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Krishna and Satyabhama ( Sathyabhama ) shared a common paternal ancestor, Anamitra.

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The rule according to rig Veda is that one cannot share a common paternal ancestor for 7 generations and maternal ancestor for 5 generations.

I had encountered this in a book on Rig Veda, but I am not able to recollect it.
Also Manusmriti 3.5 says:

"Marriage should he performed with persons not belonging to the same Pravara;—above the Seventh grade among his paternal relations;—also beyond persons of the same seed;—and above the fifth grade among maternal relations."

Animitra was at least 11 generations ago for Krishna (https://en.wikipedia.org/wiki/Vrishni)

Gotras I believe are an easy way to enforce this rule.

coder_bro
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  • Why the down vote? It will be helpful if can you please explain your reasons? It will help expand the answer – coder_bro Nov 26 '20 at 03:58
  • I am not the one who downvoted, but could be because you have cited Wikipedia as source which is not a valid source on this site. :) – TheLittleNaruto Nov 26 '20 at 04:50
  • Ah well, let me edit the answer. I had read the statement in a book, now I am unable to find it – coder_bro Nov 26 '20 at 06:06
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    You may want to look into smriti especially manu smriti. it covers gotra and marriage. – TheLittleNaruto Nov 26 '20 at 06:12
  • Also check this question: https://hinduism.stackexchange.com/q/35382/647 – TheLittleNaruto Nov 26 '20 at 06:15
  • I guess that answer pretty much provides the source – coder_bro Nov 26 '20 at 06:28
  • Let's continue discussion in chatroom: https://chat.stackexchange.com/rooms/15189/hinduism – TheLittleNaruto Nov 26 '20 at 06:30
  • joined the chat – coder_bro Nov 26 '20 at 06:36
  • You may want to change your above quote of paternal 5 generations and maternal 7 generations to the opposite. 7 On the paternal and 5 on the maternal. That’s what all scriptures say, including the Manusmriti you’ve quoted. Also the one you’ve quoted is Gautama Dharmasutra and not Manusmriti – Adiyarkku Nov 26 '20 at 10:41
  • @archit do you have other sources, can you please comment? – coder_bro Nov 26 '20 at 12:02
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    All your sources are mentioned below the Manusmriti verse cited. The Guatama Dharmasutra is also mentioned there only (that’s how I know) :D also it would be nice if you could give sources for Anamitra being more than 7 generations above Krishna and Satyabhama – Adiyarkku Nov 26 '20 at 13:07
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In case of kshatriyas, gotra-pravara is inherited from their purohita and not from a common ancestor hence krShNa-satyabAmA marriage is possible assuming both families had purohitas belonging to different gotra (in addition to 7/5 generation rule of shatapAtha brAhmaNa 1:8:3:6) :

aitareya brAhmaNa book 7 ch.4 :

Thence (if the sacrificer be a Ksattriya) they (the Brahma speakers) ask as to how the inauguration (diksa), which is, in the case of a Brahman being initiated, announced by the formula, ' the Brahmana is initiated,” should be promulgated in the case of the sacrificer being a Ksattriya ? The answer is, The formula, “ the Brahmana is initiated,” is to be kept when a Ksattriya is being initiated ; the ancestral fire of the Ksattriya’s house-priest is to be mentioned. This, this is certainly so.

[479] Having laid aside his own implements (weapons), and taking up those of the Brahma, and having thus become Brahma, by means of the Brahma form, he returned to the sacrifice. Therefore they should proclaim him as a Diksita, with the name of his house-priest’s ancestral fires, and invoke them also in the Pravara prayer.

aitareya brAhmaNa book 7 ch.5 :

The Ksattriya (when drinking the juice of the Nyagrodha) enters the form of the Brahma by the medium of another (not direct), viz, through the relationship of his purohita (with the Brahmans), his own Diksa (at which the king himself was made a Brahmana for a little while), and the Pravara of his Purohita.

ekAntika
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Satyabhama and Sri krishna both are Yadavas but their gotra is different just like how Arjuna Subhadra are chandravanshi but gotras are different.