Using basic mathematical knowledge to solve problems in our solar system.

1. The planets of our solar system
Since 1995 astronomers have detected more than 350 planets
orbiting distant stars.
Our solar system has eight planets, and astronomers have
studied their movements for thousand years.
The most interesting phenomena happen when the planets are
in direct positions.
The following picture shows us a simple system of three planets
in our solar system.
Each planet revolves around the star with a different rhythm.
So, it is a challenge to predict when they will line up again in
the same position.

2. Problem 1
An astronomer identifies three planets, A, B, C, and their star in
their line along the track every 1, 2 and 4 years, moving in a
clockwise direction.
Using the following chart, draw a series of new diagrams in
order to show where the planets in their orbits are going to be
after:
Α) 1 year Β) 2 years C) 3 years D) 4 years
Problem 2
Suppose that the three planets, A, B and C, and their star are
straight along the track every 2 years, 3 years and 12 years.
Α) How long will it take the three planets to line up again?
Β) Where are the planets going to be 6 years later?
The phenomenon of "alignment" along the trajectory
happened with Mercury, Venus and Mars on June 24, 2005.
The Earth takes three hundred sixty-five days to make a full
orbit, while Mercury 88 days and Venus 224 days. So, how
much time between alignments will each planet require to
make a whole range of orbits around the Sun and return to the
model shown?

3. Problem 3
How large or small are the planets of our solar system?
The 26 planets of the solar system on the same scale:
3.1 - What fraction expresses how many are smaller than our
Moon?
3.2 - What fraction expresses the planets that are bigger than
the Moon?
3.3 - What fraction expresses how many (including the Moon)
are about the same size as our moon?
3.4 -Oberon is 1/7 of the Earth's diameter, Io is 1/3 of the
Earth's diameter, and Titania 4/9 the diameter of Io
Oberon is 1/7 of the Earth’s diameter
Which is larger in diameter, Oberon or Titania?

4. The scale of the Solar System model - Compare our planets
1. Jupiter is 7/6 the diameter of Saturn, and Saturn is 5/2 the diameter
of Heaven.
Express as a simple fraction, how big Uranus is in relation to Jupiter.
2. The Earth is 13/50 the diameter of Uranus.
Express as a simple fraction, how much bigger Saturn is than the Earth.
3. The biggest non-planet objects in our solar system are our moon
(radius = 1,738 kilometers), Io (1,810 kilometers), Eris (1,500 kilometers),
Europa (1,480 kilometers), Ganymede (2,600 kilometers), Callisto (2,360
kilometers), Makemake (800 kilometers), Titan (2,575 kilometers), Triton
(1,350 kilometers), Pluto (1,200 kilometers), Haumeia (950 kilometers).
Create a bar graph ordering them from the smallest to the largest.
For this sample, which is the: Α) Average of their ray? Β) The average
radius?
4. Mercury is the smallest of the eight planets of our solar system.
If the radius of Mercury is 2,425 kilometers, how will you create a scale
model of non-planets if we set the diameter for the Mercury disk as 50
millimeters?
5. Saturn is 10 times larger than Venus, and Venus is 1/4 the size of
Neptune. How much bigger is Saturn than Neptune?
6. The Earth is 2 times bigger than Mars, but only 1/11 the size of
Jupiter. How much bigger is Jupiter compared to Mars?

5. The distances of the Universe
Our solar system is so large that it is almost impossible to imagine the
size of it if you use standard units such as miles.
The distance of the Earth from the Sun is 93 million miles (149 million
kilometers).
The distance to the farthest planet, Neptune, is about 3 billion miles
(4,500 million kilometers).
The best way to estimate the size of our solar system is by creating a
measurement scale which shows us how far the eight planets are from
the Sun.
Astronomers use the distance between the Earth and the Sun, which is
93 million miles, as a new unit called astronomical unit (1,00 A.U.).
The table below shows us the distance from the Sun to the eight planets
of our solar system:
Planet Distance in million kilometers Astronomical Units
Mercury 57
Venus 108
Earth 149
Mars 228
Jupiter 780
Saturn 1,437
Uranus 2,871
Neptune 4,370
How many astronomical units is Mercury from the Sun?

6. The distances of the Universe
Our solar system is so large that it is almost impossible to imagine the
size of it if you use standard units such as miles.
The distance of the Earth from the Sun is 93 million miles (149 million
kilometers).
The distance to the farthest planet, Neptune, is about 3 billion miles
(4,500 million kilometers).
The best way to estimate the size of our solar system is by creating a
measurement scale which shows us how far the eight planets are from
the Sun.
Astronomers use the distance between the Earth and the Sun, which is
93 million miles, as a new unit called astronomical unit (1,00 A.U.).
The table below shows us the distance from the Sun to the eight planets
of our solar system:
Planet Distance in million kilometers Astronomical Units
Mercury 57
Venus 108
Earth 149
Mars 228
Jupiter 780
Saturn 1,437
Uranus 2,871
Neptune 4,370
How many astronomical units is Mercury from the Sun?