Teacher's Answer Key

The IMAGE satellite's construction involves a number of different instruments. These instruments are analyzed to determine the dimensions that will provide the most efficient satellite while minimizing the weight and cost.

In order to help you understand the possible factors involved in the dimensions, mass and cost; complete the following activities.

1. Calculate the dimensions of the following instruments and spacecraft components:

Instrument Dimension Double Triple Quadruple
LENA 8100 64800 219700 518400
MENA 8100 64800 218700 518400
HENA 9000 72000 243000 576000
TAC/ADC 1620 12960 43740 103690
HV Electronics 2592 20736 69984 165888
Spectrometer 35712 285696 964224 2285568
WB Camera 5070 40560 136890 324480
Electronics 5400 39400 129600 307200
Sensors 2250 18000 60750 144000

Note: 'The dimensions for the instruments are in centimeters.

2. When the dimensions of the satellite are doubled, by what factor is the size increased? What factor is the increase when the dimensions are tripled and quadrupled?

Answer = 8,27, 64

3 . Is there any noticeable connection between two or more of these factors of increase?
Answer = Doubling and quadrupling are multiples of each other, and the results of 8 and 64 are multiples as well

4 . The mass of the IMAGE satehfite increases proportional to the volume. If the dimensions are doubled, the mass increases by the cube of the factor or 2x2x2=8. The mass of the satellite is 66. 1 kg. Determine the mass increase when the dimensions are doubled, tripled and quadrupled.
Doubled = 528.8 kg
Tripled= 1784.7 kg
Quadrupled= 4230.4 kg

5. The cost of the satellite also increases proportional to the mass. The cost for the original dimensions is $28.4 million. What is the cost for each of the various increases?
Doubled= $227.2 million
Tripled= $766.8 million
Quadrupled= $1.818 billion

6. In your own words, please write the process involved in determining the dimensions, mass and cost of the IMAGE satellite. Why would a scientist want a 'bigger' satellite?
Answer = Students response will vary. The bigger the satellites the more information that is being sent to the scientists. Bigger does not necessarily mean better.