When Krishna Paksha Chaturthi falls on a Tuesday, it becomes Angarki Chaturthi.
The tithi Chaturthi is associated with Lord Ganesha. There are two Chaturthis in every lunar month. The Chaturthi of the Krishna Paksha (dark half) is called Sankashti (Sankatahara) Chaturthi. Tuesdays are also important days for the worship of Lord Ganesha, and it is the day of Angaraka (Planet Mars). When Sankashti falls on a Tuesday, it has special significance. Then it is called Angarki Chaturthi.
Once, Sage Bharadwaja was enchanted by an apsara. He couldn't resist his libido, and his semen fell on the ground. It was caught in a crevice on the earth and matured into a child. This is planet Mars, also called Angaraka. He was called Angaraka as his color was as red as an ember. Being the son of Bhumi, he is also called Bhauma or Kuja.
Angaraka became 7 years old. He wanted to know about his father. Bhumi Devi sent him to Sage Bharadwaja. The Sage accepted him into his fold and taught him Vedas and Shastras.
At the behest of his father, Angaraka observed tapas to propitiate Lord Ganesha on the banks of the river Narmada. He stayed there without food and water for a thousand years chanting Ganesha Mantra.
Finally, on the Sankashti Chaturthi of the Magha masa, Lord Ganesha gave darshan to him. Angaraka asked for 3 boons from Ganesha:
Lord Ganesha granted him the boons and also declared that Angaraka henceforth would also be known as Mangal (auspicious).
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