Question

1. calculate the force of gravity between these two masses. show all steps/label all units

m₁ = 6.66 × 10⁶ kg m₂ = 7.77 × 10⁷ kg r = 3.33 × 10³ m

Explanation:

Step1: Write the formula for gravitational force

The formula for the gravitational force \(F\) between two masses \(m_1\) and \(m_2\) separated by a distance \(r\) is \(F = G\frac{m_1m_2}{r^{2}}\), where \(G = 6.67\times10^{- 11}\text{ N}\cdot\text{m}^{2}/\text{kg}^{2}\) (the gravitational constant).

Step2: Substitute the given values into the formula

Substitute \(m_1 = 6.66\times10^{6}\text{ kg}\), \(m_2 = 7.77\times10^{7}\text{ kg}\), \(r = 3.33\times10^{3}\text{ m}\), and \(G = 6.67\times10^{-11}\text{ N}\cdot\text{m}^{2}/\text{kg}^{2}\) into the formula:

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First, calculate the numerator \((6.66\times 10^{6})(7.77\times 10^{7})=6.66\times7.77\times10^{6 + 7}=51.7482\times10^{13}=5.17482\times 10^{14}\)
Then, calculate the denominator \((3.33\times 10^{3})^{2}=3.33^{2}\times10^{6}=11.0889\times10^{6}\)
Now the formula becomes \(F=(6.67\times 10^{-11})\frac{5.17482\times 10^{14}}{11.0889\times10^{6}}\)

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Then \(F=(6.67\times 10^{-11})(4.667\times10^{7})\)

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Answer:

\(F = 3.11\times10^{-3}\text{ N}\) (rounded to three significant figures)