8. Centripetal Forces & Gravitation

According to Kepler's laws, what is the main difference between Earth's $\mathrm{perihelion}$ and its $\mathrm{aphelion}$?

Which one of the following does Kepler's second law indirectly describe?

According to Kepler's third law, which states that $P^2=a^3$ where $P$ is the orbital period and $a$ is the semi-major axis, how does the mass of a planet affect its orbital period around the Sun?

How did Kepler's discoveries contribute to the field of astronomy?

According to the principles related to Kepler's Laws and tidal forces, when does a spring tide occur?

Which of the following statements correctly describes a planet following an $elliptical$ orbit around the Sun according to Kepler's First Law?

The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 x 10⁶ m/s . Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s . Our solar system was formed roughly 5 billion years ago. How many orbits has it completed?

According to Kepler's Laws and the geometry of the $Earth$-$Moon$-$Sun$ system, where must the $Moon$ be in its orbit for the full moon phase to be visible from $Earth$?

Which orbital effect describes how the shape of $\mathrm{Earth}$'s orbit around the $\mathrm{Sun}$ will change over time?

Which of the following phenomena is primarily caused by the tilt of $\mathrm{Earth}$'s axis rather than by $\mathrm{Kepler}’s$ Laws?

Which of the following motions of the $Earth$ is primarily responsible for the occurrence of seasons?

Why is the same side of the $Moon$ always visible from $Earth$?

While visiting Planet Physics, you toss a rock straight up at 11 m/s and catch it 2.5 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 230 min. What are the (a) mass and (b) radius of Planet Physics?

A satellite in a circular orbit of radius r has period T. A satellite in a nearby orbit with radius r + Δr, where Δr ≪ r, has the very slightly different period T + ΔT. Show that ΔT/T = (3/2) (Δr/r)

Astronomers have observed an otherwise normal star, called S2, closely orbiting an extremely massive but small object at the center of our Milky Way Galaxy called SgrA. S2 moves in an elliptical orbit around SgrA with a period of 15.2 yr and an eccentricity e = 0.87 (Fig. 6–17). In 2002, S2 reached its closest approach to SgrA, a distance of only 123 AU ( 1 AU = 1.50 x 10¹¹ m is the mean Earth–Sun distance). Determine the mass m of SgrA, the massive compact object (believed to be a supermassive black hole) at the center of our Galaxy. State m in kg and in terms of the mass of our Sun.