1.
Start by looking up and writing down any numerical quantities about the Earth and the Sun you expect to be important or useful.
Section 11.9 Application: Orbital Motion
Exercises Activities - Motion of the Earth
The Earth moves around the Sun in an approximately circular orbit.
2.
Calculate the angular velocity of the Earth’s orbit around the Sun.
3.
Sketch a free-body diagram for the Earth.
4.
Use the Law of Motion to find a symbolic expression for the mass of the Sun in terms of other physical quantities you can look up. Plug in numbers and check if your answer is close to the measured mass of the Sun!
5.
Were there any numerical quantities you expected to matter that turned out not to be important for this context? Why do you think this happened?
An orbiting object can often be treated as undergoing uniform circular motion, in which case the only force responsibly for the circular motion is the gravitational force between the orbiting and orbited object.
Principle 11.9.1. Law of Orbital Periods (Kepler’s Third Law).
The period of an orbit \(T\) is related to the semi-major axis of the orbit \(a\) by
1
for a circular orbit, this is equal to the radius
\begin{equation*}
a^3 = \frac{GM}{(2\pi)^2}T^2
\end{equation*}
where \(G\) is the universal gravitational constant and \(M\) is the mass of the object that is being orbited. This law assumes that the mass of the orbiting object is much smaller than the mass of the object being orbited.
