Speed of Sound on Mars

How can I calculate the speed of sound on Mars?
- question from Henk Kuyer
We have previously written a number of articles about how to calculate the speed of sound within Earth's atmosphere and the process of converting between speed and Mach number. The fundamental procedures used to perform these calculations also apply to the atmosphere of other worlds like the planet Mars. As we have seen in our prior discussions of this subject, the speed of sound depends predominantly on temperature. In order to determine the speed of sound on a different planet, we first need to establish a standard atmosphere model that tells us the typical temperature to expect at different altitudes on that planet.

The thin atmosphere of Mars

Luckily, NASA and other space agencies have sent several spacecraft to Mars that have collected measurements of its atmosphere to create such a model. One probe that conducted a particularly comprehensive study of the atmosphere was NASA's Mars Global Surveyor launched in 1996. NASA has used data collected by this craft to construct a preliminary standard atmosphere model for Mars comparable to the 1976 standard atmosphere developed for Earth. This model will likely be revised in the future once more readings of the Martian atmosphere are collected, but it does provide the information needed to calculate an approximation of the speed of sound on Mars.

As we have seen in previous articles, the equation used to calculate the speed of sound is

where

a = speed of sound [ft/s or m/s]
γ = specific heat ratio [dimensionless]
R = specific gas constant [ft-lb/slug/°R or J/kg/K]
T = atmospheric temperature [degrees Rankine (°R) or degrees Kelvin (K)]
We typically treat the values of γ and R as constants, but these quantities are only constant for a particular substance. In Earth's atmosphere, the values of the constants have been determined to be
γair = 1.4
Rair = 1716 ft-lb/slug/°R in English units or 287 J/kg/K in Metric units
The values of these constants change on Mars, however, since the Martian atmosphere is much thinner with a different composition than that of air on Earth. Whereas Earth's atmosphere contains large quantities of nitrogen and oxygen, the atmosphere of Mars primarily consists of carbon dioxide. Measurements of Martian air have determined the specific heat ratio and specific gas constant on the red planet are
γMars = 1.29
RMars = 1147 ft-lb/slug/°R in English units or 191.8 J/kg/K in Metric units
The final piece of information needed to compute the speed of sound is the atmospheric temperature. The NASA data available in the links listed above provide the following equations to calculate this temperature for the desired altitude.

In English units, the first equation models the lower atmosphere and applies up to an altitude of 22,960 ft. The second equation is used above that altitude for the upper atmosphere to an altitude of 100,000 ft. These two regions of the atmosphere are referred to as the troposphere and stratosphere just like on Earth.

where

T = atmospheric temperature [degrees Fahrenheit (°F)]
h = altitude [feet]
Similar equations are provided for the Metric system with a lower atmosphere equation that applies to the troposphere up to 7,000 m and an upper atmosphere model that computes the temperature in the stratosphere up to 30,500 m.

where

T = atmospheric temperature [degrees Celsius (°C)]
h = altitude [meters]
Note that the temperatures computed using these equations are in Fahrenheit or Celsius whereas those needed for the speed of sound equation are in Rankine or Kelvin. We need to convert these temperatures to the appropriate unit using the following conversion factors.

convert into conversion

We now have all the information needed to calculate the speed of sound at any altitude within the Martian atmosphere. As an example, let us use the data provided above to solve for the speed of sound at an altitude of zero. At this lowest point within the atmosphere, the temperature profile equations tell us that the "sea level" temperature within the standard atmosphere is -25.68°F or -32°C. Converting these units to an absolute temperature scale produces values of 434°R in the English system and 241 K in Metric units. Let us now solve the speed of sound equation using these values.

This methodology tells us that the standard "sea level" speed of sound on Mars is equal to

• 801.3 ft/s
• 244.2 m/s
• 546.4 mph
• 879.3 km/h
• 474.8 knots
We can use the same technique to solve for the speed of sound at higher altitudes, just as we did previously to develop Mach 1 vs. altitude tables for Earth. The corresponding table shown below is in English units and provides the speed of sound in miles per hour (mph), feet per second (ft/s), and knots (kts) for altitudes from 0 ft to 100,000 ft in 2,000 ft increments.

Mach 1 vs. altitude in English Units on Mars

This next table is in the Metric System and indicates the speed of sound in kilometers per hour (km/h), meters per second (m/s), and knots (kts) for altitudes from 0 m to 30,000 m in 1,000 m increments.

Mach 1 vs. altitude in Metric Units on Mars

Note that these tables are also color-coded like those previously presented for Earth's atmosphere. The atmosphere on our planet features regions where the temperature decreases (blue), increases (red), and remains a constant (green). The Martian atmosphere, on the other hand, grows continually colder with increasing altitude, so these tables only include the color blue. The rate at which the temperature decreases becomes more rapid around 22,960 ft (7,000 m), and this point defines the boundary between the troposphere and stratosphere.

Since the temperature within the Martian atmosphere is always decreasing, the speed of sound also decreases at the same rate. The behavior of the speed of sound within the atmosphere of Mars is compared to that on Earth in the following figure. Here we can clearly see the continually decreasing speed of sound on Mars compared to the much more complex behavior observed on Earth.

Comparison of the speed of sound on Earth and Mars

Readers should be aware that the atmosphere of Mars is much less stable than that of Earth making it more difficult to establish a standard atmosphere model. Because the atmosphere is so thin, the temperature at any given location and altitude varies considerably more so than on Earth. These fluctuations in temperature between day and night have such a strong influence on the atmosphere that the troposphere can be anywhere from 6 to 12 miles (10 to 20 km) high during the day to non-existent at night.

This behavior was observed at the sites of the Viking landers that reached Mars in 1976. At the warmest time of day, the ground temperature was near freezing but the air temperature at altitude was considerably lower. This difference in temperature created convection air currents and a troposphere. At night, both ground and air temperatures dropped much lower but were about the same temperature. This lack of a significant temperature difference eliminated the convection process and caused the troposphere to vanish. Additional fluctuations due to location and seasonal change also produce large variations in atmospheric behavior on Mars.
- answer by Jeff Scott, 30 October 2005

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