Apparent motion of the planets
- Now consider the planets. We consider the apparent motion
and appearance of planets because they provide a good exercise in
visualization, and also because observations of planetary motions were
very important historically in helping us to come to understand how
objects move in the Solar System, as we'll discuss shortly. The planets
also move around the Sun. Because of this and also because of the reflex
motion from the Earth's revolution, the planets also appear to move with
respect to the stars.
- The qualitative motions of the planets can be understood if one
- All of the planets move around the Sun in roughly the same plane
- All of the planets move around the Sun in the same direction
- The planets which are nearer to the Sun move faster than those
which are farther away
- planetary orbits.
- The apparent motion of a planet arises from:
- The motion can be complex, exhibiting
which occurs when the planet appears to move backwards in its normal
path. Retrograde motion occurs because the apparent motion of planets
arises from a combination of their intrinsic motion and the reflex
motion which appears because Earth is moving.
- The inner planets (Mercury and Venus) show retrograde motion because
they are moving around the Sun, and we are viewing this motion from
outside of their orbits. For half of their years, they appear to move
in one direction as seen from Earth; for the other half, they appear to
move in the other direction.
- The outer planets show retrograde motion because the Earth moves
around the Sun faster than the outer planets, and thus it will
periodically pass the outer planets in their orbits. When this
happens, the planets will appear to reverse direction when seen
- The time of day that we can see different planets depends on whether
they are closer to the Sun than Earth (Mercury and Venus) or farther
(all other planets)
- Because we see planets in reflected light, they have phases; not
all of the sunlit half can be seen from Earth at all times. Different
planets have different phases in which they can be seen, depending
on whether the planet is closer or further from the Sun than the Earth.
Historical development of ideas about the Solar System
- How do we know that the Earth goes around the Sun?
- The historical development of ideas about motions in the Solar
System provides a good example of the process of science.
(A nice summary by James Schombert at University of
- The history of
astronomy demonstrates that progress in scientific models often results
from either a change in world view (or preconceptions about how people expect
the universe is organized) or the availability of new, more accurate
measurements, which often result from the development of new technology.
- The current model we have of motions in the Solar System
was figured out by making careful observations of motions of objects
in the sky.
- Basic observations:
- Sun appears to go around in the sky
- Stars appear to go around in the sky, but a slightly different
- Moon appears to go around in the sky, at a different rate
- Planets are objects with more irregular motion in the sky; they
occasionally exhibit retrograde motion. Some
are visible only at certain times of day (in particular, Venus).
- summary images
- Ancient Greek astronomers, led by Aristotle & Ptolemy, preferred
an Earth-centered or geocentric universe because of the
apparent lack of observed parallax of the stars.
- group question: parallax observations. At that time, measurements were not sufficiently accurate
to detect parallax.
- In their earth-centered model, they envisiond that the Sun, the
Moon and the planets orbited the earth in circular orbits.
They preferred circles for reasons of simplicity.
- group question: geocentric model
- Since the planets were observed to undergo
retrograde motion, the Greeks developed a theory of
This is not what is actually going on, but was a clever modification
of their model to account for observed data. However, even with these,
they realized that simple models with perfect circles still failed to
match the observed data.
A detailed geocentric model was developed by
This model was quite complex motions, but did a reasonable job of
predicting future positions of planets, given the large uncertainties
in making such measurements. However, the predicted positions of the
model were not confirmed by more precise measurements.
- The problems & complexities of the geocentric model, as well as
a general philosophical shift, caused Nicholas Copernicus (1473-1543)
to examine an alternative sun-centered or heliocentric model
of the solar system. His model proposed that:
- The Sun is at the center of the Universe.
- The distance between the Earth and the stars is much greater
than the Earth-Sun distance. This would explain the lack of observed
- The east to west daily motions of stars, planets, the Moon,
and the Sun are caused by the rotation of the Earth on its axis.
- The Earth and all the planets revolve around the Sun on
circular orbits. This produces the change in constellations observed
from one time of year to the next.
- Retrograde motion is an effect caused by the fact that we are
observing other planets on the planet Earth which itself is moving
around the Sun.
- Although Copernicus' idea of a heliocentric solar system is
correct, his assumption of circular orbits made his model no more
accurate than that of Ptolemy. But, it had the beauty of simplicity.
- There was active debate in the 16-17th century about the relative
merits of the geocentric (Earth-centered) and heliocentric
(Sun-centered) models. Some of the debate was scientific and some
- Galileo Galilei's (1564-1642) contribution to astronomy &
physics was immense as a result of his careful observations &
experiments, and several of his observations provided critical evidence
for the heliocentric model:
- Copernicus' model with circular orbits still did not do a very
good job of predicting the position of planets accurately. Refinements
to the heliocentric theory were made possible by Tycho Brahe's
(1546-1601) precise observations of Mars and the other planets. These
accurate observations set the stage for Johannes Kepler (1571-1630)
to make major modifications and improvements on the heliocentric
model. Tycho's measurements provided the improvement in accuracy
necessary to distinguish between competing models.
- Kepler devised three Laws of Planetary Motion
that provide the correct description of planetary motion. The key
breakthrough was that Kepler realized that circular orbits just did
not fit the observed data, regardless of how the circles were adjusted. The
three laws are:
- Planets orbit the Sun in elliptical orbits with the Sun
located at one of the focii of the ellipse. An ellipse is characterized
by a size and an eccentricity (or "squashedness"). A circle is an
ellipse with zero eccentricity. The size of an ellipse is usually
described by the length of its semimajor axis, i.e. half the
length of the long axis of the ellipse. Planets orbit in elliptical
orbits, although these orbits are of very low eccentricity and hence
are almost circular. In fact, Kepler's laws apply to all objects
orbiting in the Solar System; for example, comets travel on very
eccentric elliptical orbits.
- In their elliptical orbits, planets travel faster when they are
closer to the Sun. This statement can be made more quantitative with
the Law of Equal Areas, which states that a hypothetical
line drawn between a planet and the Sun sweeps out equal areas in
equal intervals of time.
- The time it takes for a planet to make one full revolution
around the Sun is related to the size of its orbit. If P
planet's orbital period around the Sun (measured in Earth years) and
is the semimajor axis of the planet's orbit distance (measured
in astronomical units), then
P2 = A3.
unit is a unit which measures distance, and one astronomical unit is,
by definition, the size of the semimajor axis of the Earth's orbit.
- group question: Kepler's third law example
- So, by measuring the orbital period of a planet through careful
observations of the planet with respect to the stars, one can determine
its distance from the Sun.
- group question: Kepler's laws
- Kepler's laws are a correct description of all solar system motions.
However, Kepler's laws do not provide any explanation as to why
solar system objects move in this fashion.
- The final confirmation that the Earth orbits the Sun came from the
detection of stellar parallax in the 19th century. But by that time,
everyone was already convinced of it!
- Group question: how do we know the Earth orbits
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