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62 Modelling the Universe
62 Modelling the Universe
(d)
Incorrect. The stars are fixed on the
outermost sphere.
(e)
Incorrect. The retrograde motion was
explained using epicycles and deferents in
the Ptolemaic model.
(a)
Mercury, Venus and the Earth
(b)
Yes. This is similar to how Mars show
retrograde motion as seen on the Earth.
Checkpoint
Checkpoint 1 (p. 29)
1.
(a)
T
(b)
F
The position of the planet changes across
years.
4.
Yearly motion ≠ periodic motion
(c)
2.
F
The ecliptic is the apparent path of yearly
motion of the Sun.
(a)
Daily motion
(b)
Retrograde motion
(c)
Yearly motion
(a)
1.
2.
Earth
This is a geocentric model and the Earth is at
the centre.
(b)
3.
A is the deferent.
(a)
(iii)
(b)
(ii)
(c)
(i)
(a)
No
Mercury is orbiting around the Earth
according to the Ptolemaic model.
(b)
Yes
(c)
Yes
(a)
T
The Sun is at the focus but not at the centre.
(b)
F
The elliptical orbits were explained by
Newton.
(c)
T
This was explained by the third law.
B is the epicycle.
2.
(a)
No. The Earth instead was the centre.
(b)
No. All planets should move in circles
because heavens should be perfect and thus
made up of spheres.
(c)
(d)
4.
No. It was Ptolemy who proposed that the
Earth can be slightly off centre from the
deferent.
Yes.
Exercise 2.2 (p. 33)
Checkpoint 3 (p. 36)
2.
3.
(a)
All of them
(b)
Plato and Ptolemy
(c)
Copernicus
The three things are the Sun, the Earth and the
Moon. The larger circle is the orbit of the Earth
while the smaller circle is the orbit of the Moon.
(a)
(b)
(c)
Correct. The positions of Mercury and Venus
were explained using epicycles in the
Ptolemaic model.
Incorrect. In fact, the Copernican model
failed to predict the planets’ positions more
accurately because Copernicus held firmly to
the belief that planets move in circular
orbits.
Correct
Yes. This is similar to how Venus goes through a
complete phase change as seen on the Earth.
Exercise
1.
1.
p.1
Checkpoint 4 (p. 47)
Checkpoint 2 (p. 33)
1.
|
C
Option A is incorrect. Mercury and Venus were
closer to the Earth than the Sun in the model.
Option B is incorrect. The planets moved in
deferents in the model.
Option D is incorrect. The Earth was at the centre
in the model.
2.
B
The Ptolemaic model was influential. However,
geocentric models were proposed by Greeks well
before Ptolemy.
3.
(a)
Plato thought that heavens should be perfect
and made up of spheres. Accordingly, the
celestial bodies on the heavens should move
in circular orbits.
(b)
They need to hold firm to the perfect sphere
and at the same time they to explain the
actual observation.
Active Physics Full Solutions to Textbook Exercises
4.
5.
(a)
In the Ptolemaic model, planets moved in
circles called epicycles which in turn move
around the Earth in circles called deferents.
(b)
The centres of the epicycles of Mercury and
Venus were always fixed on the line joining
the Earth and the Sun.
(a)
Mercury should be between the Earth and
the Sun.
(b)
The centre of the epicycle of Mercury should
always be fixed on the line joining the Earth
and the Sun.
(c)
(d)
62 Modelling the Universe
8.
9.
Mercury and Venus
(b)
To comply with the observation that the two
planets are always close to the Sun in the sky.
(c)
In the Copernican model, all planets revolve
around the Sun but Mercury and Venus have
smaller orbital radii.
(a)
The Ptolmaic model cannot explain the
complete phase change of Venus but the
Copernican model can.
(b)
(i)
A crescent Venus is formed when the
Sun, Venus and the Earth almost lie on
a straight line with Venus in between.
(ii)
A full Venus is formed when the Sun,
Venus and the Earth lie on a straight
line with the Sun in between.
The centre of the epicycle of Mars did not
always lie on the line joining the Earth and
the Sun.
(iii) Venus is farther from the Earth when a
full Venus is formed than when a
crescent is formed.
Exercise 2.3 (p. 47)
C
However, Galileo was not the inventor of the
telescope.
2.
D
Note that the retrograde motion was explained by
the Ptolemaic model using epicycles and deferents
and the model existed well before Galileo.
3.
B
The drawing shows some back spot on the Sun’s
surface.
4.
B
5.
D
According to the Ptolemaic model, The side of
Venus facing the Earth was opposite to the Sun
and no sunlight is thus reflected to the Earth.
6.
B
The angular separation is the largest when the line
joining the Earth and Merucry is tangential to the
orbit of Mercury. Therefore the angle is
7.
(a)
Geocentric
(b)
(i)
(ii)
Yes.
On the Earth, a planet will show
retrograde motion when it gets closer
to the Earth.
Yes.
The centre of epicycle of a planet is
fixed on the line joining the Earth and
the Sun. The planet appears close to
the Sun as the epicycle is far smaller
than the deferent.
p.2
(a)
The Earth should be the centre of the
universe.
1.
|
10.
(c)
First, there are hilly terrains on the Moon
and sunspots on the Sun. Second, there are
four satellites orbiting around Jupiter.
(a)
First the planets and the Sun revolve around
Earth. Second, planets and the Sun move in
circular orbits with a uniform speed.
(b)
The first law rejects that planets revolve
around the Earth. Instead, all planets move
in elliptical orbits with the Sun at one of the
foci.
The second law rejects that planets move
with uniform speed. Instead, planets move
faster when they are closer to the Sun and
slower when they are farther away.
Chapter Exercise
Multiple-choice Questions (p. 51)
1.
A
2.
D
3.
C
4.
A
The distance should be between 1 – 0.7 = 0.3 and 1
+ 0.7 = 1.7 AU.
5.
D
6.
B
Structured Questions (p. 52)
7.
(a)
(i)
The retrograde motion of a planet was
explained by the combined motion on
the epicycle and the deferent.
Accordingly, the planet demonstrates
Active Physics Full Solutions to Textbook Exercises
62 Modelling the Universe
retrograde motion when it gets closer
to the Earth. (1A)
(ii)
|
p.3
As the stars and planets revolve, we
can see on the Earth that the celestial
bodies rise and fall in the sky daily. (1A)
In the Ptolemaic model, the centre of
the epicycle of Mercury was fixed on
the line joining the Earth and the Sun.
(ii)
Epicycles are needed. (1A)
Accordingly, a planet demonstrates
retrograde motion when it gets closer
to the Earth. (1A)
(1A)
Ss may explain using diagrams.
(d)
(1A)
(b)
(i)
(i)
No. (1A)
As the Earth self rotates, we can see on
the Earth that the planets and distant
stars rise and fall in the sky daily. (1A)
Venus cannot show a full phase if she is
always between the Earth and the Sun.
(1A)
(ii)
8.
The Ptolemaic model is geocentric but the
Copernican model is heliocentric. (1A)
(b)
Stars are fixed on a sphere and their relative
positions remain unchanged. (1A)
The whole sphere revolves around the Earth,
resulting in the daily motion of the stars. (1A)
(c)
(i)
Tycho built large observatories and
collected recorded huge amounts of
data about planetary motion. (1A)
Kepler based on the data and
discovered his three laws of planetary
motion. (1A)
(ii)
The first law stated that all planets
move in elliptical orbits with the Sun at
one focus. This overturned the
common belief that the planets and the
Sun revolve around the Earth and their
orbits are circular. (1A)
The second law stated that an
imaginary line joining the Sun and the
planet sweeps out equal areas in equal
time intervals. This overturned the
common belief that planets move with
uniform speeds. (1A)
9.
(a)
Figure Q9a: Aristotle’s
Figure Q9b: Copernicus’s model (1A)
(b)
Usually the planets appear to move
eastwards relative to the background stars
but they reverse direction for some time.
1A for relative to the background
1A for reverse movement
Ss may use a diagram to explain.
(c)
(i)
(ii)
Heavens are not perfect as there are
hilly terrains on the Moon and
sunspots on the Sun. (1A)
(a)
The stars and planets revolve around
the Earth. (1A)
The Earth self rotates. (1A)
Different planets move with different
speeds. (1A)
The retrograde motion is due to the
relative motion of the planets. (1A)
10.
(a)
(b)
(i)
They are the satellites of Jupiter. (1A)
(ii)
Some satellites cannot be observed
when they pass in front of or behind
Jupiter. (1A)
Any two of the following (4A):
•
Sunspots were observed.
This implied that heavens are not
perfect.
•
A complete phase change Venus was
observed.
The Ptolemaic model (and other
geocentric models as well) cannot
explain the observation and is thus
incorrect.
•
There were hilly terrains on the Moon.
This implied that heavens are not
perfect.
•
Milky way was made up of stars.
Stars were very distant and this
explained why stellar parallax was not
observed in heliocentric models.
The last point was not discussed in our
textbook.