3.3 - Universal Gravitation
1
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
2
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
3
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
4
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)