5 a) Mass = 6.0 × 10²⁴ kg; d = 12 × 10⁶ m
[tex]r = \frac{1}{2}d = \frac{1}{2} \times 12 \times10^{6}\text{ m} = 6.0 \times 10^{6} \text{ m}\\[/tex]
[tex]V = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi \times (6.0 \times 10^{6} \text{ m})^{3} = 9.05 \times 10^{20} \text{ m}^{3}\\[/tex]
[tex]\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{6.0 \times 10^{24}\text{ kg}}{9.05 \times 10^{20} \text{ m}^{3}} = \text{6600 kg/m}^{3}\\[/tex]
The average density is 6600 kg/m³.
5 b) Mass = 2.0 × 10³⁰ kg; Diameter = 1.4 × 10⁶ km
[tex]r = \frac{1}{2}d = \frac{1}{2} \times 1.4 \times10^{9}\text{ m} = 7.0 \times 10^{8} \text{ m}\\[/tex]
[tex]V = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi \times (7.0 \times 10^{8} \text{ m})^{3} = 1.43 \times 10^{27} \text{ m}^{3}\\[/tex]
[tex]\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{2.0 \times 10^{30}\text{ kg}}{1.43 \times 10^{27} \text{ m}^{3}} = \text{1400 kg/m}^{3}\\[/tex]
The average density is 1400 kg/m³.
5 c) Venus and the Sun are most like the objects in Parts a) and b). Venus has the greater density
6 a) Mass = 4.8 × 10²² km; Diameter = 3.1 × 10⁶ m
[tex]r = \frac{1}{2}d = \frac{1}{2} \times 3.1 \times10^{6}\text{ m} = 1.55 \times 10^{6} \text{ m}\\[/tex]
[tex]V = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi \times (1.55 \times 10^{6} \text{ m})^{3} = 1.56 \times 10^{19} \text{ m}^{3}\\[/tex]
[tex]\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{4.8 \times 10^{22}\text{ kg}}{1.56 \times 10^{19} \text{ m}^{3}} = \text{3100 kg/m}^{3}\\[/tex]
The average density of the moon is 3100 kg/m³.
6 b) The satellite appears to consist mostly of silicate rock.
