Godolphin colt Exosphere faces the biggest test of his career as he attempts to graduate to the big time in the TJ Smith Stakes.

The $2.5 million sprint shapes as Exosphere's chance to go from star three-year-old to genuine weight-for-age horse.

Bookmakers believe he is ready and have made him the $2.70 favourite to win the race at Randwick on Saturday.

To do so, he will have to turn the tables on Chautauqua, rated a $3.40 chance to win back-to-back TJ Smiths.

"We're looking forward to everyone seeing what he can do," Godolphin trainer John O'Shea said.

Exosphere had his final hit-out in a track gallop over 1000m on Wednesday.

O'Shea said the work was leisurely but impressive.

"That's exactly what I wanted him to do," O'Shea said.

Exosphere's first test under weight-for-age conditions came in his last start, the Lightning Stakes at Flemington in February, where he finished fourth in a six-horse field.

Chautauqua won that race with a blistering finish, but O'Shea has seen improvement in Exosphere.

"He's fit and well and there's no question that he's come on a lot since returning from Melbourne," O'Shea said.

"He's bright in himself, his coat has improved, we're all very pleased with him."

While he hasn't raced competitively since the defeat at Flemington seven weeks ago, Exosphere won a barrier trial at Randwick on March 18.

"His trial at Randwick the other day showed us he was in very good shape and his work this morning confirmed that," O'Shea said.

"We all know what a turn of foot he has and he showed in his Roman Consul win at Randwick last spring that he is right at home there."

O'Shea said he had no problem with Exosphere drawing barrier four, but indicated the colt would be ridden more positively on Saturday.

"I think you'll find he'll settle a bit closer to the pace than last time," O'Shea said.

Outside the two main hopes, Gai Waterhouse-trained filly English is a $9 chance, with Lightning Stakes runner-up Terravista on the next line of betting at $15.