Assuming circular orbits for both Mars and Earth, one can deduce that minimal distance can be observed when both planets are aligned within the common radial line:
ΔR=RM−RE Applying the 2nd Newton's law to the planetary motion, we obtain:
GRE2MmE=mEaE,aE=TE24π2RE⇒GM=TE24π2RE3The same expressions are valid for Mars (one has only to replace index "E" by "M"). Hence, we obtain:
TE2RE3=TM2RM3⇒RM=RE(TETM)2/3 As a result,
ΔR=RE[(TETM)2/3−1] Substituting the numerical values, we obtain:
ΔR=149.6⋅[(1.001.88)2/3−1]≈78.3millionkm Answer: 78.3 million km.
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