Kepler, Johannes

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Kepler, Johannes
Kepler, Johannes (1571-1630) German astronomer
and natural philosopher, noted for formulating
and verifying the three laws of planetary motion.
These laws are now known as Kepler's laws.
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Keplers Laws
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1. Law of Orbits -According to Kepler's first
law, the planets orbit the Sun in elliptical
paths, with the Sun at one focus of the ellipse.
2. Law of Areas -The second law states that the
areas described by the straight line joining the
centre of the planet and the centre of the Sun
are equal for equal time intervals that is, the
closer a planet comes to the Sun, the more
rapidly it moves.
Area of ? ASB Area of ? CSD
SUN
D
S
C
B
A
Planet
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3. Law of Periods Kepler's third law states
that the ratio of the cube of a planet's mean
distance, d, from the Sun is a constant to the
square of its orbital period, t that is, d3/t2
is the same for all planets. (Or, T2 K d3 ).

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This law explains that The farther the planet
from the sun, the more its orbital period is. As
Mercurys (the nearest planet to the sun) Orbital
Period is only 88 earth days and Plutos (the
farthest planet from the sun) Orbital Period is
about 248 earth years.
Orbital Period of a planet is the time it takes
to complete one revolution around the Sun.
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SUN
Distance , d
Orbital Period, T
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Q - Mean distance of planet Mars from the sun is
about 1.5251 times more than the mean distance of
the Earth from the Sun. If the orbital period of
the Earth is 365.25 days, find out the orbital
period of Mars.
Ans - Suppose distance of the Earth from the
Sun d1
Orbital period of the Earth, T1
365.25 days. Distance of Mars from the Sun,
d2 1.5251 d1 Suppose orbital
period of Mars T2
According to Keplers 3rd law - T2 K
d3 (Where K is a Constant)
So -
(
)
(
2
)
T2
3
d2

T1
d1
(
)
)
(
3
2
T2
d2
/2

T1
d1
)
(
3/2
T2
1.5251
d1
T1 365.25 days

T1
d1
d1
(
)
3
T2
/2
2

(1.235)
T1
Earth
T2
1.5251 d1
(1.235)3

1.88
T1
T1
T2
1.88 X
Mars
1.88 X 365.25
Orbital Period of Mars, T2
about 687 days
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Q 1 - Mean distance of planet Earth from the sun
is about 1.382 times more than the mean distance
of Venus from the Sun. If the orbital period of
Venus is 225 days, find out the orbital period of
Earth.
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Q 2 - Mean distance of planet Mars from the sun
is about 2.104 times more than the mean distance
of Venus from the Sun. If the orbital period of
Venus is 225 days, find out the orbital period of
Mars.
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Q 3 - Mean distance of planet Earth from the sun
is about 2.5833 times more than the mean distance
of Mercury from the Sun. If the orbital period of
Mercury is 88 days, find out the orbital period
of Earth.
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Q - Mean distance of planet Earth from the sun
is about 1.382 times more than the mean distance
of Venus from the Sun. If the orbital period
of the Venus is 225 days, find out the orbital
period of Earth.
Ans - Suppose distance of Venus from the Sun
d1
Orbital period of the Venus, T1
225 days. Distance of Mars from the Sun, d2
1.382 d1 Suppose orbital period of Earth
T2
According to Keplers 3rd law - T2 K
d3 (Where K is a Constant)
So -
(
)
(
2
)
T2
3
d2

T1
d1
(
)
)
(
3
2
T2
d2
/2

T1
d1
)
(
3/2
T2
1.382
d1
T1 225 days

T1
d1
d1
(
)
3
T2
/2
2

(1.1756)
Venus
T1
T2
1.382 d1
(1.1756)3

1.624
T1
T2
T1
1.624 X
Earth
1.624 X 225
Orbital Period of Mars, T2
about 365 days
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Q - Mean distance of planet Mars from the sun is
about 2.104 times more than the mean distance of
the Venus from the Sun. If the orbital period of
Venus is 225 days, find out the orbital period of
Mars.
Ans - Suppose distance of Venus from the Sun
d1
Orbital period of Venus, T1
225 days. Distance of Mars from the Sun, d2
2.104 d1 Suppose orbital period of Mars
T2
According to Keplers 3rd law - T2 K
d3 (Where K is a Constant)
So -
(
)
(
2
)
T2
3
d2

T1
d1
(
)
)
(
3
2
T2
d2
/2

T1
d1
)
(
3/2
T2
2.104
d1

T1 225 days
T1
d1
d1
(
)
3
T2
/2
2

(1.451)
T1
Venus
T2
(1.451)3

3.054
T1
2.104 d1
T2
T1
3.054 X
Mars
3.054 X 225 days
Orbital Period of Mars, T2
about 687 days
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Q - Mean distance of planet Earth from the sun
is about 2.5833 times more than the mean distance
of Mercury from the Sun. If the orbital period of
Mercury is 88 days, find out the orbital period
of Earth.
Ans - Suppose distance of Mercury from the
Sun d1
Orbital period of the Mercury, T1
88 days. Distance of Earth from the Sun, d2
2.5833 d1 Suppose orbital period of
Earth T2
According to Keplers 3rd law - T2 K
d3 (Where K is a Constant)
So -
(
)
(
2
)
T2
3
d2

T1
d1
(
)
)
(
3
2
T2
d2
/2

T1
d1
)
(
3/2
T2
2.5833
d1

T1 88 days
T1
d1
(
)
d1
3
T2
/2
2

(1.6072)
T1
Mercury
T2
2.5833 d1
(1.6072)3

4.15
T1
T2
T1
4.15 X
Earth
4.15 X 88
Orbital Period of Mars, T2
about 365 days