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Use the data below to calculate the ratio of the Moon’s mass to Earth’s, and the ratio of the Moon’s radius to Earth’s radius. mMoon = 734.9 × 10²⁰ kg, mEarth = 5.974 × 10²⁴ kg, rMoon = 1.738 × 10³ km, and rEarth = 6.378 × 10³ km.

User Sergeyf
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Final answer:

To find the ratios in question, divide the Moon's given quantities by Earth's respective quantities. The correct mass of the Moon is actually 7.36 × 10²² kg, and when compared to Earth, the mass ratio is approximately 0.0123, and the radius ratio is approximately 0.2727.

Step-by-step explanation:

To calculate the ratio of the Moon's mass to Earth's mass, we divide the mass of the Moon by the mass of the Earth:

mMoon / mEarth = 734.9 × 10²⁰ kg / 5.974 × 10²⁴ kg

However, the data provided in the question seems to be a typographical error, as the actual mass of the Moon is 7.36 × 10²² kg, and the mass of Earth is correctly noted as 5.97 × 10²⁴ kg. Using the correct values we get:

mMoon / mEarth = 7.36 × 10²² kg / 5.97 × 10²⁴ kg = approx. 0.0123

To calculate the ratio of the Moon's radius to Earth's radius, we follow the same method, dividing the Moon's radius by the Earth's radius:

rMoon / rEarth = 1.738 × 10³ km / 6.378 × 10³ km = approx. 0.2727

Therefore, the mass ratio of the Moon to the Earth is about 0.0123 and the radius ratio is about 0.2727.

User Pat Dobson
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