Question

the mass of mars is 6.42×10^{23} kg. its moon phobos is 9378 kilometers away from mars and has a mass of 1.06×10^{16} kg. what is the gravitational force between mars and phobos? o 5.16×10^{15} n o 5.16×10^{21} n o 4.84×10^{22} n o 4.84×10^{25} n

Explanation:

Step1: Recall gravitational - force formula

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

Step2: Convert distance to SI units

The distance $r = 9378\ km=9378\times10^{3}\ m$. $m_1 = 6.42\times10^{23}\ kg$, $m_2 = 1.06\times10^{16}\ kg$.

Step3: Substitute values into the formula

$F=(6.67\times 10^{-11})\frac{(6.42\times 10^{23})\times(1.06\times 10^{16})}{(9378\times 10^{3})^{2}}$
First, calculate the numerator: $(6.42\times 10^{23})\times(1.06\times 10^{16})=6.42\times1.06\times10^{23 + 16}=6.8052\times10^{39}$
Then, calculate the denominator: $(9378\times 10^{3})^{2}=9378^{2}\times10^{6}=(9378\times9378)\times10^{6}=8.7946884\times10^{7}\times10^{6}=8.7946884\times10^{13}$
Now, $F=(6.67\times 10^{-11})\frac{6.8052\times10^{39}}{8.7946884\times10^{13}}$
$F = 6.67\times\frac{6.8052}{8.7946884}\times10^{-11 + 39-13}$
$F\approx6.67\times0.774\times10^{15}$
$F\approx5.16\times10^{15}\ N$

Answer:

5.16×10¹⁵ N