Question

Help please! I hope the given possibles help

Answer 1

Answer:

The answer is "$5.184 \times 10^{23}$ kg"

Explanation:

Given:

$g= 6.003 \ \frac{m}{s^2}\\\\G= 6.67 \times 10^{-11} \ \frac{N - m^2}{kg^2}\\\\M=?\\\\radius= 2,400 \ km$

Calculating diameter:

$Diameter =radius \times 2$

                $=24\times 10^5 \times 2\\\\=48 \times 10^5 \ m$

The formula for mass calculation:

$\to g = G \times \frac{M}{(\frac{d^2}{4})}\\\\\to g=G\times \frac{4M}{d^2}\\\\\to 4M= \frac{g \times d^2}{G} \\\\\to M= \frac{g \times d^2}{4G}$

         $=\frac{6.003 \times (48 \times 10^{5})^2}{4 \times 6.67 \times 10^{-11}}\\\\=\frac{6.003 \times 2,304 \times 10^{10}}{26.68\times 10^{-11}}\\\\=\frac{13,830.912 \times 10^{10}}{26.68\times 10^{-11}}\\\\=518.4 \times 10^{21}\\\\= 5.184 \times 10^{23}$