Question

The average density of the Sun is on the order 10^3 kg/m³. (a) Estimate the diameter of the Sun.

a) 500,000 - 750,000 km
b) 750,000 - 1,000,000 km
c) 1,000,000 - 1,250,000 km
d) 1,250,000 - 1,500,000 km

Answer 1

The estimated diameter of the Sun is approximately 1.38 million kilometers.

Step-by-step explanation:

The average density of the Sun is given as 10³ kg/m³. To estimate the diameter of the Sun, we can use its mass and density.

The volume of the Sun can be calculated using the formula: Volume = Mass / Density. We know the mass of the Sun is approximately 2.0 × 10³⁰ kg and the density is given as 10³ kg/m³. Plugging in these values, we get a volume of 2.0 × 10²⁷ m³.

The formula for the volume of a sphere is: Volume = 4/3 * π * Radius³. By rearranging this formula, we can solve for the radius as follows: Radius = (3 * Volume / (4 * π))^(1/3). Substituting the volume we calculated earlier, we find that the radius of the Sun is approximately 6.9 × 10⁸ m.

The diameter of the Sun is twice its radius, so the estimated diameter would be around 1.38 × 10⁹ m, which is equivalent to approximately 1.38 million kilometers.