G-ravity is Universal
That capital (big) G is the physics symbol for an amazing number. Which we will soon come back to. But for now, it’s close cousin, little g, is what we are looking at.
That g is the ‘acceleration due to gravity g = 9.807 m/s2 (meters per second squared; which might be thought of as “meters per second, per second”)…’ source quote for that is here. That’s the value at the Earth’s surface. In other words, it’s how quickly gravity accelerates an object when you drop it.
When you do drop something, it’s quite easy to work out how far it falls in a given time (t), or how long it takes to fall a specific distance (d):
Of course, this is ignoring air resistance.
Also, as an important aside: you may have spotted something missing from those simple equations. Mass. The mass of the object – in kg – is NOT needed here. All things fall at the same rate, assuming no air resistance. Even a feather and a hammer. (That video is still quite gobsmacking no matter how many times I see it. The Moon has no air, so no air resistance)
OK, the value of (little) g is different on different planets etc. We turn to Newton to work out this value for Earth, Mars etc. Never forget Newton was working on this gravity stuff in the 1680s (!), including the maths.
Again the formula is quite basic:
- G is a constant (more next)
- M is the Mass of the planet etc (in Kg)
- r is the Radius of the planet (in Metres)
That G constant is fascinating. As far as we know it is fixed throughout the entire Universe and has the value: 6.674×10−11. As a reminder 103 is a 1 followed by 3 zeroes (1000). 10-3 is 0.01.
When I say ‘the entire Universe’ I mean for black holes too:
It’s easy to locate the Radius and Mass of assorted objects and drop them into Excel to hopefully get the correct values for g:
Here are the Excel calculations done:
We will return to this calculation in another post quite soon. Where we’ll re-do it for an asteroid, then use that g for further calculations.
Extra 1: The Units of G
I gave the value of G but not the units it’s measured in. The full value is 6.674×10−11 m3⋅kg−1⋅s−2
If you look back at the formula for g (above) and plug in the values and their units (m, kg, s etc), you see the units of g partially cancel each other out and boil down to m/s2 (aka those for acceleration. Again: phew)
Extra 2: Galileo’s Leaning Tower of Pisa experiment
Wikipedia says it well, so here it is:
Between 1589 and 1592, the Italian scientist Galileo Galilei (then professor of mathematics at the University of Pisa) is said to have dropped two spheres of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass, according to a biography by Galileo’s pupil Vincenzo Viviani, composed in 1654 and published in 1717.
According to the story, Galileo discovered through this experiment that the objects fell with the same acceleration, proving his prediction true, while at the same time disproving Aristotle’s theory of gravity (which states that objects fall at speed proportional to their mass). Most historians consider it to have been a thought experiment rather than a physical test.
