Question

Suppose that, on average, there is one large galaxy found within a sphere of diameter dsphere, and that each one contains total mass mgalaxy. What is the average density within this sphere? Enter your answer in units of kg/m³. Write your answer in scientific notation with 2 decimal places (3 significant figures).

a) 2.45 × 10²⁵ kg/m³
b) 1.23 × 10²⁵ kg/m³
c) 3.68 × 10²⁵ kg/m³
d) 5.01 × 10²⁵ kg/m³

Answer 1

To determine the average density within a sphere, we use the mass of one galaxy and the volume of the sphere. However, without specific values for the galaxy's mass and the sphere's diameter, we cannot compute the exact density or choose the correct option from the provided answers.

Step-by-step explanation:

To calculate the average density within a sphere, we need to know the mass of a large galaxy (mgalaxy) and the volume of the sphere which contains this galaxy. The volume (V) of a sphere with diameter dsphere is given by the formula V = 1/6 π dsphere³. Since there is one galaxy per sphere, the density (ρ) can be calculated using the formula ρ = mgalaxy / V. If we assume the average mass of a galaxy is similar to our galaxy, which contains about 10¹¹ Msun and Msun (the mass of the Sun) is 1.99 × 10³° kg, then mgalaxy can be expressed in kilograms.

To obtain the density in kg/m³, we can use the given information to calculate, but as we do not have specific values for mgalaxy or dsphere in the question provided, we can't complete the calculation. Hence, we can't confirm which of the provided options (a, b, c, or d) is correct without additional data. However, we can say that the average density of matter in galaxies is a tiny fraction of the critical density needed to halt the expansion of the universe.