Orbital Period Error in a Two-Body System

Question

Two satellites with masses $$m_1$$ and $$m_2$$ orbit a star of mass $$M$$, where $$m_1 + m_2 \ll M$$. What is the approximate percentage error in the orbital period that results from assuming the star is stationary?

Accepted Answer

Approximately $$(m_1 + m_2)/(2M) 	imes 100\%$$

Answer

Approximately $$(m_1 + m_2)^2/M^2 	imes 100\%$$

Answer

Exactly 0%

Answer

Approximately $$\sqrt{(m_1 + m_2)/M} 	imes 100\%$$

Orbital Period Error in a Two-Body System

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