Given that the Sun has a mass 333,000 times larger than Earth’s mass and Earth has an average distance of 1.49 x 1011 m from the Sun, at what distance from the Sun is the center of mass of the Earth-Sun system?

a. 1.00 m
b. 4.47 x 105 m
c. zero
d. 333,000 m
e. 1.49 x 1011 m

To find the distance from the Sun at which the center of mass of the Earth-Sun system is located, we can use the concept of center of mass. The center of mass of a system is the point at which the system would balance if it were made to rest on a single support.

In this case, since the Sun's mass is much larger than Earth's mass, the center of mass of the Earth-Sun system will be located closer to the Sun than to the Earth.

To calculate the distance of the center of mass, we can use the equation:

Distance of center of mass = ((mass of Earth) * (distance from Earth to center of mass) + (mass of Sun) * (distance from Sun to center of mass))/(total mass of system)

Given:
Mass of Sun = 333,000 times larger than Earth's mass
Average distance from Earth to Sun = 1.49 x 10^11 m

Let's solve the equation step by step:

1. Calculate the total mass of the system:
total mass of system = mass of Earth + mass of Sun
= mass of Earth + 333,000 * mass of Earth
= (1 + 333,000) * mass of Earth

2. Calculate the distance from Earth to the center of mass:
distance from Earth to center of mass = ?
mass of Earth * distance from Earth to center of mass = mass of Sun * distance from Sun to center of mass
mass of Earth * distance from Earth to center of mass = 333,000 * mass of Earth * (distance from Earth to Sun - distance from Earth to center of mass)
distance from Earth to center of mass = 333,000 * distance from Earth to Sun - 333,000 * distance from Earth to center of mass
distance from Earth to center of mass + 333,000 * distance from Earth to center of mass = 333,000 * distance from Earth to Sun
(1 + 333,000) * distance from Earth to center of mass = 333,000 * distance from Earth to Sun
distance from Earth to center of mass = (333,000 * distance from Earth to Sun)/(1 + 333,000)

3. Substitute the values:
distance from Earth to center of mass = (333,000 * 1.49 x 10^11 m)/(1 + 333,000)

Calculating this expression, we find that the distance from Earth to the center of mass is approximately 4.47 x 10^5 m.

Therefore, the correct answer is (b) 4.47 x 10^5 m.