The mean distance from the center of the earth to the center of the moon is rem = 3.84 × 108 m. The mass of the earth is me = 5.98 × 1024 kg and the mass of the moon is mm = 7.34 × 1022 kg. The mean radius of the earth is re = 6.37 × 106 m. The mean radius of the moon is rm = 1.74 × 106 m.
How far from the center of the earth is the center of mass of the earth-moon system located?
http://www.masteringphysicssolutions.net/chapter-6-6-the-center-of-mass-of-the-earth-moon-sun-system/
the last one plzz
To calculate the distance from the center of the Earth to the center of mass of the Earth-Moon system, we can use the formula for the center of mass:
r_cm = (m1 * r1 + m2 * r2) / (m1 + m2)
where:
r_cm is the distance from the center of the Earth to the center of mass of the Earth-Moon system,
m1 is the mass of the Earth,
r1 is the distance from the center of the Earth to the center of the Earth,
m2 is the mass of the Moon,
r2 is the distance from the center of the Earth to the center of the Moon.
Given the following values:
m1 = 5.98 × 10^24 kg
r1 = 6.37 × 10^6 m
m2 = 7.34 × 10^22 kg
r2 = 3.84 × 10^8 m
we can substitute these values into the formula:
r_cm = (5.98 × 10^24 * 6.37 × 10^6 + 7.34 × 10^22 * 3.84 × 10^8) / (5.98 × 10^24 + 7.34 × 10^22)
Simplifying the expression:
r_cm = (3.807526 × 10^31 + 2.81856 × 10^31) / (5.98 × 10^24 + 7.34 × 10^22)
r_cm = 6.626086 × 10^31 / 6.073 × 10^24
r_cm ≈ 10880.1 m
Therefore, the center of mass of the Earth-Moon system is located approximately 10880.1 meters from the center of the Earth.
To find the distance from the center of the Earth to the center of mass of the Earth-Moon system, we can use the formula for the center of mass:
xd = (m1 * x1 + m2 * x2) / (m1 + m2)
where xd is the distance from the center of the Earth to the center of mass of the system, m1 and m2 are the masses of the Earth and Moon respectively, and x1 and x2 are the distances of the Earth and Moon from their respective centers.
In this case, we know the values:
m1 = 5.98 × 10^24 kg (mass of the Earth)
m2 = 7.34 × 10^22 kg (mass of the Moon)
x1 = 0 (the Earth is at the origin, so its distance from its center is 0)
x2 = rem = 3.84 × 10^8 m (mean distance from the center of the Earth to the center of the Moon)
Substituting these values into the formula, we get:
xd = (5.98 × 10^24 kg * 0 + 7.34 × 10^22 kg * 3.84 × 10^8 m) / (5.98 × 10^24 kg + 7.34 × 10^22 kg)
Simplifying the expression:
xd = (7.34 × 10^22 kg * 3.84 × 10^8 m) / (5.98 × 10^24 kg + 7.34 × 10^22 kg)
xd ≈ 4.67 × 10^5 m
Therefore, the center of mass of the Earth-Moon system is located approximately 4.67 × 10^5 meters from the center of the Earth.