Gravity and Atmospheres
Key idea: Atmospheres are held in place by the
force (pull) of
gravity. A gravitational
force exists between all objects which have
mass. In the case of atmospheres, the gas
molecules and other
particles in the atmosphere are bound by gravity to the host planet or
satellite.
Astronomical tidbit:
Nearly all of the planets in the Solar System have atmospheres, though
the atmospheres are quite different from each other. A number of
the larger satellites in the Solar System have atmospheres as well. The
photograph on the left shows the planet Neptune with bright clouds and huge
dark storms in its atmosphere. The large dark feature at the upper left is
called the Great Dark Spot. The large feature at the lower right is
called the Small Dark Spot. The two Spots and the other features in
Neptune's atmosphere travel around the planet at different rates. The
photograph was taken by the Voyager 2 spacecraft during its August,
1989 encounter with Neptune, the outermost of the gas giant
planets.
Surface Gravity
When a force acts on a body, that body is accelerated. The
acceleration
due to gravity on the surface of the Earth is 9.8 meters per second2
(note: second2 is seconds to the 2nd power). This means that if an
object is dropped near the surface of the Earth, its
velocity
due to gravity will increase by 9.8 meters per second every second. The
surface gravity on Mars is
only 38% that of Earth. If an object is released above the surface of Mars,
it will accelerate only 38% as quickly as it will on Earth. The "surface
gravity" on Jupiter (at the 1-bar pressure level) is 22.9 times that of Earth.
To convert from meters to feet, multiply by 3.28 because
1 meter = 3.28 feet.
Weight is also determined by gravity. Weight is the force
which you exert on your bathroom scale due to the gravitational
attraction of the Earth!!! If a person weighs 100 pounds on
Earth, then he or she will weigh only 38 pounds on Mars because the
surface gravity there is 38% of what it is on Earth.
Questions:
How much will that same person weigh on Jupiter (at the 1-bar level)?
How much will each of you weigh on Mars and Jupiter???
Surface gravity (g) depends on the mass (M)
of the planet and on the planet's radius
(r). The formula which relates these parameters is:
g = G * M / r2
where G is called the
gravitational constant. If
you know the mass of a planet (or satellite) and its radius, then you
can use this formula to calculate its surface gravity. By looking at
the formula, you can see that if the mass of the body doubles while its
radius remains the same, then its surface gravity also doubles. On the
other hand, if the mass remains the same but the radius doubles, then
the gravity on the surface will decrease by a factor of four!!!
Activity: For mathematically
advanced students, calculate the surface gravity for various planets and
satellites in the Solar System and for the Sun itself!
Escape Velocity
Gas molecules (or any massive objects for that matter) which have
a velocity greater than the
escape velocity
for a given planet will not be bound to the planet by the force of
gravity. Such molecules will have sufficient energy to escape to distant
space! The escape velocity at the Earth's equator is 11.2 kilometers per
second (note that 1 kilometer is equal to 1000 meters). The escape velocity
at the surface of Mars is 5.0 kilometers per second and at Jupiter (1-bar
level again) is 59.6 kilometers per second.
Questions: What is the escape velocity of the Earth in units of
miles per hour? How fast would a person have to throw an object from the
surface of the Earth so that it would not return to the surface but rather
escape to space? Can a person throw a ball that fast? How do you suppose
that gas molecules might gain sufficient energy to travel that fast???
Like surface gravity, the escape velocity is determined by the mass of the
planet and by its radius. The more massive the planet, the greater is its
escape velocity and the more gas it is likely to have in its atmosphere.
Activity: For mathematically
advanced students again, learn to calculate the escape velocity from
the mass and radius of a body, and calculate the escape velocity for
various planets and satellites in the Solar System.
Astronomical tidbit: A black hole is an
astrophysical object whose mass is compressed into such a small volume
that the escape velocity for the black hole exceeds the speed of
light!!! Because light cannot escape the gravitational attraction of such
an object, the object is said to be black. It is not possible
for any object to exceed the speed of light, so mass cannot
escape from a black hole either. Black holes are believed to form from
the collapsed cores of large stars which have burned all their inner
fuel. Supermassive black holes are thought to exist
in the centers of many galaxies where tremendous amounts (millions of
times the mass of the Sun!) of gas are gravitationally compacted.
The center of the giant elliptical galaxy M87 is shown in the photo
at the right. Astronomers believe that a supermassive black hole
exists in the nucleus of M87. The hole itself is black, but fast moving
gas is heated as it is spirals toward and then into the black hole, and the
hot gas shines brightly in the photograph. A jet of high-speed electrons is
also shown as it exits from the vicinity of the black hole and travels at
nearly light speed toward the upper right of the picture. The photograph of
M87 was taken by the Hubble Space Telescope in 1994. The giant
galaxy M87 is located about 50 million light years away from
Earth!!! This means that it takes light 50 million years to reach Earth from
M87. By contrast, light from the Sun takes only 8 minutes to reach the
Earth.
Thermal Motion
Gas molecules move faster when they are hot than when they are cold, and
faster moving molecules are more likely to exceed a planet's escape velocity
than slower moving molecules. Mercury is the closest planet to the Sun
(and therefore very hot) and it has no atmosphere, whereas Pluto is
the furthest planet from the Sun (and therefore very cold) and it does
have an atmosphere. This is so even though the escape velocity of Mercury
is four times more than that of Pluto, and it would be expected to have
more of an atmosphere than Pluto if the atmospheres were at the same
temperature.
Activity/demonstration: Add colored
dye to water at different temperatures and observe how quickly is disperses.
At the same temperature, light molecules move faster than heavy ones.
That is why atmospheres consist largely of heavy gases like oxygen and
carbon dioxide instead of light gases like hydrogen and helium. The
lighter molecules move too fast to be easily bound to planets or
satellites by gravity.
Last updated: November 17, 1999
Joe Twicken /
joe@nova.stanford.edu
Rob Wigand
Astronomical tidbit:
Nearly all of the planets in the Solar System have atmospheres, though
the atmospheres are quite different from each other. A number of
the larger satellites in the Solar System have atmospheres as well. The
photograph on the left shows the planet Neptune with bright clouds and huge
dark storms in its atmosphere. The large dark feature at the upper left is
called the Great Dark Spot. The large feature at the lower right is
called the Small Dark Spot. The two Spots and the other features in
Neptune's atmosphere travel around the planet at different rates. The
photograph was taken by the Voyager 2 spacecraft during its August,
1989 encounter with Neptune, the outermost of the gas giant
planets.