8. Centripetal Forces & Gravitation

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?

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.

How does Earth's varying distance from the Sun affect our seasons according to $Kepler’s$ Laws?

In what direction do the planets revolve around the $Sun$ according to Kepler's Laws?

Which planet in our solar system has an orbital eccentricity most similar to $E\text{'}s$ eccentricity?

Which of the following best describes Earth's orbit according to Kepler's laws?