Jo Konta has established herself as one of the finest athletes on the women’s tour but when she plays Caroline Wozniacki in the third round here tomorrow, she’ll be facing someone who’s accomplished something she could never do.

Former world No.1 Wozniacki ran the New York marathon in 2015, having promised to do it in the wake of her very public split from golfer Rory McIlroy.

Wozniacki ran a very respectable time – 3 hours, 26 minutes – testament to her fitness and athleticism and her achievements have the respect of ninth seed Konta, who is “unlikely” to ever run a marathon herself.

“I was good at 800 metres but there’s quite a difference between 44 kilometres and 800 metres,” said Konta, who was again impressive at Melbourne Park, crushing promising Japanese Naomi Osaka 6-4, 6-2.

“That’s a testament to the athlete that she is. That’s really what has been one of her biggest weapons, the physical side that she brings to the game. When I play her I think I might be running a marathon sooner than I thought.”

The comparison between Konta and Wozniacki is even more vast when it comes to their presence on social media.

While Wozniacki is very open about what she posts, including photos of herself in a bikini, Konta is more guarded and the chances of her doing something similar are slim.

“Never say never,” she said, “but I haven’t been in the situations and under such a spotlight as her.

“The kind of things she’s been involved with are quite super high-profile. So I think it’s a bit different, I haven’t been in that situation. Who knows, never say never, but we’ll see.”

Relaxed and confident at the venue where she reached the semi-finals last year, Konta is proud of her achievements and enjoying being recognised for her efforts on court.

But the 25-year-old said she is aware of the dangers of fame, with many players having been subjected to abuse online in recent times.

“It also has a dark side as well,” she said. “Some people have a bit too much time on their hands. But it’s also filtering those things out. And if it ever becomes something that’s not appropriate you take the right course of action. But until then I think it’s ignoring it more than anything.”

Konta’s fame is rising with every win and should she win the title a week on Sunday, she’ll have even more attention to deal with.

But she doesn’t consider herself famous and when asked who is, she said: “Sir Andy Murray,” with the emphasis on “Sir” for comic effect.

Should Konta get past Wozniacki, she would be one more win away from a likely encounter with Serena Williams.

Second seed Williams, chasing a record 23rd grand slam title, took care of the challenge of Czech Lucie Safarova 6-3, 6-4.

But third seed Agnieszka Radwanska went out, surprisingly beaten by Mirjana Lucic-Baroni of Croatia, whose first-round win was her first in Melbourne since 1998.