Trishanku, the son of Prithu was a king in the Solar Dynasty, the dynasty of the great Hindu God Rama. Trishanku wished to ascend to heaven in his mortal body and requested his Guru Vasishta to perform the needful rites to achieve this goal. Vasishta refused for it was against the laws of nature for a mortal to enter heaven. Upon refusal, Trishanku approached the sons of Vasishta to help him. The request of Trishanku in spite of the refusal by their father angered the sons of Vasishta and they cursed Trishanku with a debilitating disease. Trishanku was forced to leave his country and wander the lands.
During his wanderings, Trishanku met sage Viswamitra. Upon hearing the plight of the king, Guru Vishwamithra who was a rival of Guru Vasishta accepted Trishanku's request and agreed to perform the rites required to send Trishanku to heaven as a mortal.
The yagnas (rituals) began and by the power of the great sage, the King Trishanku started ascending to heaven. The Gods were alarmed by this unnatural occurrence and under the leadership of Indra decided to not let Trishanku enter through the gates of heaven in this mortal self. Indra using his powers caused Trishanku to fall back to earth.
The furious Vishwamithra could not accept defeat at the hands of Indra. The sage used his powers to arrest the fall. Thus Trishanku was suspended mid-air in a state of unstable equilibrium.
Trishanku prayed to Vishwamithra for help and the great sage once again used his powers and started creating a parallel heaven in a portion of the southern sky. Once the heaven was built, the sage proceeded to create a parallel Indra to rule the new heaven that he created. Upon this, the Gods were alarmed and they appeared before the sage and tried to console him and withdraw him from his act. They explained to Vishwamithra, their actions and how they wished to prevent the unnatural act of a mortal entering the heaven.
Vishwamithra was gradually convinced but now he faced the dilemma of having to break his own word that he gave to Trishanku about sending him to heaven. Vishwamithra reached a compromise with the Gods to let the King inhabit the new heaven that was created for him. The new heaven shall be called Trishanku's heaven and the king shall reside in this heaven from now on. He shall not supersede the command of Indra by ruling his own heaven, and to ensure that, the king shall reside upside down in his heaven.
And thus is the story of Trishanku who is suspended in his own heaven as a compromise between earth that he belonged to and the heaven that he sought!
The phrase "Trishanku's heaven" is used widely in India to describe such situations faced in real life. It has been believed that Trishanku and Vaivasvata Manu both are same.