PLEASE SHOW ALL WORK! I have no idea what to do here. Thanks in advance! Name PH

Question

PLEASE SHOW ALL WORK! I have no idea what to do here. Thanks in advance! Name PHYSICS 1 ROSETTA MISSION HOMEWORK PROBLEM BACKGROUND The European Space Agency's Rosetta spacecraft was launched in March 2004 to explore the comet 67P/Churyumov-Gerasimenko, named after astronomer Kim Ivanovych Churyumov who discovered it by studying photographs take by Svetlana Ivanovna Gerasimenko. Discover a comet and it is named after you! Other celestial objects are named by the International Astronomy Union. The spacecraft gained velocity on its voyage to Comet 67P by using an Earth fly-by in 2005, Earth and Mars fly-bys in 2007, and a final Earth fly-by in 2009 (check Chapter 12 to see how these work). After the last boost the spacecraft was put into hibernation from May 2011 through January 2014 to save electrical energy (the available sunlight was too weak for the spacecraft's solar panels to keep the craft fully operative). After coming out of hibernation the Rosetta spacecraft entered orbit around the comet on September 10, 2014. A surprise discovered when approaching the comet was that the comet was not spherical in shape, but comprised of two parts (lobes) that are said to be said shaped roughly like a rubber duck. The orbiting Rosetta spacecraft let loose a "lander" called Philae which attempted to set down on the comet on November 12, 2014 and bounced twice, the second bounce ending two hours after initial contact. The event was covered live on the Science Channel, or as close to live as transmissions from an object about 50 light minutes distant from us could achieve. PROBLEM STATEMENT Assuming the two lobes comprising the head and body of the “rubber duck" shaped asteroid can be approximated by two equal-sized spheres, the comet's total mass is 10s kilograms, and its density is 470 kilograms per cubic meter (470 kg/m'), what is gravity's acceleration on the projection of a line connecting the lobes' centers at the surface of either lobe? See illustration below alculate gravity 's acceleration here or here! 67-P from Rosetta 8/22/2014

Explanation / Answer

Gravity's acceleration on the projection of a line connecting the lobe's centers at the surface of either lobe which is given as :

using a formula, we have

g = G M / r2

where, G = gravitational constant = 6.67 x 10-11 Nm2/kg2

M = total mass of comet's = 1013 kg

r = distance = 50 llight min = 8.99 x 1011 m

then, we get

g = (6.67 x 10-11 Nm2/kg2) (1013 kg) / (8.99 x 1011 m)2

g = (6.67 x 102 Nm2/kg) / (80.8 x 1022 m2)

g = 0.0825 x 10-20 m/s2

g = 8.25 x 10-22 m/s2

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