Using Newton's Law of Universal Gravitation, compare the gravitational pull of the Sun on the Earth to the gravitational pull of the Moon on the Earth.
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 = .)
The pull of the Sun on the Earth:
(G (Nm2)/kg2)(mass of sun, M☉ )(mass of earth, M♁ ) / (1 AU, Earth's semi-major axis, a♁ m)2 =
The pull of the Moon on the Earth:
(G (Nm2)/kg2)(mass of moon, M☽ )(mass of earth, M♁ ) / (moon's semi-major axis, a☽ m)2 =
So the pulls harder on the earth than the .
To compare the gravitational pull of the Sun on the Earth to the gravitational pull of the Moon on the Earth using Newton's Law of Universal Gravitation, we need to calculate the numerical values for each pull.
First, let's find the pull of the Sun on the Earth. According to the given constants, the mass of the Sun (M☉) is available on the Astronomy Formula Chart, and the mass of the Earth (M♁) is not given. We need to find the mass of the Earth from the available information.
Using the Moon's semi-major axis (a☽) and the Sun-Earth semi-major axis (1 AU = Earth's semi-major axis = a♁), we can use Kepler's Third Law to find the mass of the Earth. The formula for Kepler's Third Law is:
T^2 = (4π^2 / G * (M☉ + M♁)) * a♁^3
where T is the period of the Earth's revolution around the Sun. The period of Earth's revolution is approximately 365.25 days, which can be converted to seconds.
Once we have the mass of the Earth calculated, we can proceed to calculate the gravitational pull of the Sun on the Earth using Newton's Law of Universal Gravitation:
Gravitational Pull of the Sun on the Earth = (G * M☉ * M♁) / a♁^2
where G is the gravitational constant.
Now, let's find the pull of the Moon on the Earth. The mass of the Moon (M☽) and the Moon's semi-major axis (a☽) are given. We can directly use Newton's Law of Universal Gravitation to calculate the gravitational pull:
Gravitational Pull of the Moon on the Earth = (G * M☽ * M♁) / a☽^2
Finally, compare the magnitude of these two values to determine which one pulls harder on the Earth.
Please note that I've provided the step-by-step process to calculate these values, but the actual calculations require specific numerical entries provided in the question.