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Charging on Mars

Electricity and magnetism · level 4, lesson 6 of 6

A question to start

You take a solar charger to Mars. On Earth, it fills a battery in 2 hours of bright sunshine. How long would it take on Mars?

The idea

A battery's capacity is often given in amp-hours (Ah): the charge it holds. A 10 Ah battery could give 1 A for 10 hours, or 2 A for 5 hours. So the time to charge it is about

\[t = \frac{Q}{I},\]

with \(Q\) in amp-hours and \(I\) in amps.

A solar panel's current depends on the sunlight. Mars is about 1.5 times as far from the Sun as Earth, so the sunlight there is much weaker. Above the air, at noon, it is:

The same panel at noon, above the air Mars Earth
Sunlight 586 W/m² 1,361 W/m²
Current from the panel about 2.15 A 5 A
Time to charge a 10 Ah battery about 4.7 hours 2 hours

The current falls in proportion to the sunlight: \(586/1361 = 0.43\), so the panel gives only 43% of the current.

EarthMars2 hours4.7 h

Worked examples

1. On Earth. \(t = 10/5 = 2\) hours.

2. On Mars. \(I = 5 \times 0.43 = 2.15\) A, so \(t = 10/2.15 = 4.7\) hours.

3. Real days. These are noon values above the air. Air, dust and the Sun's angle all cut the current further, so a real charge takes longer on both planets, and on Mars even a whole day of sunshine might not be enough.

Try it

  1. How long does a 20 Ah battery take to charge at 4 A?
  2. Why does a panel give less current on Mars?
  3. A panel gives 3 A at noon on Earth, above the air. What would it give on Mars?
  4. On Mars, how long would that panel take to fill a 6.5 Ah battery?
Answers
  1. \(20/4 = 5\) hours.
  2. Mars is farther from the Sun, so the sunlight is weaker.
  3. \(3 \times 0.43 = 1.29\) A, about 1.3 A.
  4. \(6.5/1.29 = 5.0\) hours.

Common mistake

"A 10 Ah battery holds 10 hours of energy." It holds 10 amp-hours of charge. How long it lasts depends on the current you draw: 10 hours at 1 A, but only 1 hour at 10 A.

Where it leads