Question

Scientists once postulated the existence of a planet called Vulcan to explain

Mercury’s precession. Vulcan is supposed to be between Mercury and the sun

with the solar distance equal to 2/3 that of mercury. What would be its supposed

period?

Answer 1

$\frac{T_m^2}{T_v^2}=\frac{a_m^3}{a_v^3}\\$

$T_v=\sqrt {T^2_m\frac{a_v^3}{a_m^3}}=T_m\sqrt(\frac{2a_m}{3a_m})^3 \\ T_v=87.97\sqrt(\frac{2}{3})^3=58.65 \;d.$