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Gravity: the way things fall - acceleration. Dropping cannon balls on different planets.
When you drop something, how does it fall?
Initially it is not moving but it begins to move.
Its speed increases as it falls: it accelerates downward.
Let's get a feel for this gravitational acceleration by watching a demo of objects falling.
(If the drawing canvas does not appear, is really short, or is blank, reload the page.
The drawing canvas can be resized as you please (except on multitouch devices)
by dragging and releasing the magenta drag-handle at the lower right of the canvas; the demo will restart.)
Let's drop some cannon balls off the famous Leaning Tower of Pisa!
Let's drop one cannon ball every second from a height of 50 meters (about 164 feet).
Gravitational acceleration at the Earth's surface is about 9.8 meters per second-squared.
This means that the speed will increase by 9.8 meters per second for every second of fall: constant acceleration.
We can ignore the effect of air resistance; we're dropping cannon balls not feathers!
While the cannon ball is still falling, t seconds after we release it
its instantaneous speed will be 9.8*t meters per second.
Under constant acceleration, its speed increased linearly from zero (at rest) to this value,
so its average speed will have been half as much as the instantaneous speed, or (9.8/2)*t meters per second.
It has fallen for t seconds at average speed (9.8/2)*t meters per second,
so the distance it has fallen is the product of those two values, or (9.8/2)*t2 meters.
Each cannon ball will hit the ground 3.2 seconds after we release it: (9.8/2)*(3.2)2 = 50 meters.
Three other cannon balls will still be falling as we release each new cannon ball every second.
Before it hits the ground, its instantaneous speed is 9.8 meters-per-second-squared times 3.2 seconds = 31 meters per second - pretty fast!
Luckily our simulation doesn't get tired and doesn't run out of cannon balls!
Notice that the distance between two falling cannon balls increases over time (until one hits the ground).
This is because the ball we released first has been falling longer and has acquired more speed
than the one we dropped second: acceleration.
Good, but what about gravity on other planets?
Surface gravity is approximately proportional to a planet's density times its radius.
Mars' density is about 71% of Earth's and its radius is about 53% of Earth's.
Mars' surface gravity is about 3.7 meters per second-squared, or 0.38 times Earth's surface gravity.
We would weigh 38% what we weigh on Earth (ignoring the heavy space suit we would have to wear).
A cannon ball dropped from 50 meters above Mars' surface falls more slowly than on Earth.
Can you see that the cannon ball falls more slowly on Mars than Earth?
t seconds after we release a cannon ball, it will have fallen (3.7/2)*t2 meters on Mars.
Each cannon ball will hit the ground 5.2 seconds after we release it (versus 3.2 seconds for Earth).
Five other cannon balls will still be falling as we release each new cannon ball every second.
Before it hits the ground, its speed is 3.7 meters-per-second-squared times 5.2 seconds = 19 meters per second (versus 31 meters per second for Earth).
Can you see in the demo that the speed hitting the Earth is faster than for Mars?
The distance between successive cannon balls increases faster on Earth than on Mars: can you see this in the demo?
Good, now what about Jupiter?
Gas giant Jupiter's density is about 24% of Earth's and its radius is about 11.2 times Earth's.
Jupiter's surface gravity is about 25 meters per second-squared, or 2.5 times Earth's surface gravity.
A cannon ball dropped from 50 meters higher than Jupiter's "surface" (top cloud layer) falls faster than on Earth.
Each cannon ball will hit the "surface" 2.0 seconds after we release it (versus 3.2 seconds for Earth).
Before it hits the ground, its speed is 25 meters-per-second-squared times 2.0 seconds = 50 meters per second (versus 31 meters per second for Earth).
In the demo, can you see that the gravitational acceleration and speed hitting the ground are higher on Jupiter and less on Mars?
Great, now what about the sun and the moon?
The sun's density is about 26% of Earth's and its radius is about 109 times Earth's.
The surface gravity of the sun is 274 meters per second-squared, or 28 times Earth's.
Our simplified virtual cannon ball falls 50 meters in 0.6 seconds and hits the photosphere at 166 meters per second.
The moon's surface gravity is 1.62 meters per second-squared, or 0.17 times Earth's.
Our cannon ball falls 50 meters in 7.9 seconds and hits the surface at 13 meters per second.
Pluto's surface gravity is 0.66 meters per second-squared, or 0.067 times Earth's.
Our cannon ball falls 50 meters in 12 seconds and hits the surface at 8.1 meters per second.
The dwarf planet (asteroid) Ceres' surface gravity is 0.27 meters per second-squared, or 0.028 times Earth's.
Our cannon ball falls 50 meters in 19 seconds and hits the surface at 5.2 meters per second.
If we were to fall 50 meters on Ceres, we could probably land pretty safely with a little care.
We could jump pretty high there, too!
In the demo, can you see how gravitational acceleration and speed hitting the ground vary from the massive sun to tiny Ceres?
Note that this demo did not indicate the weight (or mass) of the cannon balls.
In the fourth century BC, Aristotle taught that an object falls in proportion to its weight:
the heavier a rock, the sooner it will reach the ground.
For many centuries, this was accepted as true.
It seemed reasonable and logical.
But in the 1600s, Galileo thought about this, conducted experiments, and concluded that differing
weight does not affect how objects fall when we can ignore the effect of air resisting the motion.
Galileo said that a musket ball and a much heavier cannon ball dropped from the same height
would hit the ground at almost exactly the same time.
Let's consider a "thought experiment".
Let's start by assuming that a heavier ball falls faster than a lighter ball
and see where that assumption leads us.
Let's attach the two balls together with a strong but thin and light wire,
then we drop the two balls connected by the wire. How fast will they fall?
If the heavier ball falls faster than the lighter ball,
then the string will let the heavier ball pull the lighter ball to go faster
than if they were disconnected, right?
Or will the lighter ball slow the heavier ball down?
But wait, attaching the two balls together makes the pair heavier than each individually.
Will the pair fall faster than the heavy ball did when disconnected?
This is pretty confusing! What if our assumption was wrong?
If the heavier and lighter balls fall at the same rate,
then they would continue to fall at that rate if they were connected by a strong, thin wire: no contradiction.
That seems to make sense.
Falling due to gravity is independent of the mass of the falling object
when we can ignore the effect of air resisting the motion.
Of course, this demo was simplified, ignoring air resistance/viscosity.
This demo also ignored that Jupiter and the Sun don't have a solid surface
and ignored the sun's radiation and solar wind.
Let me know if the balls dropping in the demo hung, were jerky (except when your PC cpu is heavily loaded), or had incorrect motion.
I hope you found this interesting, useful, and/or fun.
Is there a demo you would like me to add?
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Links for sharing, reporting a problem, or emailing me are available
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Feel free to link to my pages, screencast them to YouTube,
or reuse my source code with attribution