Question

Isaac Newton's universal law of gravitation is an expansion of the planetary motion ideas developed by Johannes Kepler. One derivative of Newton's universal law gives us a useful formula to find tidal forces on Earth caused by either the Sun or Moon. The tidal force depends on the mass m of the Sun or Moon, the radius r of Earth, and the cube of the distance d between Earth and either the Sun or Moon. (The G in the equation is known as the gravitational constant, and it doesn't change.)

F_tidal = 2G * m * r / d³
Based on the equation and your knowledge of the Sun-Earth-Moon system, which celestial body (the Sun or the Moon) has a greater influence on Earth's tides? Justify your answer.
A) The Sun
B) The Moon
C) Both equally
D) It depends on the position

Answer 1

The Moon has a greater influence on Earth's tides.

Step-by-step explanation:

Isaac Newton's universal law of gravitation states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The tidal force on Earth caused by either the Sun or the Moon can be calculated using the formula F_tidal = 2G * m * r / d³, where G is the gravitational constant, m is the mass of the Sun or the Moon, r is the radius of Earth, and d is the distance between Earth and the Sun or the Moon. Since the tidal force depends on the cube of the distance, the closer celestial body will have a greater influence on Earth's tides. Therefore, the Moon, being closer to Earth than the Sun, has a greater influence on Earth's tides.