3. When the astronauts go into space, they feel lighter. This is because weight decreases as a person rises above Earth's gravitational pull We = according to the formula W(h) so where We is person's weight in (1+ 2 h 6400 Newtons at sea level on Earth and W(h) is the weight at h kilometers above sea level. At what range of altitude will this astronaut, having We-820, have a weight less than 205 N? Use an algebraic method. NO GRAPHING SOLUTION IS ACCEPTED

The planet Saturn has an average radius of 9 Earth radii and a density of 0.7 g/cm3 (yes, less dense than water!). How many Earth radii must a moon remain beyond the center of this giant planet, if the moon is made of water ice (0.9 g/cm3)? (i) How many Saturn radii does this equal?

Chapter 5, Section 5.8, Question 32 Determine the length of a rectangular trench you can dig with the energy gained from eating one Milky Way bar (270 cal). Assume that you convert the energy gained from the food with 5% efficiency and that the trench is 7 meters wide and 1 meter deep. Use the fact that the density of soil is 1000 kg/m³ and the acceleration due to gravity is 9.81 m/s². Round your answer to two decimal places. The length of the trench is the tolerance is +/- 2% Click if you would like to Show Work for this question: Open Show Work LINK TO TEXT meters.

(3) The Moon is approximately 400,000 km from the Earth. An atom of a certain element has adiameter of 4 X 10-8 cm. Given 1 km = 1,000 m and 1 m = 100 cm, about how many atoms ofthis element can be lined up between Earth and Moon?

(f) In situation (4), give the direction of a by naming either a quadrant or a direction along an axis. (This can be done with a few mental calculations.) 46N 3N 2 N 3 N 2 N 5 N 2NV (1) (2) 3N 2N 5 N 3 N 1N 5N 4N. 4N 5 N (3) (4) O +y axis O x > 0, y > 0 O +x axis O x > 0, y 0

- The maximum distance between the transmitting and receiving TV towers is 65 km. If the ratio of the heights of the TV transmitting tower to receiving tower is 36 : 49, the heights of the transmitting and receiving towers respectively are (radius of earth = 6400 km) (a) 51.2 m, 80 m (c) 30 m, 65 m (b) 70.3 m, 95.7 m (d) 25 m, 75 m

(a) Jupiter's third-largest natural satellite, Io, follows an orbit with a semimajor axis of 422,000 km (4.22 ✕ 105 km) and a period of 1.77 Earth days (PIo = 1.77 d). To use Kepler's Third Law, we first must convert Io's orbital semimajor axis to astronomical units. One AU equals 150 million km (1 AU = 1.50 ✕ 108 km). Convert Io's a value to AU and record the result. aIo =  AU (b) One Earth year is about 365 days. Convert Io's orbital period to Earth years and record the result. PIo =  yr (c) Use the Kepler's Third Law Calculator to calculate Jupiter's mass in solar units. Record the result. MJup(Io) =  MSun (d) Based on this result, Jupiter's mass is about       that of the Sun. Jupiter has a similar fraction of the Sun's volume. The two objects therefore have rather similar density! In fact, Jupiter has a fairly similar composition as well: most of its mass is in the form of hydrogen and helium.

1) Thinking about the Scale of the Solar System As we discuss in class, the radius of the Earth is approximately 6370 km. The Sun, on the other hand, is approximately 700,000 km in radius and located, on average, one astronomical unit (1 au=1.5x108 km) from the Earth. Imagine that you stand near Mansueto Library, at the corner of 57th and Ellis. You hold a standard desk globe, which has a diameter of 12 inches, and you want to build a model of the Sun, Earth, and their separation that keeps all sizes and lengths in proportion to one another. a) How big would the Sun be in this scale model? Give your answer in feet and meters.

Galileo's telescope brought about revolutionary changes in astronomy. A comparable leap in our ability to observe the universe took place as a result of the Hubble Space Telescope. The space telescope can see stars and galaxies whose brightness is of the faintest objects now observable using ground-based telescopes. Use the fact that the brightness of a point source, such as a star, varies inversely as the square of its distance from an observer to show that the space telescope can see about seven times farther than a ground-based telescope.