Answer:
258774.9441 m
Explanation:
x = Distance of probe from Earth
y = Distance of probe from Sun
Distance between Earth and Sun = [tex]x+y=149.6\times 10^6\ m[/tex]
G = Gravitational constant
[tex]M_s[/tex] = Mass of Sun = [tex]1.989\times 10^{30}[/tex]
[tex]M_e[/tex] = Mass of Earth = [tex]5.972\times 10^{24}\ kg[/tex]
According to the question
[tex]\frac{GM_sm}{x^2}=\frac{GM_em}{y^2}\\\Rightarrow \frac{M_s}{x^2}=\frac{M_e}{y^2}\\\Rightarrow x=\sqrt{\frac{M_s\times y^2}{M_e}}\\\Rightarrow x=\sqrt{\frac{1.989\times 10^{30}\times y^2}{5.972\times 10^{24}}}\\\Rightarrow x=577.10852y[/tex]
[tex]x+y=149.6\times 10^6\\\Rightarrow 577.10852y+y=149.6\times 10^6\\\Rightarrow 578.10852y=149.6\times 10^6\\\Rightarrow y=\frac{149.6\times 10^6}{578.10852}\\\Rightarrow y=258774.9441\ m[/tex]
The probe should be 258774.9441 m from Earth
