Question

Help please! I hope the given possibles help

Answer 1

The answer is "
`5.184 * 10^(23)` kg"

Step-by-step explanation:

Given:

`g= 6.003 \ (m)/(s^2)\\\\G= 6.67 * 10^(-11) \ (N - m^2)/(kg^2)\\\\M=?\\\\radius= 2,400 \ km\\\\`

Calculating diameter:

`Diameter =radius * 2`

`=24* 10^5 * 2\\\\=48 * 10^5 \ m`

The formula for mass calculation:

`\to g = G * (M)/(((d^2)/(4)))\\\\\to g=G* (4M)/(d^2)\\\\\to 4M= (g * d^2)/(G) \\\\\to M= (g * d^2)/(4G) \\\\`

`=(6.003 * (48 * 10^(5))^2)/(4 * 6.67 * 10^(-11))\\\\=(6.003 * 2,304 * 10^(10))/(26.68* 10^(-11))\\\\=(13,830.912 * 10^(10))/(26.68* 10^(-11))\\\\=518.4 * 10^(21)\\\\= 5.184 * 10^(23)\\\\`