Sankashti Chaturthi and Vinayaka Chaturthi
The fourth day after new moon and fourth day after full moon in the Hindu calendar is observed as Chaturthi and is dedicated to Lord Ganesha. Most people must be aware of only the Ganesh Chaturti festival that takes place in the month of Bhadrapada (August-September). But there are two Chaturthis in a month -- Sankashti and Vinayaki -- and staunch Ganesha devotees observe a fast on the Chaturthi after full moon.
The monthly Chaturti day which falls after full moon in which a fast (fasting) is observed is known as Sankashti Chaturthi. The fast ends on the day after moonrise. Special Ganesh pujas are done in the evening. The monthly Chaturthi after Amavasi or new moon is known as Vinayaki Chaturthi.
When Sankashti Chaturthi falls on Tuesday, it is known as Angaraki Chatutrhi and it is considered highly auspicious.
The benefits of Chaturthi fasting include material progress, happiness and fulfillment of desires. The importance of Chaturthi vrat was explained by Lord Krishna to Yudhishtira, the eldest of the Pandavas. It is also mentioned in the Narasimha Purana and Bhavishaya Purana.
Sankashti Chaturti, or Ganesh Sankashta Chaturthi Vrata, is an auspicious day dedicated to Lord Ganesha in a Hindu lunar month. It falls on the 4th day in a Krishna Paksha lunar fortnight or on the fourth day after full moon or Purnima. Ganesha devotees observe a fast (fasting – upvaas) on Sankashta Chaturthi Vrata days.
The Sankashti, which falls on Tuesday, is known as 'Angarki Chaturthi'. On this day, the devotees observe fast. They have their meal in the night after having darshan of lord moon.
Long long ago there lived a sage called Bhrushundi.(sage Bhrushundi did penance for many years of Lord Ganesha and became great among the devotees of Lord Ganesha. While doing penance a trunk immerged from his nose, that is why he has been called as Bhrushundi. Everyone use to see him to get virtue.)
Once God Indra's plane on his way back to home from sage Bhrushundi, was going above king Shursen's kingdom. One person(who has done many sins in his life) saw the plane of God Indra in the sky. With his look the plane landed on the ground. By seeing the brightness of the plane, king went to see the plane and person travelling in the plane. By seeing God Indra king was very much pleased and he saluted God Indra and ask about the landing of the plane. God Indra told him that a sinner from your city looked at the plane, because of his sins the plane came down. By hearing the noise of the plane, everyone from the city came to see the plane. All people worshipped God Indra. King asked God Indra how the plane could start again? God Indra told him that today is Panchami from the month of the Paush. Yesterday was the Chaturthi. Check whether anyone done fasting yesterday. If that person gives his virtue to me then my plane will start. Soldiers searched the city for the person who did fasting on Chaturthi., but unfortunately they found no one. At the same time some soldiers saw Ganesh-Duta(a soldier of Lord Ganesha) who is taking away a woman died recently. Soldiers asked him that how can you take such a sinner to Ganesh-loka. Ganesh-Duta told soldiers that yesterday whole day that woman was in sleep. She has not eat anything. Late night after moon-rise she woke up and eat some food. Without her knowledge she did Sankashti-Chaturthi. She died today. A person who does Sankashti-Chaturthi even once in the life, after death goes to Ganesh-loka or Swananda-loka. Soldiers requested Ganesh-Duta to give that woman to them so that the plane of could start. But Ganesh-Duta refused to give virtue of that woman to soldiers. The wind which flown from the dead woman's body went till God Indra's plane and with the wind it could start the plane. It means that the wind which touched that virtuous body also become virtuous.
The person who does Sankashti-Chaturthi(do fasting till the moon-rise and then eat the food) will collect lot of virtues. After the death that person goes to Swanand-loka and the rebirth of that person stops. There is a belief in Hinduism that a person takes seven births before gets 'Moksha'. (becomes free, there is no rebirth afterwards.)