Universal Gravitation

Physics 11/30

Universal Gravitation

Open Ended

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Universal Gravitation and Kepler's 3rd Law

• Remember Newton's Law of Universal Gravitation

• F_g = G(m₁m₂)/r²

Universal Gravitation and Kepler's 3rd Law

• Newton stated the law of universal gravitation in terms that applied to the motion of planets about the Sun.

• This agreed with Kepler's 3rd law and confirmed that Newton's Law fit the best observations of the day.

• All of this works together to get the equation for finding the Period of a planet orbiting the Sun.

Period of a planet orbiting the Sun

 $T\ =\ 2\pi\sqrt{\frac{r^3}{Gm_S}}$  
The period of a planet orbiting the Sun is equal to  $2\pi$  times the square root of the average distance from the Sun cubed, divide by the product of the universal gravitational constant and the mass of the Sun.

Squaring both sides makes it clear that this equation is Kepler's 3rd Law of Planetary Motion.

Measuring the Universal Gravitational Constant

• How large is the constant G?

• Strange as it may seem, it took 100 years from the time of Newton's work for scientists to develop an apparatus that was sensitive enough to measure the force of gravitational attraction.

Cavendish's Apparatus

1798 - English Scientist Henry Cavendish used equipment similar to the image shown to measure the gravitational force between two objects.

Weighing Earth

• Cavendish's investigation is often called weighing Earth because it helped determine Earth's mass.

• Once "G" is determined , not only the mass of Earth, but the mass of the Sun can be determined.

• In addition the gravitational force between any two objects can be calculated using Newton's Law of Universal Gravitation.

The value of G

When it is all said and done, G is a constant value of 6.67 X 10^-11 N⋅m²/kg2

Review Questions

Google Classroom or Handout.

Open Ended

Exit Ticket - What is the value of G?