# What, if any, reduction in radiation exposure does the atmosphere of Mars provide?

In the book "The Case for Mars", cited in this answer, there is a study cited that states that 20-50 REM radiation occurs due to cosmic rays in deep space. It seems likely that the atmosphere of Mars would reduce that somewhat. By how much will the atmosphere of Mars reduce the radiation?

I found at SpaceMath ( http://spacemath.gsfc.nasa.gov ) a document stating that the density of a planetary atmosphere is defined by the exponential function:
$$N(z) = N(0) e^{-z/H}$$

where H is the scale-height of the gas.

The amount of surface shielding for radiation arriving from 90° direction (vertical) is given by evaluating the integral of N(z), which results in:

Equivalent Shielding = $$N(0)H$$

Values listed in that document are:

• Mars: D = 0.020 kg/m3 x 11.1 km = 22 gm/cm2

• Earth: D = 1.2 kg/m3 x 8.5 km = 1,020 gm/cm2

We can extract:

• Mars:

• N(0) = 0.020 kg/m3
• H = 11.1 km
• Earth:

• N(0) = 1.2 kg/m3
• H = 8.5 km

Doing again the math with all steps:

• Mars:

ES = $$0.020 \frac{kg}{m^3} * 11.1 km$$ = $$0.020 \frac{kg}{m^3} * 11100 m$$ = $$0.020 \frac{kg}{m^2} * 11100$$ = $$222\frac{kg}{m^2}$$ = $$222000\frac{g}{m^2}$$ = $$\frac{222000}{10000}\frac{g}{cm^2}$$ = $$22.2\frac{g}{cm^2}$$

• Earth:

ES = $$1.2 \frac{kg}{m^3}* 8.5 km$$ = $$1.2 \frac{kg}{m^3}* 8500 m$$ = $$1.2 \frac{kg}{m^2}* 8500$$ = $$10200 \frac{kg}{m^2}$$ = $$10200000 \frac{g}{m^2}$$ = $$\frac{10200000}{10000} \frac{g}{cm^2}$$ = $$1020 \frac{g}{cm^2}$$

Other values for comparison:

• onboard ISS: $$10 \frac{g}{cm^2}$$
• Apollo space suite: $$0.1 \frac{g}{cm^2}$$

It's worth noting that a bare body on Mars' surface receives half the radiation of an astronaut onboard ISS.

It's also worth noting that to get equivalent shielding of the whole Earth atmosphere by using a water shielding, only 10 meters thickness is required (given that water density is 1000 kg m3, compared to 1.2 kg/m3 for Earth atmosphere).

($$R_{Earth}$$ = 6378 km, $$R_{Mars}$$ = 3374 km)

In tabular format: