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
v=0.02•3•10⁸=6•10⁶ m/s
1 MegaParsec = 3.26•10⁶ ly
Hubble’s Law
v=Hd
Hubble constant
H ~70- 80 km/(s•Mpc)
=> v= 80d or v=70d
d=(6•10⁶/80 000)• 3.26•10⁶ =2.45•10⁸ ly
or
d=(6•10⁶/70 000)• 3.26•10⁶ =2.79•10⁸ ly
To determine the distance to a galaxy that is moving away from us, we can use Hubble's law. Hubble's law states that the velocity of a galaxy is directly proportional to its distance from us. Mathematically, it can be written as:
v = H0 x D
Where:
- v is the velocity of the galaxy (in this case, 2.0% of the speed of light)
- H0 is Hubble's constant (the current value is still subject to debate, but a commonly used approximate value is 70 km/s/Mpc)
- D is the distance to the galaxy
To convert the velocity from a percentage of the speed of light to km/s, we can use the equation:
v = (velocity percentage x speed of light) / 100
v = (2.0% x 300,000 km/s) / 100 = 6,000 km/s
So now we can rewrite Hubble's law equation as:
6,000 km/s = H0 x D
Rearranging the equation to solve for D:
D = (6,000 km/s) / H0
Using the approximate value of H0 as 70 km/s/Mpc:
D = (6,000 km/s) / 70 km/s/Mpc = 85.71 Mpc
Now, to convert Mpc to light years, we can use the conversion factor:
1 Mpc = 3.09 x 10^19 km = 3.26 million light years
Therefore:
85.71 Mpc = 85.71 x 3.26 million light years = 279.43 million light years
So the distance to the galaxy traveling at 2.0% of the speed of light is roughly 279.43 million light years.