The theory of Time relativity explains well the weird behavior of the interstellar object ‘Oumuamua. I find that the real solar mass is slightly higher than today’s value, which caused the mysterious Speed Boost of which the value should be 0.217 mm/s above the prediction at perihelion. Time relativity confirms that ‘Oumuamua should slow down less than prediction, in proportion of which the difference is 4.28 ×10-8 near the Sun. For Pioneer anomaly I have computed the gap between real and predicted acceleration and found the value 8.70 ×10-10 which is very close to the observation (8.74±1.33)×10−10 m/s2.

The mass of the Sun is not measured by weighting, but derived from the parameters of Earth’s orbit which is nearly circular. Let rM be the radius of the Earth’s orbit and uE its orbital velocity. By equating the orbital acceleration of the Earth (see equation (36)) with its Newtonian gravitational acceleration (see equation (34)), we obtain equation (48) which gives the today’s used value of the mass of the Sun, M0, in equation (49).

Read the article below.

https://www.academia.edu/42871661/Oumuamua_Pioneer_anomaly_and_solar_mass_with_Time_Relativity

https://pengkuanonphysics.blogspot.com/2020/04/oumuamua-pioneer-anomaly-and-solar-mass.html