Calculate the magnitude of the gravitational force between the Earth and an m = 6.00 kg mass on the surface of the Earth. The distance to the center of the Earth from the surface is 6.37×103 km and the mass of the Earth is 5.98×1024 kg.
B)Calculate the magnitude of the gravitational force between the Moon and an m = 6.00 kg mass on the surface of the Earth nearest to the moon. The distance to the center of the Moon from the surface of the Earth is 3.76×105 km and the mass of the Moon is 7.36×1022 kg.
C)Calculate the ratio of the magnitude of the gravitational force between an m = 6.00 kg mass on the surface of the Earth due to the Sun to that due to the Moon. The mass of the Sun is 1.99×1030 kg and the distance from the center of the Sun to the surface of the Earth is 1.50×108 km.
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To calculate the magnitude of the gravitational force between two objects, we can use the formula:
F = (G * m1 * m2) / r^2
Where:
- F represents the magnitude of the gravitational force,
- G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2),
- m1 and m2 are the masses of the two objects, and
- r is the distance between the centers of the two objects.
Let's calculate the values.
B) Magnitude of the gravitational force between the Earth and an m = 6.00 kg mass on the surface of the Earth:
- m1 (mass of the Earth) = 5.98 × 10^24 kg
- m2 (mass of the object) = 6.00 kg
- r (distance to the surface of the Earth) = 6.37 × 10^3 km
First, convert the distance from km to meters (1 km = 1000 m):
r = 6.37 × 10^3 km × 1000 m/km = 6.37 × 10^6 m
Now let's calculate the magnitude of the gravitational force using the formula:
F = (G * m1 * m2) / r^2
F = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.98 × 10^24 kg * 6.00 kg) / (6.37 × 10^6 m)^2
Now evaluate the expression using a calculator to find the magnitude of the gravitational force.
C) Magnitude of the gravitational force between the Moon and an m = 6.00 kg mass on the surface of the Earth nearest to the Moon:
- m1 (mass of the Moon) = 7.36 × 10^22 kg
- m2 (mass of the object) = 6.00 kg
- r (distance to the surface of the Moon) = 3.76 × 10^5 km
Convert the distance from km to meters (1 km = 1000 m):
r = 3.76 × 10^5 km × 1000 m/km = 3.76 × 10^8 m
Now use the same formula as above to calculate the magnitude of the gravitational force.
C) Ratio of the magnitude of the gravitational force between the Sun and the Earth compared to the Moon:
- m1 (mass of the Sun) = 1.99 × 10^30 kg
- m2 (mass of the object) = 6.00 kg
- r (distance from the surface of the Sun to the Earth) = 1.50 × 10^8 km
Convert the distance from km to meters (1 km = 1000 m):
r = 1.50 × 10^8 km × 1000 m/km = 1.50 × 10^11 m
Now use the same formula to calculate the magnitude of the gravitational force.
Once you have the values for all the magnitudes of the gravitational forces, you can calculate the ratio of the force between the Sun and the Earth to the force between the Earth and the Moon. Divide the magnitude of the Sun to Earth force by the magnitude of the Earth to Moon force to obtain the ratio.
1. F = m*g so 6*9.81
2. A= G*distance to moon*distance to earth
B = Mass of the moon. So your answer is A/B