# When is the arrival detected

1. Aug 9, 2010

### nickek

Hi!
Suppose a spacecraft is going to travel 10 lightyears in the velocity of 0.9c (in the Earth reference frame). Obviously, the travel takes 10/0.9=11.1 years for an observer on the Earth. According to special relativity theory, the travellers measure the time to 3.5 years. But: When is the arrival to the point 10 lightyears away from the Earth detected, i.e we can "see" the spacecraft at this point on the Earth? Is it possible to do at the time 11.1 years from start, or do we have to wait 11.1 + 10 = 21.1 years?

Thanks for input!

2. Aug 9, 2010

### Staff: Mentor

Hi nickek, welcome to PF!

You are correct, the light from the arrival event comes back to the earth at t=21.1 years. Knowing that the arrival event was 10 ly away the people on earth then calculate that the event happened at t=11.1 years.

3. Aug 9, 2010

### nickek

Great, thank you!

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