Four and a half centuries later, the projectiles being fired from Tanegashima go a lot further and higher. It is the launchpad for a space programme that aims to put a made-in-Japan unmanned spacecraft on the Moon during the first quarter of the 21st century, and ultimately to send Japanese astronauts to Earth's nearest neighbour. More than 100 launches have been made in the past 28 years, including 25 large space vehicles and 33 satellites.
Japan's steady advance into space has attracted far less attention than the Russian or American programmes, probably because none of its flights have been manned. This was noticeable last month, when the US Space Shuttle's failure to deploy a satellite on a 12-mile cable gained high publicity, but it was preceded by a less-publicised setback for Japan's space scientists. Their Hypersonic Flight Experiment vehicle, Hyflex, was successfully launched into the fringes of space, but sank after splashing down in the Pacific. Both missions suffered the loss of tens of millions of dollars' worth of equipment thanks to the most basic failure: a snapped cable, which in Hyflex's case caused it to part company with its flotation bags.
All the same, Takane Kobayashi, deputy director of Tanegashima's space centre, insisted that data for 12 of the 14 tests Hyflex had been designed to carry out were successfully captured by telemetry: "We got 90 per cent of what we needed for Hope." Hope is the name of the unmanned space shuttle designed to take off, dock with the orbiting space station being developed jointly by the US, Japan, Russia, Canada and the European Space Agency, and land back on Earth, all completely automatically.
In May, the National Space Development Agency of Japan (Nasda) is due to begin testing an automatic landing vehicle, known as Alflex. It will be dropped from a helicopter high above Australia and, if all goes well, touch down at Woomera, the site of many British rocket tests in the days when this country still aspired to an independent space programme. "The next step," said Mr Kobayashi, "will be to launch a nine-tonne experimental space vehicle, nearly half the final weight of Hope, and after that we will launch a full payload."
Nasda has grown steadily from its origins in the late 1960s, when it had a staff of 150 and a budget of 3.1bn (pounds 19.5m). Tanegashima was chosen as the launch site because of its relative proximity to the Equator - Okinawa, which is further south, was not returned to Japanese control by the US until 1972. A permanent staff of 70, all wearing Nasda's cream- coloured uniform, now works on the island, a number that swells to as many as 800 when a launch is imminent. Japan's space expenditure is expected to reach 231.2bn (pounds 1.4bn) this year.
Critics of Japanese industry often claim that it is essentially imitative - brilliant at turning others' discoveries into marketable products, and making them more cheaply than anyone else, but incapable of original ideas or research. It might be argued that these characteristics are reflected in Japan's space programme too: so far it is breaking no new scientific ground, and by concentrating on unmanned craft Nasda is going for the cheap option, since it can dispense with the safety systems that add drastically to the cost of piloted vehicles. There is even a whiff of the marketing men in "brand" names such as Hyflex, Alflex and Hope.
Mr Kobayashi says Japan must ascend the same learning curve as the nations that pioneered space research, so as to be able to work effectively with them in the future. "It's not that we want to keep to ourselves. When the scale of the project makes it necessary, we will work with others. Sending a man to the moon can be done within a nation's budget, but no single country could build a base there. That will also be a joint project.
"We are not producing new scientific data yet, but we hope to do original work later. Japan is strong in technology such as robotics and computers, so it makes sense to concentrate on unmanned flight."
Even if the Americans can say of the moon: "Been there, done that", today's technology could produce much more detailed information, argues the Nasda man. "For example, we plan to launch a vehicle called Penetrator that would bore into the moon to determine if there have been earthquakes there. The conventional view is that they could not have happened. If we could prove this either way, it would be a major piece of original research."
Some of Japan's Asian neighbours, however, feel more than a few qualms at the sight of ever-larger rockets, emblazoned with the rising sun and "Nippon" in giant letters, rising from the launchpads of Tanegashima. They fear that the island's activities could alter the regional balance of power as dramatically as those Portuguese arquebuses long ago. With the region's potential for instability being demonstrated by China firing missiles close to Taiwan, hundreds of Russian nuclear warheads still based in the Far East, and North Korea, which is suspected of attempting to develop nuclear weapons, possessing upgraded Scuds capable of reaching many of Japan's principal cities, there appear to be strong incentives to put Nasda's knowledge to military use.
The Japanese insist that their space programme, like their nuclear development, is entirely for peaceful purposes. But nobody doubts that they have the capacity to build a nuclear missile, however unlikely that might be in the light of their political and constitutional safeguards, let alone its own experience of atomic devastation.
"Our charter specifically prohibits our work being used for military purposes," said Mr Kobayashi. "Although we are not set up primarily as a commercial organisation either, we are allowed to sell our technical know-how, but there are constraints on trading in any equipment or materials that might have a military application.
"The perception remains among Asians that Japan might revert to militarism," the Nasda official added. "I admit there is always that potential fear among our neighbours. All we can do is try to prove them wrong."