Chapter 34, Problem 16TE

Early astronomers such as Kepler and Newton developed the laws of gravity based upon the motion of the planets around the Sun. How might these laws have been different if our solar system had been surrounded by a thick halo of dark matter?

To determine

The change in the Kepler and Newton’s law when the solar system is surrounded by a thick halo of dark matter.

Answer to Problem 16TE

The laws of gravity developed by Kepler and Newton change as the orbital speed of all the planets will mostly become same.

Explanation of Solution

According to the theories given by scientists, laws of gravity states that the orbital speed is a function of the force of gravity between the orbiting object and the object being orbited. This means that greater the force of gravity, greater is the orbital speed.

According to above theory, the inner planets of the solar system have more gravitational forces as compared to outer planets because they are closer to the Sun.

If the solar system had been surrounded by a thick halo dark matter, then the orbital speed of all planets of the solar system will be mostly the same. Then, in this case, the laws of gravity developed by Kepler and Newton based on the motion of the planets around the Sun will be entirely different.

Conclusion:

Therefore, the dark matter halo surrounding the planets would have caused the same speed of all the planets irrespective of the fact whether they are closer to Sun or not.