1.55 * An Earthlike Planet. In January 2006 astronomers reported the discovery of a planet comparable in size to the earth orbiting another star and having a mass about 5.5 times the earth's mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. If this planet has the same density as Neptune (1.76 g/cm), what is its radius expressed (a) in kilometers and (b) as a multiple of earth's radius? Consult Appendix F for astronomi- cal data.

1.55 * An Earthlike Planet. In January 2006 astronomers reported the discovery of a planet comparable in size to the earth orbiting another star and having a mass about 5.5 times the earth's mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. If this planet has the same density as Neptune (1.76 g/cm), what is its radius expressed (a) in kilometers and (b) as a multiple of earth's radius? Consult Appendix F for astronomi- cal data.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter1: Getting Started

Section: Chapter Questions

Problem 11PQ: CASE STUDY On planet Betatron, mass is measured in bloobits and length in bots. You are the Earth...

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CASE STUDY On planet Betatron, mass is measured in bloobits and length in bots. You are the Earth representative on the interplanetary commission for unit conversions and find that 1 kg = 0.23 bloobits and 1 m = 1.41 bots. Express the density of a raisin (2 103 kg/m3) in Betatron units.
Show that for small changes in height h, such that hRE , Equation 13.4 reduces to the expression U=mgh .
In 2011, artist Hans-Peter Feldmann covered the walls of a gallery at the New York Guggenheim Museum with 100,000 one-dollar bills (Fig. P1.48). Approximately how much would it cost you to wallpaper your room in one-dollar bills, assuming the bills do not overlap? Consider the cost of the bills alone, not other supplies or labor costs. FIGURE P1.48
A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed ?esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ?=2.93×106 g/m3 and volume ?=1.94×1012 m3 . Recall that the universal gravitational constant is ?=6.67×10-11 N·m2/kg2 .vesc = ? m/s
In Michael Johnson's world-record 400 mm sprint, he ran the first 100 mm in 11.20 ss; then he reached the 200 mm mark after a total time of 21.32 ss had elapsed, reached the 300 mm mark after 31.76 ss, and finished in 43.18 ss. During what 100 mm segment was his speed the highest?
In the ammonia (NH3) molecule of the figure, three hydrogen (H) atoms form an equilateral triangle, with the center of the triangle at distance d = 9.40 × 10–11 m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms forming the base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is L = 10.14 × 10–11 m. What are the (a) x and (b) y coordinates of the molecule's center of mass?
A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed ?escvesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ?=4.10×106 g/m3ρ=4.10×106 g/m3 and volume ?=1.25×1012 m3V=1.25×1012 m3 . Recall that the universal gravitational constant is ?=6.67×10−11 N·m2/kg2G=6.67×10−11 N·m2/kg2 .
What is vector producer between vector (A) = 2.00 (i) + 3.00 (j) + 1.00 (k) and vector (B) = 1.00 (i) -3.00 (j) - 2.00 (k)?
Consider the observation that the acceleration due to the gravitational force acting on a mass around a host planet decreases with the square of the separation between the objects. We can ask ourselves: why is it still accurate to consider a gravitational acceleration value of 9.8\frac{m}{s^2}9.8s2m for all of our projectile motion problems and all of our gravitational potential energy from prior modules? Let's analyze a situation and justify this analysis method: consider an object being launched from ground level to an altitude of 10,000 meters, roughly the cruising altitude of most jet liners, and far above our everyday experiences on Earth's surface. Compare the gravitational acceleration of the object at Earth's surface (the radius of Earth is about r_E=6.37\times10^6mrE=6.37×106m) to the acceleration value at the 10,000 meter altitude by determining the following ratio: g10,000m/gsurface
A 1000 kg spacecraft is approaching Jupiter (which is at the origin). The position of the spacecraft is given by the vector RSC = (0.0,-2.533) x 106km. The velocity is given by VSC= (+6.00, +8.00) km/sec. The mass of Jupiter, (MJ=318 MEarth) and MEarth = 5.97 x 1024 kg. A) What is the potential and kinetic energy of the spacecraft (write each to 3 sig figs.) What is the total energy of the spacecraft? Call the total energy Ei. B) Can it escape Jupiter? Justify your answer. C) What is the angular momentum of the spacecraft around Jupiter? Call this Li.
The gravitational force (in lb) of attraction between two objects is given by F=k/x2 , where x is the distance between the objects. If the objects are 55 ft apart, find the work required to separate them until they are 5050 ft apart. Express the result in terms of k.
Please don't provide handwritten solution .... Use the definition of scalar product, · = ab cos ?, and the fact that · = axbx + ayby + azbz to calculate the angle between the two vectors given by = 5.0 + 5.0 + 5.0 and = 5.0 + 8.0 + 4.0.