ASTRONOMY 18 th-century math sets stage for future space exploration Columbus Dispatch Tuesday, October 05, 2004 TOM BURNS In the mid-18 th century, mathematicians and scientists such as J.L. Lagrange were obsessed with the three-body problem - mathematical rules behind the mutual attraction of three large bodies, such as two planets orbiting the sun or a moon orbiting a planet orbiting the sun. Almost 250 years later, Lagrange's elegant solution has implications that will determine the course of space exploration over the coming decades. It works like this: If one object orbits another, there are five places near the orbiting object where another object can lock into a stable and permanent orbit. Think of them as naturalgravity wells. To put a space station in a stable orbit near Earth, the No. 4 and No. 5 sun-Earth natural-gravity wells - known as Lagrange points - can't be beat. They are located along Earth's orbit 60 degrees on either side of Earth. One precedes Earth and the other trails it. Unfortunately, they are each 50 million miles from our planet, a bit distant for things such as supply shipments, rescues and maintenance missions. Much better is Lagrange point No. 3, about 1 million miles toward the sun. At that location, your space telescope is locked as a minor planet orbiting the sun. But because of its sunny location, Lagrange point No. 3 is not a great place to observe stars. However, the No. 3 Solar and Heliospheric Observatory, or SoHo, has for years produced beautiful images of our home star. About 1 million miles directly away from the sun is Lagrange point No. 2, also known as the "gateway." Eventually, the Hubble Space Telescope's replacement will orbit the sun there. Its "dark-side" location will produce a panoramic view of the heavens unrestricted from the sun's glare. The same location also is well suited for a manned space station, perhaps where astronauts will assemble a craft for a trip toward Mars. Unfortunately, a human trip to Lagrange point No. 2 would take about 15 expensive days, five times longer than a trip to the moon. However, we could use technologies we mastered in the 1960s with the Apollo missions to get there. Telescopes located there would be far easier to use than satellites in low-Earth orbit, the only real option to date. The initial rocket power would be much greater than that required for low-earth orbit, but from point No. 2, considerably less rocket power would be required to begin trips to Mars and beyond. Lagrange's heady mathematical calculations found for us a place to stand and contemplate a gateway to distant worlds. Tom Burns directs Ohio Wesleyan University's Perkins Observatory in Delaware. [email protected] .