Transcript How fast do the Planets move? - Teaching Mathematics | "It

INVESTIGATION
How fast do the Planets move?
What is the order of the planets, from closest to the sun to furthest away?
How fast are you travelling right now?
What information would a scientist
need to investigate the speed of an
object?
1. Speed = Distance
Time
2. Need to know: The orbital distance of each
Planet and the time it takes for the planet to
move around the sun.
3. What units should we use to represent speed?
What´s appropriate?
An Astronomical Unit (AU)
One Astronomical Unit is the approximate
distance between the Earth and the Sun.
1 AU ≈ 149,600,000 km.
Why is 1 AU an approximate
distance and not exact?
1. The Earth´s orbit is an ellipse not a perfect circle.
2. There are slight variations in the Earth´s Orbit.
Problem that we now face:
How do you find the circumference of an ellipse?
Formulae do exist but it requires advanced mathematical
techniques to derive.
Are there any shapes that are slightly more simple than an
ellipse that we do know how to find the circumference of?
Assumptions in Mathematics
We can assume that the orbit is
circular to decrease the complexity of
the problem and find an approximate
answer.
Often Mathematicians cannot always find
exact answers to problems because it would
make the problem too difficult to solve.
In these cases, we make simpler assumptions.
Data
Planet
Mercury
Venus Earth
Orbital Radius
(AU)
0.38
0.72
Time to orbit
Sun
88 days
225
days
1
Mars
Jupiter
1.52
5.2
9.45
19.2
30.06
11.9
years
29.45
years
84
years
164.8
years
365 .25 687
days days
Saturn Uranus
Neptune
Pair Challenge 1:
a) The approximate speed of Mercury is 172800 km/h.
Use the data to confirm this.
b) Change your answer to part a) into km/s and then m/s.
Write these answers to 3 significant figures.
Data (1 AU = 149600000 km)
Planet
Mercury
Venus Earth
Orbital Radius
(AU)
0.38
0.72
Time to orbit
Sun
88 days
225
days
1
Mars
Jupiter
1.52
5.2
9.45
19.2
30.06
11.9
years
29.45
years
84
years
164.8
years
365 .25 687
days days
Saturn Uranus
Neptune
Pair Challenge 2:
a) Use Excel to find the speeds of all the planets in the
solar system in km/h, km/s and in m/s.
b) Look at the answers you have in km/s. Do you notice
anything? How could would represent this
information in a more visual way?
Topics Discussed
Content
1.12, 1.13 - Speed, Distance and Time
6.3 - Circumference of Circles
6.1 - Converting between measurements.
11.3 - Scatter Graphs and Correlation.
1.10 - Significant Figures
1.9 – lead onto Standard form.
Skills
Simplifying a problem by making assumptions.
Ways of displaying data.
Appropriate Answers