66 ASTRONOMY • APRIL 2019A: To address your second
question first, Bode’s law was
announced by astronomer
Johann Titius in 1766, but pop-
ularized in 1772 by Johann
Bode. The law states that the
spacing between planets in our
solar system can be predicted
based on a sequence of num-
bers: 0, 3, 6, 12, and so on. After
0 and 3, each subsequent num-
ber is twice the value of the
previous one. Next, add 4 to
each number — which gives 4,
7, 10, 16, etc. — and divide by- The results — 0.4, 0.7, 1.0,
1.6, 2.8, 5.2, 10, and so on —
are roughly the distances of the
planets (and the main asteroid
belt, in the case of 2.8) from the
Sun in astronomical units (AU;
1 astronomical unit is equal to
the average Earth-Sun distance
of 93 million miles or 150 mil-
lion kilometers).
Bode’s law holds out to
Uranus at a distance of about
19 AU, but it fails for Neptune.
The predicted distance of
Astronomy’s experts from around the globe answer your cosmic questions.
BODE’S LAW
insignificant. In the case of
Earth, for example, tidal effects
are pushing us away from our
star at about one micrometer per
year — more than 10 times less
than the width of a human hair.
As the Sun converts some
small percentage of its mass
into energy, this mass loss can
also affect a planet’s distance by
reducing the Sun’s gravitational
pull — but again, only by a
small amount. Based on the
rate the Sun is burning energy,
it will have lost about 0.1 per-
cent of its total mass over the
course of its hydrogen-burning
lifetime of about 10 billion
years. This results in Earth
moving away from the star at
just 0.6 inch (1.5 centimeters)
per year — a total of about
93,000 miles (150,000 km) over
the course of 10 billion years, or
only about 0.1 percent of its
orbital distance.
This effect does increase as
you move outward through the
solar system, though it still
remains small. Saturn is mov-
ing away from the Sun at about
5.5 inches (14 cm) per year, or a
total of 870,000 miles (1.4 mil-
lion km). That total is just
1 percent of its orbital distance
in 10 billion years.
Alison Klesman
Associate EditorASKASTR0
Q: ARE ANY OF THE PLANETS’ AVERAGE
DISTANCES FROM THE SUN CHANGING? IS
NEPTUNE MOVING AWAY TO FIT BODE’S LAW?
Bob, Victorville, CaliforniaNeptune using Bode’s law is
nearly 39 AU, but the planet
actually sits at about 30 AU. It
also fails for Pluto, which is on
a highly eccentric orbit.
Most important to note
about Bode’s law is that it is an
empirical law. Empirical laws
are rules based on observa-
tions, but not grounded in
physical theory. While Bode’s
law is a great observation with
regard to much of the solar
system, it is not ref lective of
the physics that dictates the
planets’ motions or distances.
So, Neptune is not moving far-
ther from the Sun to better fit
with this rule, and most
astronomers no longer really
consider Bode’s law useful.
As for your first question,
the distances of the planets
from the Sun do very slightly
change over time. Tidal effects
due to the tug of gravity
between the Sun and a planet
can induce orbital changes, but
the change is so tiny as to beQ: ARTISTS ALWAYS SHOW
A BLACK HOLE’S ACCRETION
DISK ORIENTED IN ONE
PLANE. BUT STARS NEAR
SAGITTARIUS A* ORBIT
IN A VARIETY OF PLANES.
IF EACH OF THOSE STARS
IS EVENTUALLY DIGESTED,
WOULDN’T THERE BE
MULTIPLE ACCRETION DISKS
IN MULTIPLE PLANES?
Jim McLeod
Charlotte, North CarolinaA: The answer here is that real-
ity is far more complex than
the pictures you reference. At
present, our technology does
not allow us to get a clear snap-
shot of the material accreting
ont o S a g it t a r iu s A* (S g r A*),
so we are limited by our math-
ematically driven models in
determining what geometry is
possible and under what condi-
tions it might form.
First, think about the artist’s
conception and why the accre-
tion disk is simply a disk. The
accretion disk forms when dif-
fuse material is attracted to a
massive central body, like a
black hole. The f lattened shape
of the accretion disk is due to
angular momentum, which
dictates the particles’ motion as
they rotate around the black
hole. As collisions happenThese antennas at the Goldstone Deep Space Communications Complex
in California’s Mojave Desert are part of the Deep Space Network, which
NASA uses to send and receive signals from spacecraft. NASA/JPL-CALTECHAccretion disks are typically depicted as flat, like in this artist’s rendition,
because mathematical models suggest that over time, particles in the disk
lose angular momentum and flatten out into similar orbits. ROBIN DIENEL,
COURTESY OF THE CARNEGIE INSTITUTION FOR SCIENCE