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(1) the mass of the farth is \( 6 \times 10^{24} \mathrm{~kg} \). If the centres of the earth and moon are \( 3,9 \times 10^{\circ} \mathrm{m} \) apart, the force of gravitational attraction between them is \( 1,9 \times 10^{20} \mathrm{~N} \). what is the approximate mass of the moon (2) calculate the value of g at a point \( 8,10^{6} \mathrm{~m} \) from the center of the earth use \( 6 \times 10^{24} \mathrm{~kg} \) as the mater of the earth (3) ure the following data to calealerte the mass of the earth : g is equal to \( 9,8 \mathrm{~m} . \mathrm{s}^{-2} \) \( r=6 \times 10^{6} \mathrm{~m} \) \( G=6,7 \times 10^{-11} \mathrm{~N} . \mathrm{m}^{2} \) per \( \mathrm{kg}^{2} \)

Ask by Osborne Griffiths. in South Africa
Mar 14,2025

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- **Mass of the Moon:** Approximately \(1.73 \times 10^{22} \, \text{kg}\) - **Value of \( g \) at \(8.1 \times 10^{6} \, \text{m}\):** Approximately \(0.2457 \, \text{m/s}^2\) - **Mass of the Earth:** Approximately \(1.301 \times 10^{13} \, \text{kg}\)

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To determine the mass of the moon, we can use Newton’s law of gravitation which states that the force of gravity between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between them. Rearranging this formula will help find the moon's mass when paired with Earth's mass and the given gravitational force. For calculating the value of \( g \) at a distance of \( 8 \times 10^{6} \) m from the Earth's center, you would apply the formula \( g = \frac{GM}{r^2} \). Here, \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the distance from the Earth's center. This will provide an approximation of gravitational acceleration at that point.

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