Question

Kepler, around 1600, upon his meticulous observations and measurements, had established a remarkable relationship between the revolution period T of a planet around the Sun, and the distance R of it to the Sun, as T²-R³. Show, how Newton about a century later, could, not only derive this relationship, as (with the familiar notation), T²=[(4π²/GM]R³, but also, could fix Kepler’s “proportionality constant”, thusly becoming 4π²/GM. The quantity G, is the gravitation constant, and M is the mass of the Sun.

b) ( p) We can well apply Kepler’s Law not only to the System made of the Sun and the planets revolving around the Sun, but also to any celestial system, and in particular to Earth and the Moon revolving around Earth. Thus, show that the square of the period of rotation T_M of the Moon around Earth, can be expressed as T_M²=[(4π²/gR_E²]R_M³, where g is Earth’s acceleration, we defined in Question 1, and R_M, is the distance from Earth to the Moon.

c) () The period T_M, is, as we well know, about 1 month. Find then R_M, taking R_E to be 6000 km. Make sure that, you use coherent units. As you see one can determine the distance between Earth and the Moon,from where he sits.

1. Attach File

Answer 1

answered by: anonymous