Will you please walk me through the calculations in more detail for solving this problem? I am a bit rusty on calculus and confused about the specific steps of the derivation: https://www.bartleby.com/solution-answer/chapter-3-problem-15e-modern-physics-2nd-edition/9780805303087/7cf8c31d-9476-46d5-a5a9-b897b16fe6fc

Why might Tycho Brahe have hesitated to hire Kepler? Why do you suppose he appointed Kepler his scientific heir? What is limited about Keplers third law P2 = a3, where P is the time in units of years a planet takes to orbit the Sun and a is the planets average distance from the Sun in units of AU? (Hint: Look at the units.) What does this tell you about Kepler and his laws?

Can you think of classification systems used to simplify what would otherwise be complex measurements? Consider foods, movies, cars, grades, and clothes.

Suppose you want to determine the average educational level of people throughout the nation. Since it would be a great deal of work to survey every citizen, you decide to make your task easier by asking only the people on your campus. Will you get an accurate answer? Will your survey be distorted by a selection effect? Explain.

The average density of the Sun is on the order 103kg/m3 . (a) Estimate the diameter of the Sun. (b) Given that the Sun subtends at an angle of about half a degree in the sky, estimate its distance from Earth.

Kepler’s third law says that the orbital period (in years) is proportional to the square root of the cube of the mean distance (in AU) from the Sun (Pa1.5) . For mean distances from 0.1 to 32 AU, calculate and plot a curve showing the expected Keplerian period. For each planet in our solar system, look up the mean distance from the Sun in AU and the orbital period in years and overplot these data on the theoretical Keplerian curve.

Because Newtons first law is counterintuitive, it is important to take some time to think about what the law says and about how and why it differs from our intuition. a. Why did the unavoidable presence of friction make it difficult for earlier scientists to come to the conclusion expressed in Newtons first law? b. What is the natural state of an object? c. How much force does it take to keep an object moving at constant velocity?

A neutron star is a cold, collapsed star with nuclear density. A particular neutron star has a mass twice that of our Sun with a radius of 12.0 km. (a) What would be the weight of a 100-kg astronaut on standing on its surface? (b) What does this tell us about landing on a neutron star?

A trapper walks a 5.0-km straigt4ine distance from his cabin to the lake, as shown in the following figure. Use a graphical method (the parallelogram rule) to determine the trapper’s displacement directly to the east and displacement directly to the north that sum up to his resultant displacement vector. If the trapper walked only in directions east and north, zigzagging his way to the lake, how many kilometers would he have to walk to get to the lake?

The distance from the Sun to the nearest star is about 4 1016 m. The Milky Way galaxy (Fig. P1.56) is roughly a disk of diameter 1021 m and thickness 1019 m. Find the order of magnitude of the number of stars in the Milky Way. Assume the distance between the Sun and our nearest neighbor is typical. Figure P1.56 The Milky Way galaxy.