Answer :
Meteorite’s distance from the sun is [tex]2.6 \times 10^{10}[/tex] kilometers
Solution:
Given that,
[tex]\text{Jupiters average distance from the Sun } = 7.8 \times 10^8 \text{ kilometer }[/tex]
Also, given that,
The ratio comparing Jupiter’s distance from the Sun to a meteorite’s distance from the sun is [tex]3 \times 10^{-2}[/tex]
Which means,
[tex]\frac{\text{Jupiters distance from the Sun}}{\text{meteorite’s distance from the sun}} = 3 \times 10^{-2}[/tex]
Substitute the given value in above fraction,
[tex]\frac{7.8 \times 10^8}{\text{meteorite’s distance from the sun}} = 3 \times 10^{-2}[/tex]
Solve for meteorite’s distance from the sun
[tex]\text{Meteorites distance from the sun} = \frac{7.8 \times 10^8}{3 \times 10^{-2}}\\\\\text{Meteorites distance from the sun} = \frac{2.6 \times 10^8}{10^{-2}}\\\\\text{Use the law of exponent }\\\\\frac{a^m}{a^n} = a^{m-n}\\\\\text{Meteorites distance from the sun} =2.6 \times 10^{8-(-2)}\\\\\text{Meteorites distance from the sun} = 2.6 \times 10^{8+2}\\\\\text{Meteorites distance from the sun} =2.6 \times 10^{10}\\\\[/tex]
Thus, meteorite’s distance from the sun is [tex]2.6 \times 10^{10}[/tex] kilometers