the mass of the sun is 1.99×10³⁰ kg. jupiter is 7.79×10⁸ km away from the sun and has a mass of 1.90×10²⁷…

Explanation:

Step1: Recall gravitational - force formula

The gravitational - force formula is $F = G\frac{m_1m_2}{r^2}$, where $G = 6.67\times10^{- 11}\text{ N}\cdot\text{m}^2/\text{kg}^2$, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.

Step2: Convert distance to SI units

Given $r = 7.79\times10^{8}\text{ km}=7.79\times10^{11}\text{ m}$, $m_1 = 1.99\times10^{30}\text{ kg}$, and $m_2 = 1.90\times10^{27}\text{ kg}$.

Step3: Substitute values into the formula

$F=6.67\times 10^{-11}\times\frac{1.99\times 10^{30}\times1.90\times 10^{27}}{(7.79\times 10^{11})^2}$. First, calculate the numerator: $1.99\times 10^{30}\times1.90\times 10^{27}=1.99\times1.90\times10^{30 + 27}=3.781\times10^{57}$. Then, calculate the denominator: $(7.79\times 10^{11})^2=7.79^{2}\times10^{22}=60.6841\times10^{22}$. So, $F = 6.67\times10^{-11}\times\frac{3.781\times10^{57}}{60.6841\times10^{22}}$. $F=6.67\times\frac{3.781}{60.6841}\times10^{-11 + 57-22}$. $F=6.67\times0.0623\times10^{24}$. $F = 0.415541\times10^{24}=4.16\times10^{23}\text{ N}$.

Answer:

C. 4.16