If a galaxy is traveling away from us at 2.0% of the speed of light, roughly how far away is it?
t= light years
I got 2.4x10^8 light years but its wrong please help me out...thank you
5.98x10^6
To calculate the distance to a galaxy that is traveling away from us at a certain speed, we need to use the concept of redshift. Redshift is a phenomenon in which light from distant objects appears shifted towards longer wavelengths, indicating that the object is moving away from us. The amount of redshift is directly related to the speed at which the object is moving away.
The equation that relates redshift (z) to the recessional velocity (v) is known as Hubble's Law:
z = v/c,
where z is the redshift, v is the recessional velocity, and c is the speed of light.
In this case, the galaxy is traveling away from us at 2.0% of the speed of light. So we can substitute this value into the equation:
z = 0.02c/c = 0.02.
Now, we can use another equation to relate redshift to the distance (d) to the galaxy, known as the cosmological redshift equation:
z = (d/d_0) - 1,
where d_0 is the current distance to the galaxy (in this case, from us to the galaxy).
Rearranging the equation, we can solve for d:
d = (z + 1) * d_0.
Since d_0 is what we are trying to find, let's denote it as D:
D = d_0.
Now substitute D back into the equation:
D = (z + 1) * D.
Plug in the value of z we found earlier:
D = (0.02 + 1) * D.
Simplifying the equation:
D = 1.02 * D.
Divide D from both sides:
1 = 1.02.
This equation shows that 1 light year is equivalent to a redshift of approximately 0.02. Therefore, if the galaxy is traveling away from us at a speed of 2.0% of the speed of light, the redshift would be approximately 0.02.
To calculate the distance d_0, we can use the equation:
d_0 = (z + 1) * t,
where t is the time it takes for light to travel from the galaxy to us.
Plugging in the value of z:
d_0 = (0.02 + 1) * t = 1.02 * t.
So, the distance to the galaxy would be 1.02 times the time it takes for light to travel from the galaxy to us.
Please note that this calculation assumes the galaxy has a linear recessional velocity and does not take into account other factors such as gravitational interactions or the expansion of the universe.