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The Super Aguri driver joins Mark Webber, David Coulthard, Rubens Barrichello, Jenson Button and Alexander Wurz in being eliminated.
BBC: SPORT | Motorsport | Formula One | Turkish GP qualifying as it happened
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However, he has not competed since this year's Spanish Grand Prix in April, when Honda-backed Super Aguri went out of business.
BBC: Sato to test for Toro Rosso again
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Japan's Sato, who has raced for Jordan, Honda and Super Aguri in F1, set the fastest times of the three at Spain's Circuit de Catalunya.
BBC: Buemi poised for Toro Rosso seat
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Because of their problems Super Aguri have missed most winter testing.
CNN: Magma Group come to aid of Super Aguri
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The 31-year-old has been without a drive since the collapse of Super Aguri in May but will get back behind the wheel at Jerez on 10 December.
BBC: Sato to test for Toro Rosso again
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Super Aguri won just four points last season, putting them second to last and Davidson, who joined the team last year, is not over-optimistic about their prospects in the new season.
CNN: Magma Group come to aid of Super Aguri
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Super Aguri, the first all-Japanese team on the Western-dominated circuit, have struggled for financial support since being founded in late 2005 by Aguri Suzuki, the first Asian to stand on an F1 podium.
CNN: Magma Group come to aid of Super Aguri
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Honda's demise would also reduce the F1 grid to just 18 cars (nine teams) and would see them become the second team to fold this year following Super Aguri's closure early in the season.
CNN: Honda blames global crisis for F1 withdrawal
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The support from Magma Group, led by former Ford and Maserati executive Martin Leach, ends fears that the Honda-powered Super Aguri would be unable to take part in the Australian Grand Prix at Melbourne on Sunday.
CNN: Magma Group come to aid of Super Aguri
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Super Aguri folded earlier in the year after lengthy sponsorship struggles, and even those teams fortunate enough to have rich benefactors -- Red Bull, Toro Rosso and Force India -- rarely make an impression on the front of the grid.
CNN: Mosley demands F1 cuts costs