An average diameter of a star is approximately 109 m and an average diameter of a galaxy is 1021 m. Considering the given data, apply a sense of scale calculation to determine if when a galaxy’s diameter is scaled down to the length of Manhattan (21.6 km long), would the star be larger or smaller then you?
I think your star/galaxy sizes are mistyped.
An average diameter of a star is approximately 1 X 10^9 m and an average diameter of a galaxy is 1 X 10^21 m. Considering the given data, apply a sense of scale calculation to determine if when a galaxy’s diameter is scaled down to the length of Manhattan (21.6 km long), would the star be larger or smaller then you?
this is what i meant
To determine if the star would be larger or smaller than you when a galaxy's diameter is scaled down to the length of Manhattan, we need to perform a sense of scale calculation.
First, we need to compare the diameters of the star and the galaxy. The star has an average diameter of 109 meters, while the galaxy has an average diameter of 10^21 meters (1 followed by 21 zeros).
Now, let's calculate the scaling factor:
Scaling factor = Diameter of the galaxy / Length of Manhattan
Scaling factor = 10^21 m / 21,600 m
To simplify the calculation, let's express both values in scientific notation:
Scaling factor = 1 x 10^21 m / 2.16 x 10^4 m
Dividing the scaling factor, we get:
Scaling factor = (1/2.16) x (10^21 / 10^4)
Scaling factor = 0.46 x 10^17
So, when scaling down the diameter of the galaxy to the length of Manhattan, each meter in the galaxy would be represented by 0.46 x 10^17 meters.
Finally, we can determine if the star would be larger or smaller than you:
Comparing the star's diameter (109 meters) with the scaling factor (0.46 x 10^17 meters), we can see that the scaled-down galaxy would be much larger than the star.
Therefore, the star would be smaller than you when the galaxy's diameter is scaled down to the length of Manhattan.