Conversations with the Earth
Tom Burbine
tburbine@framingham.edu
Quiz on Thursday
• Metric system
• Scientific notation
Why do we use the metric system in
science?
Remember
• A system based on multiples of 10 is much more
intuitive for humans
• We are born with 10 fingers and toes
• The math system that we use is based on 10,
Metric System
• Any system of measurement needs three
fundamental units
– Length - meter
– Mass - kilogram
– Time - second
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1 kilometer = 1,000 meters
1 meter = 100 centimeters
1 centimeter = 10 millimeters
1 kilogram = 1,000 grams
Things you need to know because we will
use the metric system
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one kilometer is 5/8 of a mile
one meter is 3.28 feet
one centimeter is 0.39 inches
1 kg (mass) is equivalent to 2.2 pounds (force) on Earth
We will use the metric system in this class
Does anybody remember the Mars Climate Orbiter?
Mars Climate Orbiter
• Software calculated forces for the
thrusters in English units (pounds).
• People controlling the spacecraft thought
the calculated forces were in Newtons
(metric). (One English pound of force
equals 4.45 Newtons.)
• Changes made to the spacecraft's
trajectory were actually 4.45 times greater
than what the JPL navigation team
believed.
• The spacecraft missed its intended 140 150 km altitude above Mars during orbit
insertion, instead entering the Martian
atmosphere at about 57 km.
http://en.wikipedia.org/wiki/Image:Mars_Climate_Orbiter_2.jpg
• The spacecraft was destroyed
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1 kilometer = 1,000 meters
1 meter = 100 centimeters
1 centimeter = 10 millimeters
1 kilogram = 1,000 grams
one kilometer is 5/8 of a mile
one meter is 3.28 feet
1 kg (mass) is equivalent to 2.2 pounds (force) on Earth
Meter
• How is the meter defined?
Meter
• Originally intended to be one ten-millionth of the
distance from the Earth's equator to the North Pole
• International Prototype Meter was defined as
the distance between two lines on a
standard bar composed of an alloy of
ninety percent platinum and ten percent
iridium, measured at the melting point of ice.
Meter
• Now defined as equal to the distance travelled by light in
vacuum during a time interval of 1⁄299,792,458 of a
second.
Gram and Kilogram
• How are the gram and kilogram defined?
Gram and Kilogram
• How are the gram and kilogram defined?
Gram and Kilogram
• A gram was first decreed to be equal to “the absolute
weight of a volume of water equal to the cube of the
hundredth part of the meter, at the temperature of melting
ice.”
• Now, the International Prototype Kilogram is used as the
standard.
• It is made of a platinum alloy known as “Pt-10Ir”, which is
90% platinum and 10% iridium
International Prototype Kilogram
• Photo of Danish national
kilogram prototype
Second
• The solar day was divided into 24 hours, each of which
contained 60 minutes of 60 seconds each
• So the second was 1⁄86 400 of the mean solar day.
• Now defined as the duration of 9,192,631,770 periods of
the radiation corresponding to the transition between the
two hyperfine levels of the ground state of the cesium-133
atom.
Scientific Notation
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10000 = 104
100000000 = 108
10000000000 = 1010
100000000000000000000 = 1020
0.001 = 10-3
0.0000001 = 10-7
How do you write numbers?
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31,700,000 = 3.17 x 107
2,770,000 = 2.77 x 106
0.00056 = 5.6 x 10-4
0.0000078 = 7.8 x 10-6
How do you do multiply?
• 106 x 108 = 10(6+8) = 1014
• 10-5 x 103 = 10(-5+3) = 10-2
• (3 x 104 ) x (4 x 105) = 12 x 10(4+5) = 12 x 109
= 1.2 x 1010
How do you divide?
• 108/106 = 10(8-6) = 102
• 10-6/10-4 = 10(-6-(-4)) = 10-2
• (3 x 108)/(4 x 103) = ¾ x 10(8-3) = 0.75 x 105
= 7.5 x 104
Always use units for your answers
Stars in the Universe
• Say there are 100 billion galaxies
• Each galaxy has 100 billion stars
• So how many stars in the universe
Answer
• Number of stars in universe
• = (100 x 109) x (100 x 109) = 10000 x 1018
= 1 x 1022 = 10,000,000,000,000,000,000,000
• This is about the same number of grains of sand
in every beach in the world
Questions:
• How many of these 1022 stars have planets?
• How many of these planets have life?
Any Questions?