Neal Goren, the founding artistic director of the enterprising Gotham Chamber Opera, after taking his nephew to the Hayden Planetarium in the American Museum of Natural History one day, thought it would be the perfect place to present a production of Haydn’s fanciful opera “Il Mondo Della Luna.”

Mr. Goren’s brilliantly eccentric idea came to fruition on Tuesday night when the Gotham Chamber Opera, in association with the museum, presented the first of six performances of this seldom-heard work at the planetarium before a packed house. Still, for all the clever theatrical trappings, bizarre sci-fi costumes and special effects, which included, naturally, wondrous video images of the starry cosmos projected on the domed ceiling, the production indulged in stock comic bits and lame overacting. The singers often sounded tired, which was understandable, since this frenetic, eager-to-please production demanded such nonstop physical exertion.

The director Diane Paulus and the video and production designer Philip Bussmann had to figure out how to present a chamber opera in the planetarium, which has no stage and no pit. A makeshift platform just large enough to accommodate the 25-piece orchestra was constructed over some of the seats that encircle the space.

The harder challenge was coming up with a stage area in the center of the circular floor so that the singers could be seen from the back rows. That was accomplished with a long wooden table and several metal staircases that were wheeled out by a stage crew wearing white lab coats. That meant, however, that the singers continually had to climb up and down steps and leap onto and off the table. I hesitate to assess the quality of their voices, since performing in this production must have been like a workout on a Stairmaster.

Still, give the company credit for taking opera to an unconventional setting and for championing this overlooked 1777 work. With a libretto by Carlo Goldoni, “Il Mondo Della Luna” tells of Buonafede, the wealthy and protective father of two marriageable daughters, who disapproves of the men they love. Ecclitico, a wily astrologer who knows that his profession is a sham, is determined to marry Buonafede’s daughter Clarice. He convinces the gullible father that they can all travel to the moon, a magical world where the mores of male-female relations favor males.

Once there the daughters, along with their maid, Lisetta, are ordered into matches with moon men (actually their lovers) by the emperor. The stupefied Buonafede cannot object, and when the scam is revealed, he relents and blesses the unions.

It would have been interesting for a production to tap into the spiritual resonances of this opera. Haydn’s music is not just witty but also elaborate, rich and tender, qualities Mr. Goren captured in his conducting. Buonafede is the victim of a joke. Yet something about the fantasy of life in another realm transforms him. How touching it might have been to see the elderly man actually awestruck by his phony lunar exploit.

Instead Ms. Paulus relies on comic shtick. As the cavalier Ernesto grooms himself to court Buonafede’s other daughter, Flaminia, Ernesto’s ragtag servant, Cecco, recoils at his master’s bad underarm odor. Later, during one ensemble, Ernesto hops atop the sprawled Flaminia and leeringly pokes his head under her skirts, a crude bit out of keeping with the sweet tone of Haydn’s score (sensibly trimmed here to 100 minutes without intermission). Several times the sisters and their maid break into disco dancing routines. At moments like these you sense the director straining for laughs.

Using bright stage lights would have made it impossible to project images onto the ceiling during the scenes on the moon. Anka Lupes, the costume designer, came up with the ingenious idea of lighting the actual costumes the characters wear during the lunar excursion, which included three dancers in white tights twirling illuminated hoops. The costumes were wildly inventive if a bit tacky. Cecco, portraying the emperor of the moon in a spiked crown and luminous cape, looked like the star of a sci-fi version of “La Cage aux Folles.”

The baritone Marco Nisticò was a robust-voiced Buonafede. The tenor Nicholas Coppolo was a dashing Ecclitico, although his singing was sometimes tight. The soprano parts of the daughters are replete with coloratura roulades and passagework, ably handled by Albina Shagimuratova (Flaminia) and Hanan Alattar (Clarice). The mezzo-soprano Rachel Calloway as Lisetta did the sexpot maid thing asked of her, but managed to sing well. The tenor Matthew Tuell brought his appealing voice to Cecco.

The officials of the museum deserve many thanks for making the planetarium suitable for opera.