Question

If the sun and the planets carried huge amounts of opposite charges,
(A) All three of Kepler’s laws would still be valid
(B) Only the third law will be valid
(C) The second law will not change
(D) The first law will still be valid

Answer 1

Hint : To answer this question, we need to analyse the basic concept behind each of the Kepler’s law. Then connecting them with the effect of addition of the electrostatic force, we can get the answer.

Complete step by step answer
We know that the planets move around the sun due to the gravitational force of attraction which acts on each of the planets due to the sun. Let $M$ be the mass of the sun and $m$ be the mass of one of the planets. Then the gravitational force of attraction on the planet due to the sun is given by
 $F_G={\displaystyle \frac{GMm}{r^2}}$ .....................(i)
Now, if the sun and the planets carried opposite charges, then in addition to the gravitational force, the planets will begin experiencing the electrostatic force. Let $Q$ be the charge on the sun and $q$ be the opposite charge on a planet. Then the electrostatic force is given by
 $F_E={\displaystyle \frac{KQq}{r^2}}$ .....................(ii)
As the charges are opposite, this force will also be attractive in nature. So the net force on the planet is given by
 $F=F_G+F_E$
From (i) and (ii)
 $F={\displaystyle \frac{GMm}{r^2}}+{\displaystyle \frac{KQq}{r^2}}$
 $F={\displaystyle \frac{\left(GMm+KQq\right)}{r^2}}$ .....................(iii)
Kepler's first law states that the planets move around the sun in elliptical orbits, and the sun is situated at one of the foci of this ellipse. This law follows from the inverse square dependence of the force on the distance. As we can see from (iii) that this dependence still holds. So the shape of the orbit will still be elliptical.
So the option D is correct.
The Kepler’s second law states that the line joining a planet to the sun sweeps equal areas in equal intervals of time. This law is a consequence of the law of conservation of angular momentum. The addition of the electrostatic force will not add any external torque and so the angular momentum will still be conserved. Therefore the second law will not change
Hence the option C is also correct.
Now, Kepler's third law states that the square of the time period is proportional to the cube of the semi major axis of the ellipse. This law is also followed from the inverse square dependence of the force on the distance. Therefore the third law will also be valid.
Thus we have seen that all of the three Kepler’s laws would still be valid.
So the option A is also correct.
Hence the correct options are A, C and D.

Note
We should not get confused that the presence of the electrostatic form will have no effect due to the addition of the electrostatic force on the gravitational force. The answer is that the distance of the planets from the sun will get decreased. This is because of the increased attractive force on the planets due to the sun.