Ranked by degree, not by house
Chara means movable. These karakas are not the fixed ones, such as the Sun as a natural significator of father. They are assigned from the janam kundli by comparing the degrees each graha has travelled inside its own sign, from 0 to 30. The graha with the highest degree is Atma Karaka, the significator of the self and the soul's work in this life. Next comes Amatya Karaka, career and the people who advise. Then Bhratru Karaka, siblings and courage. Matru Karaka, mother and the ground of home. If eight karakas are used, Pitru Karaka, father, sits next. Then Putra Karaka, children and intelligence. Gnati Karaka, relatives, rivals, and the difficult people. Dara Karaka, the spouse, is the graha with the lowest degree. Ketu is never a chara karaka. The houses still matter. This list is a second language laid over the same chart.
Why they get replaced, and what changes
Replacement happens when two grahas are so close in degree that they compete for the same seat. Often they share the same integer degree, and the one with more minutes holds the karaka. The other is the replacement. In that graha's dasha, or after a clear event, the first karaka's job can pass to the second. Life then changes in the area that karaka rules. A career that was going one way starts being lived through another planet's nature. A bond changes hands. A role in the family is filled by someone else, or by a different version of you. This is not a small mood. It is a handover of who does that work in the life.
When Atma Karaka is replaced
Atma Karaka can be replaced. It is uncommon, and it is the heaviest of these handovers. The AK is the planet that has travelled furthest in its sign. It describes what the life is for, the grain of the person, the work the soul came to do. If another graha sits almost as far, that second graha can take the throne, share it, or wait and take it in its own dasha. The person may live two purposes. A first identity gives way to a second. A vocation turns. After a crisis, the life that made sense under the first AK no longer fits, and the replacing graha names the new path. The soul is not gone. Another graha is now speaking for it.
When the other karakas are replaced
Each of the other seats has its own handover. Amatya Karaka replacement changes work, the advisor, the way a profession is done. Bhratru Karaka replacement changes siblings, peers, and courage: who stands with you, and whether you stand alone. Matru Karaka replacement touches mother and home. Pitru Karaka, when the eight-karaka list is used, touches father and guides. Putra Karaka replacement changes children, students, and the intelligence that creates. Gnati Karaka replacement changes rivals, illness, and the people who obstruct. Dara Karaka replacement changes the spouse or the kind of partnership the life will hold. In each case the first karaka sets the scene. The second takes the seat. Ask which part of life has already turned. The replaced karaka is often that part.
A mantra for holding the teaching
To grasp chara karakas, sit with the Atma Karaka of the chart, not with a generic lucky sound. Repeat the mantra of whichever graha holds that seat: the Sun's, the Moon's, Mars, Mercury, Jupiter, Venus, Saturn, or Rahu, according to the janam kundli. That graha is the door into the whole list. For the teaching itself, a short Brihaspati mantra is used: Om brim brihaspataye namah. Jyotish is Brihaspati's craft. The sound is for attention, not a bargain with the sky. Recite it when you study the degrees. Then look at the chart again.
How retrogression affects replacement
A retrograde graha is moving backwards through its sign, so its degree is falling. That motion is why replacement is more likely. A retrograde planet can give up the karaka it currently holds as its degree drops, or take the karaka of the planet just above it, the one it already occupied. Rahu is always retrograde. In the eight-karaka scheme many Jaimini readers therefore count Rahu as thirty degrees minus the listed degree in the sign, so its rank is not read as a direct planet's rank. A retrograde Atma Karaka is a soul that looks back: unfinished work, a second take, a purpose that returns. Read the listed degree first. Then ask whether that graha is retrograde. The replacement often lives in that gap.
Eight chara karakas or seven
Parasara gives both lists. Seven chara karakas use the Sun, Moon, Mars, Mercury, Jupiter, Venus, and Saturn. Rahu is left out. There is no separate Pitru Karaka. Father is then read from Bhratru Karaka, from the ninth house, or from the Sun, as the rest of the chart requires. Eight chara karakas include Rahu and add Pitru Karaka, father, between mother and children. Ketu is still never used. The eight-fold list is the one most often used for worldly life: work, marriage, parents, children. The seven-fold list is the older shorter scheme, and some readers keep it for questions of path and release. If two grahas sit at identical degrees, some drop Rahu and use seven so the list can be counted cleanly. A reading should say which scheme it is using. The janam kundli is the same sky. The ranking is the choice.
How to ask this here
You do not need to rank the degrees by hand before you ask. Bring the date, time, and place of birth. VedicAstrology.com calculates the sidereal janam kundli. Then ask who the Atma Karaka is, whether a karaka is being replaced, or what a change of work, parent, child, or partner has to do with this list. The houses and the dasha still belong to the answer. Chara karakas name which graha is doing that job. They do not replace the rest of the chart.

