Find the ratio of the gravitational force on the Moon due to the Earth to the gravitational force on the Moon due to the Sun. (The mass of the Earth is 5.97 1024 kg, the mass of the Moon is 7.36 1022 kg, the mass of the Sun is 1.99 1030 kg, and the average Earth-Moon distance is 385,000 km, and the average distance between the Earth and the Sun is 1.50 1011 km.)
ForcemoonEarth=GMeMm/(dEM)^2
ForceEarthSun= GMeMs/(dES)^2
ratio= Mm/Ms * (DES/DEM)^2
So what in the world is hard about that?
To find the ratio of the gravitational force on the Moon due to the Earth to the gravitational force on the Moon due to the Sun, we need to calculate the two forces separately and then divide them.
Let's calculate the gravitational force between the Moon and the Earth first using Newton's law of gravitation:
F_earth-moon = G * (m_earth * m_moon) / r^2
where:
F_earth-moon is the gravitational force between the Earth and the Moon,
G is the gravitational constant (6.67430 × 10^-11 N(m/kg)^2),
m_earth is the mass of the Earth (5.97 x 10^24 kg),
m_moon is the mass of the Moon (7.36 x 10^22 kg),
and r is the average Earth-Moon distance (385,000 km or 385,000,000 meters).
Plugging in the values:
F_earth-moon = (6.67430 × 10^-11 N(m/kg)^2) * ((5.97 x 10^24 kg) * (7.36 x 10^22 kg)) / (385,000,000 meters)^2
Now, let's calculate the gravitational force between the Moon and the Sun using the same formula:
F_sun-moon = G * (m_sun * m_moon) / r^2
where:
F_sun-moon is the gravitational force between the Sun and the Moon,
m_sun is the mass of the Sun (1.99 x 10^30 kg),
and r is the average distance between the Earth and the Sun (1.50 x 10^11 meters).
Plugging in the values:
F_sun-moon = (6.67430 × 10^-11 N(m/kg)^2) * ((1.99 x 10^30 kg) * (7.36 x 10^22 kg)) / (1.50 x 10^11 meters)^2
Now that we have both forces, we can calculate the ratio by dividing the gravitational force on the Moon due to the Earth by the gravitational force on the Moon due to the Sun:
Ratio = F_earth-moon / F_sun-moon
Plug in the calculated values to get the final ratio.