How You'd Fall from Space on Solar System Planets?
Have you ever seen a fruit or object fall from a tree? Have you ever tried to throw
a stone by observing how it falls to the ground? This force that "pushes" things down is called
the force of gravity. We are constantly drawn toward the Earth by
its gravitational force. That is why we always stay with our feet on the ground.
In essence, gravity depends on mass: all objects-from stars, planets, and galaxies to light and
subatomic particles-are attracted to each other. Depending on the size, mass, and density
of the object, the gravitational force it exerts varies. And when it comes to the planets
in our solar system, which vary in size and mass, the gravitational force on their surfaces
varies greatly.
The gravity exerted between two objects is directly proportional to the product of their
mass and inversely proportional to the square of their mutual distance: in short, the more
massive two bodies are, the more they attract each other, but this force diminishes very
rapidly from the moment they begin to move away from each other...
And moving away from the center of our planet is precisely what we try to do with spacecraft.
To get out of Earth's gravitational hole, we must reach and exceed the so-called "escape
velocity," which is about 11.2 km/s (at this speed we could move from London to New York
in just ten minutes!). When a shuttle reaches this speed, it can escape Earth's gravitational
field and travel freely in the solar system. Gravity is a fundamental force of physics,
one which we Earthlings tend to take for granted. You can't really blame us. Having evolved
throughout millions of years in Earth's environment. So it's not easy to imagine what it would
be like to move, walk, to run, on other planets where the acceleration of gravity might be
very different from that of our planet of origin...
In this video, we are about to give you a complete review of the strange situations
you might encounter.
Based on their sizes and masses, the gravity on another planet is often expressed in terms
of g units as well as in terms of the rate of free-fall acceleration, i.e., in meters
per second... Earth's gravity is equivalent to 9.8 m/s2.
This means that an object if held above the ground and let go, will accelerate toward
the surface at a speed of about 9.8 meters for every second of free fall. This is the
standard for measuring gravity on other planets, which is also expressed as a single "g."
Basically, it works like this--near the Earth's surface an object falls with an acceleration
that causes it to fall 4.9 meters after one second, nearly 25 meters after 2 seconds,
nearly 45 meters after 3 seconds, and so on… and there is a very simple formula for calculating
this:
space = ½ g time2
Try doing the calculations yourself! If we then wanted to know the time it takes
for an object to reach the ground from a height let's say 100 meters, we would just transform
the formula like this:
time=(100 / (½ g))0.5
and in this case, the result will be 4.5 seconds! But what if we wanted to calculate the speed
with which the same object impacts the earth's ground?
Well, we would simply apply the formula:
speed = g time
to get a result of 44 meters per second, or 159 km per hour!
Okay, this whole discussion might be quite boring, but it will certainly be useful for
you to understand and verify what we are about to discover.
Now let's leave the formulas alone and go on to put what we have just said into practice,
trying to visualize what very normal terrestrial physical activities would look like on other
planets... Like a soccer game, for example... Let's try to consider two classic phases of
the game: the aerial take-off of the soccer player who under the goal tries to hit the
ball with his head... and the waiting time for the return to the ground of a ball hurled
up to a certain height.
A normally gifted soccer player on Earth can get off the ground (jumping with feet together)
by at least half a meter... But how would this go on all the other objects in the solar
system? How far would he be able to jump? A ball thrown 30 meters high, here on Earth
returns to the ground after just 2.5 seconds ... but on Mars? on Jupiter, on Phobos?
Let's try to find out by reviewing all the classic planets of the solar system, plus
a few objects with "more extreme" characteristics!
Gravity on Mercury:
With a mean diameter of about 4,888 km, Mercury is approximately one-third the size of Earth,
and about 18 times less massive than Earth... This makes Mercury the smallest and least
massive planet in the solar system. However, thanks to its high density -- a robust 5.43
grams per cubic centimeter, which is just slightly lower than Earth's 5.5 g/cm3 -- Mercury
has a surface gravity of 3.7 m/s2, which is the equivalent of 0.38 g.
Okay... if we played soccer on Mercury, a soccer player jumping to hit the ball head-on
would be 1.3 meters off the surface! While players on the field would have to wait 4
seconds for the ball to become playable again after a 30-meter flight!
Gravity on Venus:
Venus is similar to Earth in many ways, which is why it is often referred to as "Earth's
twin." With a diameter of 12,200 km, a mass that is 0.815 times that of Earth's and roughly
0.95 times as dense, it is no surprise why the gravity on Venus is very close to that
of Earth's: 0.9 g or 8.9 m/s2. Thus, we should also not be surprised that a soccer game on
Venus would be played under almost the same conditions as on Earth: a soccer player would
jump 0.6 meters and the ball would take 2.6 seconds to return to the ground.
Gravity on the Moon: This is an astronomical body where humans
have experienced firsthand the effects of decreased gravity. Based on the average diameter
(3474 km), mass (81 times smaller than Earth's) and density (3.3 g/cm3), the Moon's surface
gravity has been measured to be 1.62 m/s2, or 0.165 g.
Applying the formulas we discussed earlier, from these data we get that a soccer player
would be able to jump onto the Moon to a height of 2.7 meters! And the players on the field
would have to wait 6 seconds before the ball would descend again from a height of 30 meters.
Gravity on Mars:
Mars is also similar to Earth in many key respects. However, when it comes to size,
mass, and density, Mars is comparatively small. In fact, its mean diameter of 6,678 km is
the equivalent of roughly 0.53 Earths, while its mass is just 0.107 Earths. Its density
comes in at a relatively modest 3.9 g/cm3. Because of this, Mars has 0.38 times the gravity
of Earth, which works out to 3.7 m/s2. It might be surprising to see that despite
Mars being twice as massive as Mercury, the gravitational pull at the surface of the two
planets is actually the same (0.38 g). This indicates that Mercury is much denser than
Mars, and therefore its surface is closer to its center of mass than Mars' is. And as
we saw earlier, gravity is stronger when the distance between two masses is smaller.
As for the soccer game, a player on Mars would therefore jump the same size jumped on Mercury,
or 1.3 meters. And the ball would also take the same time of 4 seconds to descend to the
ground.
Gravity on Jupiter:
Jupiter is the largest and most massive planet in the solar system. Its mean diameter, at
140,000 km, makes it 11 times the size of Earth, while its mass is the equivalent of
318 Earths. But being a gas giant, Jupiter is naturally less dense than Earth and other
terrestrial planets, with a mean density of 1.33 g/cm3.
What's more, being a gas giant, Jupiter does not have a true surface. If one were to stand
on it, they would simply sink until they eventually arrived at its (theorized) solid core. As
a result, Jupiter's surface gravity (which is defined as the force of gravity at its
cloud tops), is 24.8 m/s2, or 2.5 g. Imagining playing a game on a space platform,
a soccer player would barely be able to get 0.2 meters off the "ground! And the ball would
take only 1.5 seconds to descend from a height of 30 meters.
Even in the case of Jupiter, the low density, and thus the distance of the "surface" from
the planet's center of mass, greatly scales down the effects of a mass that would suggest
a much stronger gravity.
Gravity on Saturn:
Like Jupiter, Saturn is a huge gas giant that is significantly larger and more massive than
Earth, but far less dense. In short, its mean radius is 116,500 km, its mass is (95 times
as massive), and has a density of 0.7 g/cm3. As a result, its surface gravity (again, measured
from the top of its clouds) is just slightly more than Earth's: 10.4 m/s2 (or 1.07 g).
One would think that such a large and massive planet should have a very high gravity at
the "surface," but for the reasons already stated, the hypothetical soccer game played
at the top of its clouds would be played almost as well as on Earth! A soccer player would
come off to a height of 0.4 meters and the ball would return to the ground in 2.4 seconds!
Gravity on Uranus:
With a mean diameter of 50,700 km, Uranus is approximately 4 times the size of Earth
and 14.5 times as massive. However, as a gas giant, its density (1.27 g/cm3) is significantly
lower than Earth's. Hence, why its surface gravity (measured from its cloud tops) is
slightly weaker than Earth's: 8.7 m/s2, or 0.9 g.
Again, despite its size, there is not much difference with Earth's gravity--a soccer
player would be able to jump 0.6 meters and the ball would fall back to the ground in
just over 2 seconds.
Gravity on Neptune:
With a mean radius of 49,000 km, Neptune is the fourth largest planet in the solar system.
All told, it is 4 times the size of Earth and 17 times as massive. But, being a gas
giant, it has a low density of 1.6 g/cm3. All of this works out to a surface gravity
of 11 m/s2 (or 1.14 g), which again is measured at Neptune's cloud tops.
In short, on the last planet in the solar system, a soccer game would turn out to be
quite smooth, with players coming off the ground by 0.4 meters and balls taking 2.3
seconds to descend from a height of 30 meters.
Gravity on Ceres: The dwarf planet king of the Asteroid Belt
has an average diameter of 940 km - and a mass that is only six-thousandths of Earth's.
Its surface gravity is just 0.27 m/s², which would allow a football to come off the ground
to a height of as much as 16 meters! In contrast, the ball, falling from a height of 30 meters,
would take 15 seconds to descend again! Imagine how a game might unfold, where players kick
the ball and then stand with their noses up to wait for its return?
Gravity on Phobos:
The larger of the two Martian moons is nevertheless very small. In fact, it possesses an average
diameter of only 22.5 km and a virtually insignificant mass. Its surface gravity, as a result, averages
just 0.0057 m/s2
So that a soccer player could rise by jumping feet-first to a height of ... 88 meters!
And the return of the ball to the ground would have to wait for 102 seconds.... almost two
minutes! With the danger then of dozens of balls being
lost in space during the game, the escape velocity from Phobos being only 41 kilometers
per hour... a speed that a soccer ball tossed from one side of the field to the other could
easily overcome.
And on the Sun? We almost forgot about the "host!" The Sun
has a huge diameter of almost 1.4 million kilometers - and a mass that is 333,000 times
that of Earth. The density is not much, but still, the force of gravity measured on the
photosphere is 274 m/s2 Playing a game on our star would mean having
players jumping less than a couple of inches and balls coming back down in as little as
0.5 seconds!
All in all, gravity runs the gamut here in the solar system, ranging from 0.38 g on Mercury
and Mars to a powerful 2.53 g atop Jupiter's clouds. And on the Moon, where astronauts
have ventured, it is a very mild 0.165 g, which allowed for some fun experiments in
near-weightlessness!
Understanding the effect of zero-gravity on the human body has been essential to space
travel, especially where long-duration missions in orbit and to the International Space Station
have been concerned. In the coming decades, knowing how to simulate it will come in handy
when we start sending astronauts on deep space missions.
And of course, knowing just how strong it is on other planets will be essential to manned
missions (and perhaps even settlement) there. Given that humanity evolved in a 1 g environment,
knowing how we will fare on planets that have only a fraction of the gravity could mean
the difference between life and death.