Every sign divides into three ten-degree segments. Which planet rules each segment depends on which scheme you are using, and there is more than one.
The Chaldean order of faces. This is the scheme used throughout this site, and it should be named rather than assumed. Run the seven visible planets in the Chaldean order, Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon, which is their order by apparent speed, slowest first, start with Mars at zero degrees of Aries, and assign one planet to each ten-degree segment continuously around the circle. Because thirty-six is not a multiple of seven, the sequence does not repeat by sign, and after five turns it closes exactly at the end of Pisces. That elegance is part of why the scheme stuck.
The segments assigned this way are the faces, prosopa in Greek. In the traditional scheme of essential dignity they are the weakest rank there is, below rulership, exaltation, triplicity and term. A planet in its own face was described by later writers as being like a man defending his own house from the doorway: it has something, but barely.
The triplicity scheme. The competing arrangement gives the three decans of a sign to the rulers of the three signs of its own element, in zodiacal order. The decans of Aries then go to Mars for Aries, the Sun for Leo, and Jupiter for Sagittarius. This is the drekkana of Indian astrology and it has a Western following too.
They disagree, and not marginally. Compare the two across the first two signs:
- Aries, first decan: Mars in both schemes. Agreed.
- Aries, second decan: the Sun in both. Agreed.
- Aries, third decan: Venus by the faces, Jupiter by triplicity.
- Taurus, first decan: Mercury by the faces, Venus by triplicity.
- Taurus, second decan: the Moon by the faces, Mercury by triplicity.
Two decans in every three come out differently. Any interpretation that leans on the sub-ruler is therefore an interpretation of one scheme, and a reader who has met the other one elsewhere is not looking at a mistake.
The Golden Dawn attribution is not a third scheme. The Golden Dawn mapped the thirty-six numbered minor arcana, the twos through tens of the four suits, onto the thirty-six decans in zodiacal order from zero Aries, and took the planet for each card straight from the Chaldean faces. Two of Wands is Mars in Aries because Mars is the face ruler of the first decan of Aries. It is an overlay on the face scheme, not a rival to it, and the tarot material elsewhere on this site agrees with the decan rulers here for that reason.