Question

the force that causes the moon to orbit the earth is called ___.
question 8 1 pts
calculate the gravitational force between earth (mass = 5.97×10^{24} kg) and an object with mass = 1000 kg located 6.45×10^{6} m from the center of the earth. (use g = 6.67×10^{-11} n·m^{2}/kg^{2} )

Explanation:

Step1: Identify the gravitational - force formula

The formula for gravitational force is $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers.

Step2: Substitute the given values

We have $G = 6.67\times10^{-11}\ N\cdot m^2/kg^2$, $m_1 = 5.97\times 10^{24}\ kg$, $m_2=1000\ kg$, and $r = 6.45\times 10^{6}\ m$.
Substitute these values into the formula:
$F=(6.67\times 10^{-11})\frac{(5.97\times 10^{24})\times(1000)}{(6.45\times 10^{6})^2}$

Step3: Calculate the numerator

$(5.97\times 10^{24})\times(1000)=5.97\times 10^{27}$
Then $(6.67\times 10^{-11})\times(5.97\times 10^{27})=6.67\times5.97\times10^{-11 + 27}=39.8299\times 10^{16}=3.98299\times 10^{17}$

Step4: Calculate the denominator

$(6.45\times 10^{6})^2=6.45^2\times10^{12}=41.6025\times 10^{12}=4.16025\times 10^{13}$

Step5: Calculate the force

$F=\frac{3.98299\times 10^{17}}{4.16025\times 10^{13}}=\frac{3.98299}{4.16025}\times10^{17 - 13}\approx0.9574\times 10^{4}=9574\ N$

Answer:

$9574\ N$