In this brand-spanking new ‘Under The Radar’ series I will be focusing on specific topics of interest and wonder in science and stripping them down to make sense of them. I’ll be examining difficult but important phenomena in our mysterious but marvellous world and I’ll be giving my all to try and simplify mind-bending concepts so that everyone can appreciate it’s glory and beauty.
First up it’s gravity. As explained in in my previous post (which I strongly suggest you read) https://therealdegree.wordpress.com/2012/07/26/the-badasses-of-science-issac-newton/ Newton was the first person to give a definitive definition of the concept of gravity and explain it in a mathematical format. This revelation allowed people to make sense of the natural world around them and for the best part of 200 years Newton’s theory of gravity was the best and the most widely accepted.
It basically set forth the idea that gravity was a predictable force that acts on all matter in the universe, and is a function of both mass and distance. The theory states that each particle of matter attracts every other particle (for instance, the particles of “Earth” and the particles of “you”) with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
So the farther apart the particles are, and/or the less massive the particles, the less the gravitational force. The standard formula for the law of gravitation for measuring the gravitational force in Newtons is:
Where F is the gravitational force.
G = Universal Gravitational Constant* = 6.6726 x 10-11N-m2/kg2
m1 = Mass of Object 1
m2 = Mass of Object 2
r = Distance Between the Objects.
So what does the standard formula tell us?
This equation gives us the size of the force, which is an attractive force and therefore always directed toward the particles in the other mass . If you remember Newton’s Third Law of Motion, this force is always equal and opposite.
Despite two different objects having different mass and sizes, they pull on each other with equivalent force. Newton’s Three Laws of Motion give us the tools to interpret the motion caused by the force and we see that the particle with less mass (which may or may not be the smaller particle, depending upon their densities) will accelerate more than the other particle. The same gravitational force acts on the two objects but because one of them has less mass, the effect is more noticeable on the smaller object. This is why light objects fall to the Earth considerably faster than heavier objects fall. Still, the force acting on the light object and the heavier object is identical in size (magnitude), even though it doesn’t look that way. Gravity doesn’t just apply to objects on Earth. It’s a comprehensive force that applies everywhere in the universe, in fact, gravity emerged just ten-millionth of a trillionth of a trillionth of a trillionth of a second after the big bang. So, it’s one of the earliest things in existence and what’s more, it played a huge role in our existence.
Gravity is universal and acceleration due to gravity on Earth, is 9.8 m/s² — it never changes, regardless of an object’s mass.
It is also significant to note that the force is inversely proportional to the square of the distance between the objects. As objects get further apart, the force of gravity drops very quickly. At most distances, only objects with very high masses such as planets, stars, galaxies, and black holes have any significant gravity effects.
Here’s a physics question about the gravitational formula:
Determine the force of gravitational attraction between the earth 5.98 x 1024 kg and a 70 kg boy who is standing at sea level, a distance of 6.38 x 106 m from earth’s center.
We know m1 = 5.98 x 1024 kg m2 = 70 kg r = 6.38 x 106 m G = 6.6726 x 10-11N-m2/kg2
The gravitational constant is just that- constant, it’s always the same. On Earth anyway.
Substitute the values in the below Gravitational Force formula:
And Volia! You now know the gravitational force acting on the two objects. Pretty neat huh?
Of course, this is algebra and in algebra you can manipulate a formula to find different values. To find the mass of the first object you:
To find the mass of the second object you:
And Finally, to find the distance between the two objects you:
That my amigos is Newton’s theory of gravity. It’s proved popular among scientists and it’s stood unchallenged. For hundreds of years, Newton’s theory of gravity pretty much stood alone in the scientific community. That changed in the early 1900s. When a certain German scientist came along.
Albert Einstein, who won the Nobel Prize in Physics in 1921, contributed an alternate theory of gravity in the early 1900s. It was part of his famous General Theory of Relativity, and it offered a very different explanation from Newton’s Law of Universal Gravitation. To avoid over complicating things, the most challenging of all Einstein’s concepts is the idea that time is a part of space. Out instinct is to believe that nothing can disturb it’s steady tick. In fact, according to Einstein, time is variable and ever-changing. It even has a shape.
Einstein called this ‘spacetime’. Spacetime is usually explained by asking you to imagine something flat but soft and bendy like a mattress where a heavy round object like an iron ball is resting. The weight of the iron ball causes the material on which it is sitting to stretch and sag slightly. This is similar to the effect that a massive object such as the Earth (Iron ball) has on spacetime (mattress). It stretches and curves and warps it. Now if you roll a smaller ball (the satellite in the picture) across the ‘mattress’ (spacetime), it will try to go in a straight line, but as it nears the Earth, it rolls downwards, drawn to the massive object. This is Gravity- a product of the bending on spacetime.
I won’t go over the complicated maths related to this subject because I hardly understand it myself but I hope you have a good general understanding of gravity. And if you don’t, the next time someone says ‘space-time continuum’ on sci-fi shows, at least you’ll know what they’re talking about. 😀
*The gravitational constant, called G in physics equations, is an empirical physical constant. It is used to show the force between two objects caused by gravity. The gravitational constant appears in Newton’s universal law of gravitation.