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5.15

# Your mission to Mars: the data

The following scenario is much more demanding in terms of the maths problems you are going to tackle, but there are lots of hints and help, which you don’t need to use, but are there if you get stuck.

The following bar chart illustrates the rate of muscle loss experienced by SkyLab crews during their various missions.

Reference for this bar chart

Below is a data set, created solely for the purposes of this exercise. It describes the reduction in three health indicators with increasing mission length.

Days into mission % Reduction in body mass % Reduction in leg strength % Reduction in cardiac output
10 2.15% 2.50% 1.50%
20 4.30% 5.00% 3.00%
30 6.45% 7.50% 4.50%
40 8.60% 10.00% 6.00%
50 10.75% 12.50% 7.50%
60 12.90% 15.00% 9.00%
• Journey times vary considerably according to the relative positions of Earth and Mars at the time of launch. For your mission use a figure of 220 days each way.

• Acceleration due to gravity on Earth is approximately 10 m s-2. (Actual value is 9.8 m s-2, but it is usually rounded up to 10.) Then Acceleration due to gravity on mars is is 3.8 m s-2. To match what we do with Earth gravity, we will round this up to 4 m s-2.

• If an astronaut has a mass of 100 kg on Earth, their weight would be = 100 kg x 10 m s-2 = 1000 kg m s-2 or 1000 Newtons (N)

• On Mars the weight of this astronaut would be 100 kg x 4 m s-2 = 400 N

What would be the mass and the weight of the astronaut in deep space?

Using the data in the table, what would the mass of the astronaut be 30 days into the mission?