# Formula to calculate round-trip travel time based on current distance to far-away galaxy

Cross-posted from Physics Stack Exchange - original

The question was closed as HW-like there.

### The Premise

You travel at a constant velocity towards a far-away galaxy. You then travel back at the same velocity. How long will have passed for the people on Earth? Answers must take into account the expansion of the universe.

### Definitions:

• now is defined as 21st century

### Parameters:

• Time from now you will depart (in years)
• Distance away that the galaxy is now (in light-years)
• Velocity (in % of light-speed)

### Output:

• number of years that will have passed on Earth between the time you depart and the time you get back

This was inspired by this question: At 50% c, I go party to IC1101 galaxy, and back home. How many times can i go before the expansion of the universe will lock me on one side? .

### Significance

This will allow for many different astronomical calculations by moving the elements of the formula around (eg. how long until we won't be able to communicate with a distant galaxy?).

• Please let me if know if this should be moved to Space Exploration. Commented Jul 19, 2021 at 19:48
• Just a quick note: Cross-posting is discouraged on Astronomy SE. Commented Jul 20, 2021 at 21:19
• @fasterthanlight I thought it would be fine as the question is no longer open on Physics SE. Commented Jul 20, 2021 at 22:10