Question

A particle of charge -q & mass m moves in a circular orbit about a fixed charge +Q in a circle of radius r and time period T. which of the following may be correct

• A. $r^3{\alpha T}^2$
• B. $r^2{\alpha T}^{3/2}$
• C. $r^3{\alpha T}^{2/3}$
• D. None of these

Answer 1

The correct option is C $r^3{\alpha T}^{2/3}$

Charge $=-q$

mass $=m$

fixed charge $=+Q$

radius $=r$

Time period $=T$

according to Kepler's celestial body law, we get that,

$r^3$ $\alpha$ $T^2/3$

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

(2) A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time.

Kepler's third law provides an accurate description of the period and distance for a planet's orbitals about the sun. Additionally, the same law that describe that $T^2/R^3$ ratio for planet's orbitals about the sun also accurately describes the $T^2/R^3$ ratio for any satellite.

$\Rightarrow$ Then, the ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The law of harmonics).