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# Universal Law of Gravity

## Gravity is a constant force of attraction felt between all objects in the universe.

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Earth's Orbit

### Earth?s Orbit

Credit: Laura Guerin
Source: CK-12 Foundation

Initially believed to have a circular orbit, the Earth's orbit is actually elliptical. As the Earth orbits around the Sun in 365 days, its distance from the Sun varies between 147 and 152 million kilometers.

#### Amazing But True

Credit: NASA(NOAA)
Source: http://www.flickr.com/photos/gsfc/8575328570/

A satellite captures this image of Earth during the Spring Equinox [Figure2]

• According to Newton's law, every object in the universe attracts every other object with a force that is directly proportional to the square of the distance that separates them:

\begin{align*}F = G \frac{M_1 M_2}{R_2}\end{align*}

\begin{align*}G\end{align*} is the universal gravitational constants and \begin{align*}M_1\end{align*} and \begin{align*}M_2\end{align*} are the masses of the objects. Since the Earth is in orbit around the sun, we can define the force on the earth to be a centripetal force:

\begin{align*}\frac{Mv_2}{R_2} = G \frac{M_1 M_2}{R_2}\end{align*}

if we rewrite the speed of the orbit in terms of its period we get,

\begin{align*}T_2 = \left(\frac{4 \pi^2}{GM}\right) R_3\end{align*}

\begin{align*}R\end{align*} is the radius for a circular orbit or for the length of a semi major axis for an elliptical orbit.

#### Show What You Know

Using the information provided above, answer the following questions.

1. What force is keeping the Earth in orbit around the Sun?
2. From the link provided, determine the reduced mass if \begin{align*}m_1 = 4 \ kg\end{align*} and \begin{align*}m_2 = 6 \ kg\end{align*}
3. If the Earth had a uniform density, how would you expect the force of gravity to change as you get closer and closer to the center of the earth?

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