Could someone please solve question (b) and (c) ? Msun = 1 .99×1030 kg MMoon 7.3

Question

Could someone please solve question (b) and (c) ?  

Msun = 1 .99×1030 kg MMoon 7.35x1022 kg MEarth = 5.97×1024 kg Ayoon 384x105 km aEarth = 1 AU = 1.50×108 km RMoon = 1740 km REarth-6370 km (2) Today the Earth's lone Moon dominates our tides. But the Moon is migrating outward over time, and its tidal influence will therefore decrease. Write a simplified algebraic expression, using only the symbols above, for the distance of the Moon from Earth when the Sun and Moon exert equivalent tidal forces on Earth. b. (3) The Moon is currently migrating outward from Earth at a rate of -3.8 cm/year. Assume this rate remains constant with time, and compute the time, in years, until the Moon and Sun exert equivalent tidal forces on Earth. Compare to the expected remaining lifetime of our solar system of -5 billion more years. c.

Explanation / Answer

Answer:b

Since, tidal forrce can be calculated as follows;

F= GMm/R2

Where, G= gravitational constant, M= mass of the earth, m= mass od the moon, R= distance between the earth and moon.

Therefore, R= Square root of GMm/F

Answer:c

Since, rate is constant for remaining time, therefore, 5*10 9 years / 3.8 = 1.315* 109 years.

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