# Observed speed of a receding light source

Let’s say there’s a planet 4 light years away from Earth and we send a rocket ship towards that planet at 99.9% light speed. We stay behind on Earth and watch the rocket ship travel towards the other planet.

Eventually we should be able to see our rocket ship reach it’s destination. How much time will have elapsed for us until we see that occur?

My intuition would say about 4 years. But I also know that when we observe such a far-away planet, we are ”seeing it as it was 4 years ago”. Well 4 years ago the rocket was still on Earth, so how can I be seeing it landing on the planet now?

Something has to give, but what? Will it appear as if the trip took 8 years to complete?

Will it appear as if the trip took 8 years to complete?

Yes.

• Thanks! Figures that the time delay would build up along the way... Now I just have to get comfortable with that idea!
– zath
Dec 6, 2019 at 22:41
• 8.04 years, ship is <c Dec 7, 2019 at 2:48

It takes the spaceship 4 years to get there, and then it takes light from the spaceship getting there 4 years to get back, i.e. 8 years for an observer on Earth to see it land on the planet.

• Thanks! If I imagine communicating with the planet using lasers, the 8 year round trip makes sense. It felt less obvious in the scenario I described, probably because it feels like a 1-way trip.
– zath
Dec 6, 2019 at 22:46

It all depends on what the meaning of the word "appear" is.

In about eight years, you'll see the ship land, and you'll say "Ah. I see the ship landing at a place four light years away, so it must have landed four years ago".

Does "appear" refer to what you see, or to the meaning you attribute to what you see after you've made the necessary corrections? If the first, the ship appears to land in eight years. If the second, it appears to land in four.

An analogy: Suppose I stand really really far away from you. Would you say that I "appear" to have shrunk to half my height? By one meaning of the word "appear", the answer is clearly yes. By another, no, I don't appear to have shrunk, I just appear to be really far away, but to still be six feet tall.

• Thanks for the answer! I was indeed referring to the first kind of ”appear”, i.e what we would see.
– zath
Dec 6, 2019 at 22:48
• @zath : also, this question has nothing to do with relativity. You'd get the same answer in any theory with a finite speed of light, e.g. classical 19th century physics. Dec 6, 2019 at 22:51
• Good point of clarification, the relativity-tag has been removed.
– zath
Dec 6, 2019 at 23:04