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The solar wind

Electricity and magnetism · level 8, lesson 2 of 6

A question to start

The Sun is always blowing a thin wind of charged particles out into space. How hard does it push by the time it reaches Mars?

The idea

The solar wind is a stream of protons and electrons flowing out from the Sun's hot outer atmosphere in every direction. Near Earth's orbit it moves at about 400 km/s on average, with about 3 to 10 particles in each cubic centimetre. Fast streams reach 750 km/s and more.

As it spreads out, its density falls with the square of the distance from the Sun, while its speed stays about the same. It pushes on whatever it meets with a dynamic pressure

\[p = \rho v^2 = n m_p v^2,\]

where \(n\) is the number of protons per cubic metre and \(m_p = 1.67\times10^{-27}\) kg.

The solar wind Mars Earth
Distance from the Sun 227.9 million km (1.52 AU) 149.6 million km (1 AU)
Protons per cm³, if Earth's is 5 about 2.2 5
Pressure at 400 km/s about 0.58 nPa about 1.34 nPa
Earth: 1 AUMars: 1.52 AU

Worked examples

1. At Earth. \(n = 5\) per cm³ \(= 5\times10^6\) per m³: \(p = 5\times10^6 \times 1.67\times10^{-27} \times (4\times10^5)^2 = 1.34\times10^{-9}\) Pa.

2. At Mars. \(1.524^2 = 2.32\), so the density is \(5/2.32 = 2.2\) per cm³ and the pressure \(1.34/2.32 = 0.58\) nPa.

3. The trip. At 400 km/s, the wind takes \(1.496\times10^{11}/4\times10^5 = 3.7\times10^5\) s, about 4.3 days, to reach Earth from the Sun, and about \(4.3 \times 1.52 = 6.6\) days to reach Mars.

Try it

  1. What is the solar wind made of?
  2. Why does the solar wind thin out with distance?
  3. A fast stream at Earth has 3 protons per cm³ at 750 km/s. Find its pressure.
  4. Jupiter is 5.2 AU from the Sun. By what factor is the solar wind's density lower there than at Earth?
Answers
  1. Protons and electrons streaming out from the Sun.
  2. It spreads over a sphere whose area grows with the square of the distance.
  3. \(3\times10^6 \times 1.67\times10^{-27} \times (7.5\times10^5)^2 = 2.8\times10^{-9}\) Pa.
  4. \(5.2^2 = 27\) times lower.

Common mistake

"A tiny pressure cannot matter." A nanopascal is minute, but it acts on a whole planet's upper air, nonstop, for billions of years.

Where it leads