Using Newton's Law of Universal Gravitation, compare the effect of the Sun and the Moon on the tides.
Constants: Mass of the Moon, M☽= 7.348E22 kg. Moon's semi-major axis, a☽= 3.844E8 m. You can find the other constants you will need on the Astronomy Formula Chart.
(In Moodle, enter large numbers with scientific E notation. Example: 100 = 1.00*102 in scientific notation, or 1.00E2 in scientific E notation. Don't forget measurement units! If there are two blanks, enter the numerical value in the first blank, and the measurement unit in the second blank. Example: 1.0 m + 1.0 m = .)
Start with two equal volumes of ocean water, one on the near side of the Earth, and the other on the far side of the Earth. Assume the mass of each volume of water equals 1000 kg.
The pull of the Sun on the water on the near side of the Earth:
(G (Nm2)/kg2)(mass of sun, M☉ )(mass of water, 1000 kg) / (1 AU, Earth's semi-major axis, a♁ m - Radius of the Earth, R♁ )2 = (enter at least 5 significant digits)
The pull of the Sun on the water on the far side of the Earth:
(G (Nm2)/kg2)(mass of sun, M☉ )(mass of water, 1000 kg) / (1 AU, Earth's semi-major axis, a♁ m + Radius of the Earth, R♁ )2 = (enter at least 5 significant digits)
The tides are caused by difference in forces from the near side to the far side. The difference in the forces from sun = (enter at least 2 significant digits)
The pull of the Moon on the water on the near side of the Earth:
(G (Nm2)/kg2)(mass of moon, M☽ )(mass of water, 1000 kg) / (moon's semi-major axis, a☽ m - Radius of the Earth, R♁ )2 = (enter at least 3 significant digits)
The pull of the Moon on the water on the far side of the Earth:
(G (Nm2)/kg2)(mass of moon, M☽ )(mass of water, 1000 kg) / (moon's semi-major axis, a☽ m + Radius of the Earth, R♁ )2 = (enter at least 3 significant digits)
The tides are caused by difference in forces from the near side to the far side. The difference in the forces from moon = (enter at least 2 significant digits)
So the has a bigger influence on earth's tides than the .
Mass35kg
Velocity 15mls
To compare the effect of the Sun and the Moon on the tides using Newton's Law of Universal Gravitation, we need to calculate the gravitational force exerted by each celestial body on the water on the near and far sides of the Earth.
First, let's calculate the gravitational force exerted by the Sun on the water on the near side of the Earth. The formula for gravitational force is given by:
Force = (G * Mass1 * Mass2) / Distance^2
Where G is the gravitational constant, Mass1 is the mass of the Sun, Mass2 is the mass of the water, and Distance is the distance between the Sun and the water.
Using the given constants from the Astronomy Formula Chart:
- Mass of the Sun (M☉) = value from the chart.
- Mass of the water = 1000 kg.
- Distance = 1 AU (Earth's semi-major axis, a♁) minus the Radius of the Earth (R♁).
Calculating the force on the near side of the Earth:
Force_sun_near = (G * M☉ * 1000 kg) / (1 AU - R♁)^2
Now let's calculate the gravitational force exerted by the Sun on the water on the far side of the Earth. The distance will be the sum of 1 AU and the Radius of the Earth.
Calculating the force on the far side of the Earth:
Force_sun_far = (G * M☉ * 1000 kg) / (1 AU + R♁)^2
Next, let's calculate the gravitational force exerted by the Moon on the water on the near and far sides of the Earth. Using similar calculations as before:
Calculating the force of the Moon on the near side of the Earth:
Force_moon_near = (G * M☽ * 1000 kg) / (Moon's semi-major axis, a☽ - R♁)^2
Calculating the force of the Moon on the far side of the Earth:
Force_moon_far = (G * M☽ * 1000 kg) / (Moon's semi-major axis, a☽ + R♁)^2
Now, let's calculate the difference in forces from the near side to the far side caused by the Sun:
Difference_sun = Force_sun_near - Force_sun_far
And the difference in forces from the near side to the far side caused by the Moon:
Difference_moon = Force_moon_near - Force_moon_far
Comparing the two differences, if the difference caused by the Sun is greater than the difference caused by the Moon, then the Sun has a bigger influence on Earth's tides. Otherwise, the Moon has a bigger influence.
So, to compare the effect of the Sun and the Moon on the tides using Newton's Law of Universal Gravitation, you need to input the given constants into the formulas and calculate the respective forces and differences.