SCSA Physics Science Understanding

This describes Kepler's First Law, also known as the Law of Ellipses, which states that planets move in elliptical orbits with the Sun at one focus.

Kepler's laws are not derived from combining Newton's first law with uniform circular motion; rather, the third law relates orbital period to distance.

This describes Kepler's Second Law, or the Law of Equal Areas, which states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

Kepler's Third Law ($T^2 \propto r^3$) is physically derived by equating the centripetal force in uniform circular motion to the gravitational force defined by Newton's Law of Universal Gravitation.

This value is incorrect and does not result from the proper application of Newton's Law of Universal Gravitation.

This result is obtained by multiplying the gravitational constant by the two masses but failing to divide by the distance ($F = G m_1 m_2$).

This calculation incorrectly divides by the distance $r$ instead of the distance squared $r^2$ ($F = G \frac{m_1 m_2}{r}$).

Using the formula $F = G \frac{m_1 m_2}{r^2}$ with $G \approx 6.67 \times 10^{-11} \, \text{N}\cdot\text{m}^2/\text{kg}^2$, the calculation is $(6.67 \times 10^{-11}) \frac{(65.0)(75.0)}{(1.50)^2} \approx 1.45 \times 10^{-7}$ N.