Hernando Ferraro-Cordoba, 60, attended the gym on 15 November 2021.
He began speaking to the woman and after a short conversation, he grabbed her and kissed her multiple times on the face.
The woman managed to push him away and he was ejected.
Later, as the woman left the gym, she found him in the car park waiting for her.
He approached again and said, “The moon looks so beautiful, it looks like you”, and asked if he could go home with her.
A member of staff saw he had approached her again and confronted him, at which point he cycled away.
The woman reported what had happened to the police and he was arrested the following week.
Ferraro-Cordoba, of Hanover Court, Cambridge, pleaded guilty to sexual assault at Cambridge Crown Court.
He was sentenced at the same court on Friday to 18 weeks in prison. He was also handed a restraining order, a seven-year Sexual Harm Prevention Order and placed on the Sex Offenders register for seven years.
DC Paul Evans said: “Violence against women and girls is a force priority. People like Ferraro-Cordoba are a danger to women, and I am pleased we were able to put him in front of the courts and get justice for the victim.
“Public harassment and violence is not acceptable and we are aiming to make the streets and public areas of Cambridgeshire a hostile place for potential offenders.”