Exploring Gliese 581 - Could It be a New Home?

[AfRoMaNn]

scientists just discovered a planet Gliese 581, located 20 light years away from Earth in the constellation Libra. scientists believe that one part of this planet may be habitable. do you think it may be possible to travel to this planet one day if for some reason the Earth becomes inhabitable or destroyed?

 

[DaveC426913]

Already a thread on Gliese 581:
https://www.physicsforums.com/showthread.php?t=433389

It may be feasible to visit Gliese 581, but alas, it won't be this century.

 

[kungfuscious]

It's quite possible to go there, it just depends on how fast we can go. Unfortunately, we don't make space ships travel all that fast yet. The fastest 'thing' we've ever sent out was the Voyager spacecraft , which is on its way out of our own solar system. It travels at roughly the speed of 40,000mph, which is 17 882 m/s. In order to find out how long it would take to travel 20 light years, it's just a matter of converting units, and using the fact that:

$$velocity = \frac{distance}{time}$$

The distance of 20 light years is converted by knowing that 1 light year is 9.46 x 10¹⁵m. Then, the time it would take to travel to the star is:

t = 1.06 x 10¹³seconds, which is 34 016.43513 years.

However, using special relativity (which states that time for the person in the rocket will actually be a little less than what people on Earth think).

$$\Delta T = \gamma \Delta T_0$$, where delta T is the time as measured by those on Earth (we just found it to be 34016.43513yrs), and delta T₀ is the time as measured by those on the rocket.

We can then just find the Lorentz factor $$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}} = 1.000000002$$

Then, the time it would take to get there, according to those on the rocket would be

$$\Delta T_0 = \frac{\Delta T}{\gamma} = 34016.43506$$ years. You don't really save much time.


What if v = 0.5c?

If we could somehow travel at a much faster speed, let's say half the speed of light, then things would get much better.

The time it takes to get there according to those on Earth would be:

$$\Delta T = \frac{d}{v} = \frac{20}{0.5} = 40yrs$$

Then, we can find the time the people on the ship would measure:
$$\gamma = \frac{1}{\sqrt{1 - 0.5c^2/c^2}} = 1.1547$$

$$\Delta T_0 = \frac{\Delta T}{\gamma} = \frac{40}{1.1547} = 34.6yrs$$

That wouldn't help all that much.


What if v = 0.99c?

If we could somehow travel at 99 % the speed of light, things would be much better!

The time it takes to get there according to those on Earth would be:

$$\Delta T = \frac{d}{v} = \frac{20}{0.99} = 20.2yrs$$

Then, we can find the time the people on the ship would measure:
$$\gamma = \frac{1}{\sqrt{1 - 0.99c^2/c^2}} = 7.09$$

$$\Delta T_0 = \frac{\Delta T}{\gamma} = \frac{20.2}{7.09} = 4.9yrs$$

This would make a huge difference. If you could travel at 99% the speed of light, those on the Earth would measure your travel time to be 20.2 yrs, while your actual travel time if you were on the spaceship would be only 4.9yrs.

Too bad we can't travel that fast yet!