Answer to Question #160130 in Physics for Yolande

Question

State
(i) Kepler's law of gravitation
(ii) Newton's law of gravitation
(iii) Coulomb's law

Answer 1

(i) The Kepler's law of gravitation states that the square of the planet's orbital period is proportional to the cube of the length of semi-major axis of its orbit:

$$\dfrac{P_1^2}{a_1^3}=\dfrac{P_2^2}{a_2^3},$$

here, $P_1, P_2$ are the orbital periods of the first and second planet, respectively; $a_1, a_2$ are the semi-major axis of the first and second planet, respectively.  

(ii) Newton's law of gravitation states that every two objects attract one another with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them:

$$F=\dfrac{Gm_1m_2}{r^2},$$

here, $G$ is the universal gravitational constant; $m_1, m_2$ are the masses of first and second objects, respectively; $r$ is the distance between two objects.

(iii) Coulomb’s law states that the force of attraction or repulsion between two electrically charged particles is directly proportional to the magnitude of their charges and inversely proportional to the square of the distance between them:

$$F=\dfrac{kq_1q_2}{r^2},$$

here, $k$ is the Coulomb’s constant; $q_1, q_2$ are the point charges; $r$ is the distance between two point charges.