E1 Astronomy and Space Science
2
Chapter 2 Astronomy through History
Astronomy through History
Practice 2.1 (p. 46)
By Kelper’s third law,
1
D
TA 2
2
D
a A3
3
A
263 2
4
Use circles for the orbits.
a A3
Use epicycles.
5
(a) Geocentric.
as planets and stars) and understand their
motions and features. The observations led
scientists to develop more completed theories
about the solar system and the universe.
year. However, there is a period when
For example, the phases of Venus observed
Mars’s eastward motion stops and
through the telescope provided strong
moves westwards before reversing
evidence to support the heliocentric model.
direction again. This backward loop is
6
called retrograde motion.
craters.
around the Sun, with Mars moving
The Sun has dark patches which are
outside the Earth. Since the Earth is
sunspots, and the Sun rotates.
moving faster than Mars, sometimes
There are four moons orbiting Jupiter.
Mars is passed by the Earth, and it
Venus shows a complete cycle of
appears to move backwards in the sky.
phases.
This produces the apparent retrograde
(b) Any two of the following
motion of Mars.
(corresponding to (a)):
The Moon was thought to be a perfect,
Practice 2.2 (p. 58)
B
(a) Any two of the following:
The Moon has mountains, valleys and
(b) Both the Earth and the Mars revolve
3
3
This helped us observe celestial objects (such
moves from west to east throughout a
B



5
(a) On the celestial sphere, Mars generally
2
 aA

 2
C
Earth.
B
TB 2
4
assumed to move together around the
1
aB3
The orbital period of planet B is 93.0 years.
B is an epicycle. The epicycles of
Mercury, Venus and the Sun were
6
=
TB 2
TB = 93.0 yr
(b) A is a deferent.
(c)
=
smooth sphere.
The Sun was thought to be a perfect
sphere.
The Earth was thought to be the centre
of everything.
Venus moved around the Earth.
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E1 Astronomy and Space Science
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Chapter 2 Astronomy through History
(a) The Sun rotates, approximately once per
month, around an axis roughly
perpendicular to the ecliptic plane.
Moon
(b) Never look at the Sun with naked eyes
or through telescopes directly.
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log a
log T
Io
5.63
0.25
Europa
5.83
0.55
Ganymede
6.03
0.85
Callisto
6.27
1.22
(a)
(b) Distance of perihelion from the star
= 0.06 AU
Distance of aphelion from the star
= 0.54 AU
(c)
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Semimajor axis of the orbit
 0.06  0.54 
=
 AU
2


The graph is a straight line with slope
= 0.3 AU
satellites satisfy the Kelper’s third law.
1.50. This satisfies equation (*).
Therefore, the motion of Galilean
(a) Jupiter
Revision exercise 2
(b) The square of a planet’s orbital period is
(c)
proportional to the cube of its semimajor
Multiple-choice (p. 61)
axis of its orbit.
1
D
From Kepler’s third law,
T2
=k
a3
2
C
3
C
By Kelper’s third law,
TA 2
T2 = ka3
a A3
2log T = log k + 3log a
log T = 1.5log a + constant ……(*)
TA 2
Consider the data given in Table a and
TB 2
plot a graph of log T against log a.
TB 2
=
a A3
aB3
aB3
a
TA
=  A
TB
 aB
4
New Senior Secondary Physics at Work
=
2
3

2 2
2
 =   =
1
1

3
B
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E1 Astronomy and Space Science
Chapter 2 Astronomy through History
Conventional (p. 61)
The point of greatest distance from the
1
Sun is called the planet’s aphelion.
(a) Semimajor axis of Ceres
 2.99  2.54 
=
 AU
2


(1A)
= 2.765 AU
(b) Semimajor axis of Jupiter’s orbit
 5.46  4.95 
=
 AU
2


(1A)
(b) By Kelper’s third law,
T2 (in Earth years) = a3 (in AU)
(1M)
= 5.205 AU
3
(c)
T = 2.765 yr
= 4.60 yr
2
(a) Ptolemy
(1A)
By Kelper’s third law,
T2 (in Earth years) = a3 (in AU)
(1A)
(1M)
3
T = 5.205 yr
(1A)
= 11.9 yr
(b)
(1A)
(d) No.
(1A)
Thebe orbits Jupiter, not the Sun.
Therefore we cannot find its orbital
period from the information provided in
(Correct region.)
(c)
(1A)
this question.
Venus never moves very far from the
Sun.
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(1A)
Its speed increases as it approaches the Sun.
(1A)
When it comes to the perihelion (C), it moves
never be observed from the Earth. (1A)
with the highest speed.
In Ptolemaic model, each planet moved
speed decreases.
(1A)
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A deferent is the orbit on which the centre of
epicycle moves uniformly around the Earth.
(1A)
(1A)
By Kelper’s third law,
(1A)
T2 (in Earth years) = a3 (in AU)
(a) The point of closest approach to the Sun
is called the planet’s perihelion.

 AU


= 39.4 AU
(b) It suggested that the Moon should be a
5

 km


(1A)
(b) 5.91  10 km
 5.91 10 9 10 3
=
 1.50 10 11

(a) The Moon had mountains, valleys and
perfect, smooth sphere.
(a) Semimajor axis of Pluto
 7.38 10 9  4.44 10 9
=

2

9
(1A)
craters.
(1A)
= 5.91  109 km
A deferent is usually larger than an epicycle.
4
(1A)
Then when it moves away from the Sun, its
uniformly around a circular orbit called an
epicycle.
(1A)
(1A)
In Ptolemaic model, the full Venus can
3
When the comet is at the aphelion (A), it
moves with the lowest speed.
(d) Galileo found that Venus showed a
complete cycle of phases.
(1A)
T = 39 .4 yr
(1A)
= 247 yr
New Senior Secondary Physics at Work
(1M)
3
3
(1A)
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E1 Astronomy and Space Science
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Chapter 2 Astronomy through History
A complete cycle of phases appears in Figure
(ii)
f but not in Figure e. (Full Venus cannot be
observed from the Earth in the geocentric
model.)
(1A)
Therefore, the geocentric model could not
explain Galileo’s observation but the
heliocentric model could.
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(1A)
(a) On a celestial sphere, Mars generally
moves from west to east throughout a
year.
(1A)
However, there is a period when Mars’s
eastward motion stops and moves
westwards before reversing direction
(Concentric circular paths with the
again. This backward loop is called
Sun at the centre.)
retrograde motion.
The Earth moves faster than Mars.
(1A)
(b) (i)
(1A)
Sometimes the Earth passes Mars.
(1A)
When this happens, Mars appears
to move backwards in the sky as
observed on the Earth, as shown in
the figure above.
10
11
(1A)
The graph is a straight line
(1A)
passing through the origin.
(1A)
(a) (i)
The geocentric model is the theory
(Include epicycle and deferent, and
that the Earth is at the centre of the
with the Earth at the centre.) (1A)
universe, and the Sun and other
The motion of a planet is
celestial objects move around it.
(1A)
composed of two separate circular
(ii) People liked to think that the Earth
motions as shown in the figure
above.
was the centre of the universe
(1A)
When the planet moves from B to
because they thought that human
C, retrograde motion occurs. (1A)
should be at an important place of
the universe.
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(1A)
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E1 Astronomy and Space Science
(b) (i)
Chapter 2 Astronomy through History
Kepler’s first law states that the
(ii) Any one of the following
planets orbit the Sun in ellipses,
(corresponding to (i)):
with the Sun at one focus. /
The Moon with mountains, valleys
Kepler’s second law states that the
and craters disagreed with the
line joining the Sun and a planet
earlier thought that the Moon was a
sweeps out equal areas in equal
perfect, smooth sphere.
intervals of time.
The Sun with sunspots disagreed
(1A)
(ii) Venus moves in an elliptical orbit
12
(a) (i)
(1A)
with the earlier thought that the
around the Sun./ Comet Halley
Sun was a perfect sphere.
sweeps quickly through the inner
The four moons orbiting Jupiter but
part of the solar system and moves
not the Earth disagreed with the
slowly through the outer space.
earlier thought that the Earth was
(1A)
the centre of everything.
Use circles for the orbits.
(1A)
The complete cycle of phases
Use epicycles.
(1A)
shown by Venus could not be
(ii) Ptolemaic theory suggested that the
explained by the earlier thought
Earth was the centre of universe
that Venus moved around the
while Copernican theory suggested
Earth.
that the Sun was the centre of
universe.
(c)
(1A)
In Ptolemaic view, the looping
motions of planets were real while
in Copernican view, they were
(b) (i)
apparent.
(1A)
Any one of the following:
(1A)
The Moon has mountains, valleys
(Elliptical orbit with the Sun at a focus,
and craters.
shaded areas of equal sizes.)
The Sun has dark patches which
(1A)
If Comet Kohoutek sweeps out equal
are sunspots, and the Sun rotates.
areas in equal intervals of time on its
There are four moons orbiting
orbit, it must move much slower (shown
Jupiter.
by a much shorter part of its orbit of the
Venus shows a complete cycle of
swept area) and spend more time beyond
phases.
the outermost planets.
(1A)
This supports Kelper’s second law.
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E1 Astronomy and Space Science
Chapter 2 Astronomy through History
Physics in articles (p. 64)
(a) A moon orbits a planet while a planet orbits a
star.
(1A)
(b) The fact that another planet has moons (1A)
proved that the Earth is not the centre of
(c)
everything.
(1A)
Any one of the following:
(1A)
The Moon has mountains, valleys and craters.
The Sun has dark patches which are sunspots,
and the Sun rotates.
Venus shows a complete cycle of phases.
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