Answer:
3.456 × 10^(8) m
Explanation:
We are given;
Mass of earth; m_e = 5.98 × 10^(24) kg
Mass of moon; m_m = 7.36 × 10^(22) kg
Distance from earth to moon; L = 3.84 × 10^(8) m.
We are told that the Moon’s gravitational pull is stronger than that of Earth’s.
Thus;
F_EA ≤ F_MA
Formula for force due to gravity is;
F = GMm/r²
Applying to this question, we have;
(Gm_e•m_a)/x² ≤ (Gm_m•m_a)/(l - x)²
Where x is his distance from the center of the Earth
Now, G and m_a will cancel out from both sides and we plug on other values to get;
(5.98 × 10^(24))/x² ≤ (7.36 × 10^(22))/(3.84 × 10^(8) - x)²
Taking square root of both sides gives;
2445403852127.4966/x ≤ 271293199325.0107/(3.84 × 10^(8) - x)
Rearranging gives;
2445403852127.4966(3.84 × 10^(8) - x) ≤ 271293199325.0107x
Simplifying this gives;
9.0139(3.84 × 10^(8) - x) ≤ x
(34.613 × 10^(8)) - 9.0139x ≤ x
(34.613 × 10^(8)) ≤ x + 9.0139x
(34.613 × 10^(8)) ≤ 10.0139x
x ≥ (34.613 × 10^(8))/10.0139
x ≥ 3.456 × 10^(8)