3.3 - Universal Gravitation

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Gravity

Thus, it is the force of gravity which causes objects to orbit one another.

Recall,

Near the surface of the Earth, g 9.81 m/s2.

In general,

But, what is g? Where does it come from?

g is the magnitude of the gravita&'onal fi'e produced by an object of

mass m at a point a distance of r from its center!

3.3 - Universal Gravitation

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Consider the following:

The force of gravity on m2 is given by:

Whereas, the gravita��onal fi�eld produced by 1 at the

point where m2 is located is given by:

Thus, This is known as:

Newton’s Law of Universal Gravita&'o !

General Conclusions

How does the force of gravity vary with:

m1?

m2?

r?

3.3 - Universal Gravitation

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Example

Calculate the weight of a 75 kg man on Mars, which has a mass of

6.40 × 1023 kg and a radius of 3400 km. (G = 6.67 × 10-11 N·m2/kg2)

Example

How much more does a man weigh on a planet that is 3 ��mes

more massive and has ½ the radius of Earth?

3.3 - Universal Gravitation

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Satellites

A satellite falls to Earth at the same rate as

Earth’s curvature.

We can use uniform circular mo��on to

analyze a satellite:

Example

Calculate the speed of a satellite that orbits Earth at an al��tude of

6.38 × 106 m. (mE = 5.98 × 1024 kg and G = 6.67 × 10-11 N·m2/kg2)

3.3 - Universal Gravitation

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Homework