Classical Mechanics

PS.3.1 Worked Example - Orbital Circular Motion

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A person on a spherical asteroid of mass ${\displaystyle m_1}$ and radius ${\displaystyle R}$, sees a small satellite of mass ${\displaystyle m_2}$ orbiting the asteroid in a circular orbit of period ${\displaystyle T}$.

Express you answer in terms of some or all of the following: ${\displaystyle m_1}$,${\displaystyle m_2}$, ${\displaystyle \pi }$, ${\displaystyle T}$, and the universal gravitational constant ${\displaystyle G}$.

(Part a) What is the radius ${\displaystyle r_{\text{sat}}}$ of the satellite’s orbit?

Worked Example - Orbital Circular Motion – Radius

(Part b) What is the magnitude of the velocity of the satellite?

Express you answer in terms of some or all of the following: ${\displaystyle m_1}$, ${\displaystyle m_2}$, ${\displaystyle \pi }$, ${\displaystyle T}$, and the universal gravitational constant ${\displaystyle G}$.

Orbital Circular Motion - Velocity

(Part c) If the asteroid rotates about its axis with a period ${\displaystyle T_{\text{a}}}$, at what radius must the satellite orbit the asteroid so that the satellite appears stationary to the person on the asteroid?

Express you answer in terms of some or all of the following: ${\displaystyle m_1}$, ${\displaystyle m_2}$, ${\displaystyle \pi }$, ${\displaystyle T_a}$, and ${\displaystyle G}$.

Orbital Circular Motion - Period

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