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ASTR 1101-001
Spring 2008
Joel E. Tohline, Alumni Professor
247 Nicholson Hall
[Slides from Lecture14]
Scientific utility of the
Copernican Heliocentric Model
• Can deduce the true “sidereal” (as
opposed to readily measured “synodic”)
orbital periods of each of the planets [see
textbook BOX 4-1 and Table 4-1]
• Can deduce the distance that each planet
is from the Sun, relative to the Earth’s
distance from the Sun (1 AU); [see
textbook discussion associated with Table
4-2]
Scientific utility of the
Copernican Heliocentric Model
• Can deduce the true “sidereal” (as
opposed to readily measured “synodic”)
orbital periods of each of the planets [see
textbook BOX 4-1 and Table 4-1]
• Can deduce the distance that each planet
is from the Sun, relative to the Earth’s
distance from the Sun (1 AU); [see
textbook discussion associated with Table
4-2]
Determining the size
of the orbit of Mars
• Suppose that at sunrise,
Mars is on the western
horizon; does Mars lie in
Direction #1 or direction
#2?
• Suppose that at sunrise,
Mars is seen directly
overhead; does Mars lie
in Direction #1 or
direction #2?
Determining the size
of the orbit of Mars
• At sunrise, if Mars is on
the western horizon, Mars
must lie in Direction #1.
• At sunrise, if Mars is seen
directly overhead, Mars
must lie in Direction #2.
Determining the size
of the orbit of Mars
• But until we know the size
of the orbit of Mars, we
don’t know precisely
where it resides along
either line of sight.
• Consider the three
possible orbits shown on
the next few slides …
Determining the size
of the orbit of Mars
• But until we know the size
of the orbit of Mars, we
don’t know precisely
where it resides along
either line of sight.
• Consider the three
possible orbits shown on
the next few slides …
Determining the size
of the orbit of Mars
Determining the size
of the orbit of Mars
Determining the size
of the orbit of Mars
Determining the size
of the orbit of Mars
Determining the size
of the orbit of Mars
Determining the size
of the orbit of Mars
• So, by measuring the amount of time it takes
Mars to travel from point “A” to point “B” each
orbit, Copernicus was able to determine the
size of the orbit of Mars (and of Jupiter,
Saturn, Mercury, and Venus).
Determining the size
of the orbit of Mars
• So, by measuring the amount of time it takes
Mars to travel from point “A” to point “B” each
orbit, Copernicus was able to determine the
size of the orbit of Mars (and of Jupiter,
Saturn, Mercury, and Venus).
Scientific utility of the
Copernican Heliocentric Model
• Can deduce the true “sidereal” (as
opposed to readily measured “synodic”)
orbital periods of each of the planets [see
textbook BOX 4-1 and Table 4-1]
• Can deduce the distance that each planet
is from the Sun, relative to the Earth’s
distance from the Sun (1 AU); [see
textbook discussion associated with Table
4-2]
Summary Results
(deduced by Copernicus)
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
P (years)
0.241
0.615
1.000
1.88
11.86
29.46
84.10
164.86
D (AU)
0.387
0.723
1.000
1.524
5.203
9.554
19.194
30.066
P2
0.058
0.378
1.00
3.53
141.
870.
7070.
27,200.
D3
0.058
0.378
1.00
3.54
141.
870.
7070.
27,200.
Summary Results
(all 8 planets)
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
P (years)
0.241
0.615
1.000
1.88
11.86
29.46
84.10
164.86
D (AU)
0.387
0.723
1.000
1.524
5.203
9.554
19.194
30.066
P2
0.058
0.378
1.00
3.53
141.
870.
7070.
27,200.
D3
0.058
0.378
1.00
3.54
141.
870.
7070.
27,200.
Notice …
• There is a strong correlation between a
planet’s orbital period and its distance
from the Sun … Planets that are farther
and farther from the Sun exhibit longer
and longer orbital periods
Summary Results
(all 8 planets)
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
P (years)
0.241
0.615
1.000
1.88
11.86
29.46
84.10
164.86
D (AU)
0.387
0.723
1.000
1.524
5.203
9.554
19.194
30.066
P2
0.058
0.378
1.00
3.53
141.
870.
7070.
27,200.
D3
0.058
0.378
1.00
3.54
141.
870.
7070.
27,200.
Additional Realization …
(first noticed by Kepler)
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
P (years)
0.241
0.615
1.000
1.88
11.86
29.46
84.10
164.86
D (AU)
0.387
0.723
1.000
1.524
5.203
9.554
19.194
30.066
P2
0.058
0.378
1.00
3.53
141.
870.
7070.
27,200.
D3
0.058
0.378
1.00
3.54
141.
870.
7070.
27,200.
Additional Realization …
(first noticed by Kepler)
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
P (years)
0.241
0.615
1.000
1.88
11.86
29.46
84.10
164.86
D (AU)
P2
0.387
0.058
0.723
0.378
1.000
1.00
1.524
3.53
5.203
141.
9.554
870.
19.194
7070.
2
3
P = D !!
30.066 27,200.
D3
0.058
0.378
1.00
3.54
141.
870.
7070.
27,200.
P2 = D3
(works for all 8 planets)
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
P (years)
0.241
0.615
1.000
1.88
11.86
29.46
84.10
164.86
D (AU)
0.387
0.723
1.000
1.524
5.203
9.554
19.194
30.066
P2
0.058
0.378
1.00
3.53
141.
870.
7070.
27,200.
D3
0.058
0.378
1.00
3.54
141.
870.
7070.
27,200.
Kepler’s Observed
Laws of Planetary Motion
• …