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Let’s look at important things here –
Jupiter - It is the most benefic planet and it represents all the auspicious things like Knowledge, Wisdom, Law, Guru, Spirituality, Religion, Philosophy, Literature, Elderly People and Children etc. For a girl, Jupiter also represents Husband.
Ardra - Ardra is nakshatra of transformation, turmoils and chaotic events. This can be most closely related with accidents and emergencies. For more information on Ardra, please check this link - https://www.astrosaxena.com/ardranaksh.
Gemini - As Ardra is part of Gemini, Gemini sign and its representations become important here. Gemini is the 3rd sign of zodiac belt, so it represents many things related with 3rd house of horoscope like, Communication Skills (either written, oral or even by sign language), Marketing, Business etc. It is a sign basically related with communications and business ideas. Gemini is divided into 2 and half nakshatra of Mrigashira, Ardra and Punarvasu. Gemini's lord is Mercury, which is significator of Communications.
Mercury - As Mercury rules Gemini, Mercury’s position and dignity is important to know about the overall functioning of any planet in Mrigshira/Gemini.
Rahu - As Ardra is ruled by Rahu, Rahu's position and dignity will also have an important role in functioning and results of any planet in Ardra.
Houses Involved – Also, we can’t afford to forget the houses involved as a planet can be ruling different houses and sitting in different house for every person as per ascendant and planet’s position. To know overall affect, we have to consider the houses involved as those areas of life are being impacted.
Interpretation of Jupiter in Ardra Nakshatra – Jupiter is in enemy sign here and it is in a difficult nakshatra of Rahu. As Ardra is all about chaos & changes and Jupiter is all about expansion of things, here Jupiter can expand the chaos and changes in life. It can expand the chaos related with house where Jupiter is placed and houses which Jupiter rules. As Jupiter also represent person's belief system, person can go through major change in beliefs, either religious or spiritual. They can be rebellious in matters of what they believe-in. At the same time, they can be counselors or guides to others who are going through chaos in their lives. They can also be seen as Doctors or Scientists.
In relationship matters, they can go through major changes and instabilities. It would be normal for them to go through multiple relations.
Role of Mercury – Mercury's placement is important to guide Jupiter in right direction as it is Gemini's lord.
Role of Rahu - Rahu's placement is important to guide Jupiter in right direction as it is Ardra's lord.
Other Factors – And of course, we need to consider conjunction, aspects, house lordship, house position and dashas etc to know the exact results of Jupiter in Ardra. So, we always need to take a holistic view of chart rather than just 1 planetary position.
Conclusion – So, this is how I see Jupiter in Ardra can work in a chart.