Having some trouble with a formula

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Jan 3, 2020
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I'm trying to get the distance to the center of mass from either the star or the planet.
m1 is the mass of the star and m2 is the mass of the planet. r1 is the distance from the center of mass to the star and r2 is the distance from the planet to the center of mass
m1 = 1.9885×1030
m2 = 5.97237×1024
r = 147,098,070
r = r1 + r2
m1 x r1 = m2 x r2

I know what m1, m2 and r are, but i need to know what r1 and r2 are.
Could someone help me?
 
Last edited:
Very good! For those who are still wondering, we have two equations for \(\displaystyle r_1\) and \(\displaystyle r_2\):
\(\displaystyle r_1+ r_2= 147,098,070= 1.4709807×10^8\) and
\(\displaystyle 1.9885×10^{30}r_1= 5.97237×10^{24}\).

From the first equation, \(\displaystyle r_2= 1.47098070×10^8- r_1\) so we can write the second equation
\(\displaystyle 1.9885×10^{30}r_1= 5.97237×10^{24}(1.7098070×10^8- r_1)= 1.02116×10^{32}- 5.97237×10^{24}r_1\).

I would write that as \(\displaystyle ar_1= b- cr_1\) with \(\displaystyle a= 1.9885×10^{30}\), \(\displaystyle b= 1.02116×10^{32}\), and \(\displaystyle c= 5.97237×10^{24}\) then solve for \(\displaystyle r_1= \frac{b}{a+ c}\).
 
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