SUMMARY

• Kepler’s 3 laws (pages 3-4-5)• Illustration of Kepler’s laws (page 6)• Newton’s law of universal gravitation (pages

7-8)• Illustration of Newton’s law (page 9)• Exercises (pages 11-12-13)• Conclusion (page 14)

Kepler’s firt law: an orbiting body travels in an elliptical path around a

central, massive body, wich is located at one of the ellipse’s foci.

Kepler’s second law: If a line is drawn between the central massive body

and the orbiting satellite, area is swept out by the line at a costant rate.

Kepler’s third law:

the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

where P is the orbital period of the planet and a is the semi-major axis of the orbit.

The constant of proportionality is:P²/a³=K

Video: Illustration of Kepler’s laws

Newton’s law of universal gravitation: Newton's law of universal gravitation states that

every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

where:

• F is the force between the masses,• G is the gravitational constant,• m1 is the first mass,• m2 is the second mass, and• r is the distance between the centers of the masses.

Video: Illustration of Newton’s law of universal gravitation

Now let’s have some practice!

Turn the page for some exercises!

Exercise n.1

The planet trajectory around the Sun is described by:

1)a circumference2)an hyperbole3)an epicycle4)an ellipse

Exercise n.2

Calculate the force of attraction between the earth and the sun knowing that the mass of the Sun Ms = 1,98 · 10³⁰ kg, the mass of the Earth Me = 5,98 · 10²⁴ kg, and the average radius of the Earth orbit r = 1,50 · 10¹¹ m.

[3,51 · 10²² N]

Exercise n.3 Calculate the force of attraction between two

boys who weigh 60 kg at the distance of 1 m. [2,4 · 10¯⁷ N]

Thanks for watching! Brunetti P. Cipriano D. Siciliano M.

WRONG!

RIGHT!