Snowflakes with the SKA

In 1980, Carl Sagan famously stated

The total amount of energy from outside the solar system ever received by all the radio telescopes on the planet Earth is less than the energy of a single snowflake striking the ground

This remarkable statement was true¹ in the 1980s. But how does this stack up in the era of the Square Kilometre Array?

Here's a small calculation to test Sagan's claim. There is a galaxy far, far away called TGSS1530. TGSS1530 is one of the most distant galaxies detected in the radio band.

We can estimate the amount of energy received using the equation

$$E=SABt$$

Where

• S is the source flux density in Jy (W m-2).

• A is the collecting area of the telescope in m².

• B is the receiver bandwidth in MHz.

• t is the observation time in seconds.

For TGSS1530, S \= 170 mJy. For SKA-Low, A = 419,000 m² and B \=300 MHz.

If we observed TGSS1530 for an entire year, the amount of energy received would be

from astropy import units as u

S = 0.17 * u.Jy
t = 1 * u.yr
A = 419000 * (u.m**2)
B = 300e6 * u.Hz
(S * A * t * B).to('J')
>> 6.743 uJ

That is, about 7 microJoules. Here, I've used astropy.units to handle unit conversions and to make sure the calculation is dimensionally consistent.

How does this compare to the kinetic energy of a snowflake? Taking some ballpark numbers from Google that a snowflake has a mass of 3 mg, and average velocity of 2.4 km/h. Using \(E = mv^2\):

snowflake_mass = 3 * u.mg
snowflake_vel  = 2.4 * u.km / u.hr  
E_snowflake = 1/2 * snowflake_mass * snowflake_vel**2
E_snowflake.to('J')
>> 0.667 uJ

That is, a snowflake has about 0.7 microJoules of energy. So, SKA-Low will receive 10 snowflake's worth of kinetic energy from TGSS1530 within a year.

So Carl Sagan's quote is now out-of-date. Nevertheless, the fact that we can measure the amount of energy in "units of snowflake kinetic energy" really drives home just how sensitive modern radio telescopes are, and just how faint the signals that radio telescopes measure are.

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1. There is a small caveat: "received" in this context means "picked up by the receiver", the telescope component that converts electromagnetic waves from space into a signal on a coaxial cable. This is important as receivers have a finite bandwidth, and in the 1980s the receiver bandwidth was generally smaller than today's telescopes.