Engineering Expert Witness Blog

      Last time we saw how centripetal force is responsible for keeping a child’s ball moving in a circular path when twirled above his head.   Today we’ll see how that same force is responsible for keeping Earth in its rotation around the sun.   We’ll use Isaac Newton’s Second Law of Motion as it relates to centripetal force to bear that out today.

      Our example from last week,

Figure 1

      According to Newton’s Second Law of Motion, F_c, the centripetal force acting upon the ball, is calculated by the equation,

F_c = [m_ball × v²] ÷ r_string

where, m_ball is the ball’s mass, v the ball’s velocity, and r_string is the length of the string.

      The mechanics are obviously different with regard to Earth and its orbit around the sun, where there’s no obvious physical link between the objects in rotation.   In this case the sun’s gravitational force, F_g, acts to tether Earth to it.   And just like the string and ball, the sun’s gravitational tether creates a centripetal force, F_c, which prevents Earth from leaving its orbital path.  See Figure 2.

Figure 2

      Newton concluded that for the Earth to remain on its permanent, fixed path of orbit around the sun, F_c must be equal to F_g,  and that the forces in play between the sun and Earth were like a gigantic tug of war where neither side is able to pull any harder than the other.   This stalemate is responsible for keeping Earth stably in place in its orbit.

      According to Newton’s Second Law, the sun’s gravitational force acting upon the Earth is calculated by,

F_g = F_c = [m × v²] ÷ r

where, m is Earth’s mass, v its orbital velocity, and r the distance between Earth and the sun.   Thanks to early scientists like Edmund Halley and Henry Cavendish, the values for m and r had already been determined.   That left v, Earth’s orbital velocity, the only variable remaining to be solved.

      We’ll see how 19^th Century scientists accomplished that next time.

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