Superman can go to the past simply by flying around the earth in the opposite direction at a faster speed than the earth’s rotation and then back to the present (and presumably the future) by flying in the direction of its rotation.

Considering that the earth rotates at 1000 miles per hour at the equator, would it actually be feasible to do what the caped crusader can do by simply flying at speeds in excess of 1000 mph? For example, if you could fly at 10,000 miles per hour around the earth keeping close to the equator, could you travel 9 or 10 hours into the past every hour (I can’t do the math)?

First off, its generally not a good idea to use the Superman movies from the 70s as a physics reference. Second, in the movie he went back in time by flying faster than the speed of light. As he began to travel back in time (delta-t became negative) the rotation of the earth also went into reverse, then he slowed down and time began running normally again for him.

-AntonK

Why did he have to travel faster than light?

If objects could travel faster than c then special relativity predicts that they can be sent back in time. This is why it is so often stated that relativity says that nothing can travel faster than light which isn't a conpletely accurate statement.

For example consider relative simultaneity. Lets say a probe is rocketing away from the earth. Superman starts standing on the earth and then flies of faster than light, virtually instantaneously(according to the earth) landing on the probe. Due to relative simultaneity, according to the frame of the probe the event that he left the earth will have occured at a time after the event that he landed on the probe. Now lets say he immediately takes off from the probe faster than light, virtually instantaneosly(according to the probe) ariving back on the earth. Since his departure from earth happened sometime after this instant, he therefor arrived back at earth at a time prior to leaving. Really the outcome depends on how he accelerates in the turn around. One could just as well find a path where he winds up way in the future.