An Epsilon rocket blasts off from the launching pad at the Uchinoura Space Center in Kimotsuki, Japan.
Japan sends a rocket into space using a low-cost rocket coordinated from a laptop computer.
The Japan Aerospace Exploration Agency (JAXA) launched the Epsilon rocket from the Uchinoura Space Centre in Kagoshima, cheered on by 1,000 people to witness blast-off of the country's first new rocket in 12 years.
The Epsilon - 24 metres (79-feet) long and weighing 91 tonnes - released the "SPRINT-A" telescope at an altitude of about 1,000 kilometres (620 miles) as scheduled, JAXA said.
SPRINT-A is the world's first space telescope for remote observation of planets including Venus, Mars and Jupiter from its orbit around Earth, according to the agency.
Lift-off had originally been scheduled for 27 August, according to AFP, but the first attempt was suspended with just seconds to go after a ground control computer falsely detected a positional abnormality.
Japan hopes the rocket, launched with just two laptop computers and a crew of just eight people, will become competitive in the global multi-billion dollar space business, paving the way for cheaper launches.
The small-sized rocket is equipped with artificial intelligence "for the first time in the world" that allows autonomous launch checks by the rocket itself, JAXA has said.
At the control centre only eight workers were engaged in the launch operation, compared with some 150 people usually needed when Japan launches its mainstream H2-A rocket.
The agency has halved the production and launch costs to 3.8 billion yen (£23 million) compared with the previous M-5 rocket.
Prime Minister Shinzo Abe said the success of a genuinely homemade rocket was a fruit of Japan's expertise and technology in space development.
"It demonstrates Japanese space technology is highly reliable," he said in a statement. He added that the success would lead to a self-sustainable space transportation system and to help Japan's economic growth.
Watch the rocket launch of the computer-controlled Epsilon
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