When we consider the orbit of celestial objects in Physics 101 we usually consider systems where a small object orbits around a much larger object. To make it easier to solve problems, we assume that the center of the small object's orbit is located at the large object's center of mass. In reality, the center of the orbit of celestial objects is their shared center of mass, called the barycenter. When there is a big difference between the large and small objects' masses, we can assume the barycenter is near the center of the object, but when the masses are closer in value to each other the barycenter can be located in the space between the objects (see the animation below, the barycenter is indicated by the red + symbaol). Let's explore some of the relationships between our Sun and some planets in the solar system to get a sense of how this works. This question uses astrological symbols as labels: @ (Sun), & (Earth), and & (Jupiter). 1) The Earth has a mass Mg= 5.972 x 10* kg. The Sun has a mass M= 1.99 x 10% kg = 333, 000Mg. The average Earth-Sun center-to-center orbital distance is R = 1.5 x 10% km. How far in km from the center of the Sun is the Earth-Sun system's barycenter located? (Express your answer to three significant figures.) 450 km Submit | Your submissions: | 450 ; Computed value: 450 Submitted: Wednesday, March 6 at 11:01 PM Feedback: Right answer ! 2) The radius of the Sun is Re= 696000 km. How many Sun-radii distances is the Earth-Sun barycenter from the center of the Sun? (Express your answer to three significant figures. You can enter numbers in scientific notation using the 'E\" notation, e.g. 3 % 10% can be input as 3E8.) | Submit | Your submissions: | 6.47e-1 | X Computed value: 6.47e-1 Submitted: Wednesday, March 6 at 11:02 PM Feedback: [t appears you have made a power of ten error. 3) Jupiter has a mass Ma= 318Me and orbits the Sun at an average center-to-center distance of R = 7.78 x 10 km. How far in km from the center of the Sun is the Jupiter-Sun system's barycenter located? (Express your answer to three significant figures.) km Submit Your submissions: 750 | X Computed value: 750 Submitted: Wednesday, March 6 at 11:02 PM Feedback: 4) How many Sun-radii distances is the Jupiter-Sun barycenter from the center of the Sun? (Express your answer to three significant figures.) 1.07 Ro Submit Your submissions: 1.07 Computed value: 1.07 Submitted: Wednesday, March 6 at 11:01 PM Feedback: That's correct. The barycenter of the Jupiter-Sun system is located outside the Sun