law. The commented obsession of Sr. Newton with the moon was based on one question, it is possible that, as the described apple, the Moon is falling as well? To deduce this, he created models that required new mathematics, and to cope with his analysis he had the need to invent a new little mathematical trick called calculus! With it, he did his analysis that confirmed his theory about these laws. Just another day in the office.

When I was introduced to these laws they were explained to me in a theoretical way, and it was fun, but with no much reflection on how they work on us and the objects we see without even notice; the understanding of how all bodies interact, and how all of them attract each other (as the earth attract us, giving us weight), and how orbiting bodies like the Moon are actually in free fall around bigger and more massive bodies as the Earth; this was a revelation. To get this clear, we need to describe how free fall, orbital and escape velocity works, which are the principles used in all space operations by the way.

 A hypothetical example.

Orbital and escape velocity
(http://nasaphysics.cet.edu)

To illustrate this, we can use an analogy of a hypothetical cannon located at a high point on Earth, shooting at the horizon. With these conditions and the cannon power, we will see the cannonball falling in a parabolic trajectory (describing an arc while it ascends and descends), and at certain distances. Now, what will happen if we increase the cannon’s power? we will notice how the cannonball will travel farther and farther over the earth as the cannon power is increased. So, if we keep increasing the cannon’s power there will be a point in which the cannonball will not land on earth, but instead will be spinning around it, where the falling equals the earth’s curvature. This is called orbital velocity. And this is the purpose of the rockets used to put objects in space. This works with artificial satellites and other objects as the International Space Station (ISS); all these bodies are essentially in free fall, going sideways around the earth; and by consequence requiring to move at the extraordinary speed of 27500 Km/h (17,100 miles/h), or about 8 Kilometers per second (5 miles/Sec). Due to this condition the ISS experience 16 sunrises and sunsets every day, or roughly one every 90 minutes, while it travels around our planet.

The same situation is happening with the Moon orbiting around the Earth, and the Earth and the rest of the planets orbiting around the sun; all of them are subject to the same interaction and the condition of “free fall” around the Sun, moving extremely fast and, in a very simplistic description, avoiding to “fall” into the sun’s surface. For Earth, this velocity is 29 Km/Sec. (18 miles/Sec.). And, following this law, you might deduce, the farther you are from the Sun, the slower you can move. In the case of Jupiter moves at an orbital velocity of 13 Km/s (8.1 miles/Sec.), around the Sun, being this part of the reason why Jupiter completes an orbit around the sun in 12 earth years (considering it must cover a wider path as well).

But returning to our hypothetical cannon, what happens if we keep increasing its power? Well, after orbital velocity, the next step is to be able to escape from the earth’s gravity once for all, this is called escape velocity, and it is required to absolutely overcome the Earth’s gravitational influence without requiring further impulse. That’s the speed the Rockets had to reach on the Apollo mission during the sixties and seventies to go to the moon; a speed of 40,000Km/h (25,000miles/h). At this point, the energy due the craft’s motion (or Kinetic energy) equals Earth’s Gravitational Potential.

As the escape velocity depends on the planet’s mass, for Apollo missions that landed on the Moon, the craft to leave the Moon required less energy, as the Moon’s gravity pull is much lower, and is also why Astronauts move in a funny way mostly jumping than walking due their lightness event with all the gear they had. But in the opposite, the escape velocity from Jupiter is over five times higher that Earth’s, as it is much more massive.

So, then?

Considering this information; let’s put the case of Mars; one good reason to visit it, aside from the adventure, is to quickly “lose” weight. Being Mars less massive, a 90Kg (200 lb), a person will shed over half the weight instantly! to merely 34Kg (75 lb). Is Mars lower gravity the reason why there are more dramatic landscapes there as Olympus Mons, a mountain two and a half times taller than Earth’s Mount Everest, and the second biggest peak of the solar system. (Number one is the Rheasilvia Central peak in the asteroid Vesta, by the way)

So, if you’re not happy with your weight, you can argue Earth’s gravity as the responsible, and in a technical way, you will be right!

Regards, Alex – Science Kindle.