I seriously doubt any aliens have visited Earth in the past 500 years, and surely not in the past 60 for the simple fact we would see them coming.
Its possible to detect the maneuvering thrusters of the shuttle from beyond the orbit of Mars. A tiny ion drive like used by the SMART-1 probe that produced 1/1000 of a g of acceleration could be spotted at 1 AU. How far away could we spot a drive that puts out 1 or more g of acceleration necessary for interstellar travel (say by Bussard Ramjet)?
Someone else can do the math but the range would be in light years.