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As Jupiter (or any planet) orbits the sun, the sun responds

Resolved Question:

As Jupiter (or any planet) orbits the sun, the sun responds by orbiting in a much smaller “orbit” around their mutual center of mass.

a) At what distance from the center of the sun is the Sun-Jupiter center of mass?

b) What is the sun’s circular velocity around that center of mass?

c) If an alien civilization were observing our solar system (conveniently edge-on so they see the maximum velocity), how small a velocity would they need to be able to detect to infer the presence of Earth by observing the sun’s radial velocity?
Submitted: 3 years ago.
Category: Homework
Expert:  Ray Atkinson replied 3 years ago.

Ray Atkinson :

What units are desired for the velocity? m/s? km/yr?

JACUSTOMER-205xr11h- :

m/s

Ray Atkinson :

A. The Sun-Jupiter barycenter is 742000 km from the center of the Sun.
B. 742000 * 2π =(NNN) NNN-NNNN Divide that by the 11.86 years that Jupiter takes to orbit, and you get 393096 km/yr. Translate that to m/s and you get 12.46 m/s
C. The Sun-Earth barycenter is measly 449 km from the Sun's center, and the sun revolves around that point once a year. 449 * 2π = 2820 km/yr or 0.089 m/s or about 9 cm/sec

JACUSTOMER-205xr11h- :

Thank you! Could you explain B a little more to me? I'd just like to know what equations you used and/or where the numbers are coming from? For instance, what's the 2n at the beginning?

Ray Atkinson :

C = 2·pi·r
742000 · 2 · pi =(NNN) NNN-NNNN This is the distance the sun will travel around that point. Jupiter takes 11.86 years to go around the Sun, so the Sun will move around that point in the same period. (NNN) NNN-NNNN/ 11.86 = 393096 km/yr

(393096) km/yr * (1000) m/km * (1 / 31536000) yr/sec = 12.465 m/sec

JACUSTOMER-205xr11h- :

Ah, of course. Thank you again! (:

Ray Atkinson :

I am of course simplifying things a bit, making the orbit circular, but the difference probably is less than the significant figures.

Ray Atkinson :

Jupiter's eccentricity is only 0.0484, so it is not much of a simplification.

Category: Homework
Satisfied Customers: 1889
Experience: Inner-city high school substitute teacher. Degrees in mathemetics, accounting, and education. Years and years of tutoring.

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