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Unformatted text preview: Homework #5: Solutions Astro 10, spring 2010 General Notes to Graders: If numerical answers are roughly correct, do not take marks off. Award part marks if the student has made some progress with the question. Be generous. 1. [15 points] (a) Alright, to begin, recall the force equation is F = GMm/r 2 , where m is your mass. We can treat the mass of the planet as being entirely concentrated at the central point. Therefore, if you are on the surface, your distance from the central mass is simply the radius of the planet. Thus, to find the ratio of the gravitational force on the surface of the Earth ( F E ) to that on the Moon ( F M ), we do: F E F M = ( GM E m ( R E ) 2 )( ( R M ) 2 GM M m ) F E F M = ( M E M M )( R M R E ) 2 = ( 6 10 27 g 7 . 3 10 25 g )( 1 . 7 10 8 cm 6 . 3 10 8 cm ) 2 F E F M = 5 . 98 (b) Lets do the same thing except now well compare the force on the surface of the Earth ( F E ) to the surface of Jupiter ( F J ) (though in reality, Jupiter has no surface....) F E F J = ( GM E m ( R E ) 2 )( ( R J ) 2 GM J m ) F E F J = ( M E M J )( R J R E ) 2 = ( 6 10 27 g 2 10 30 g )( 7 10 9 cm 6 . 3 10 8 cm ) 2 F E F J = 0 . 37 or equivalently F J F E = 2 . 7 (c) Now, remember that your weight is simply the gravitational force you feel at the surface of the planet. As a result, you would weigh 6 times more on the surface of the Earth than on the surface of the Moon, but you would weigh 2.7 times more on the surface of Jupiter, than on the Earth. So, you would weigh the most on the surface of Jupiter. Notes to graders: Parts a and b are worth 6 points each and part c is worth 3 points. 1 point off (total) if correct but careless with units (these ratios have no units!!). Students do not need to have a full explanation for full credit in part c - just that you would weigh the most on Jupiter...
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This note was uploaded on 07/18/2011 for the course ASTRO 10 taught by Professor Norm during the Spring '06 term at University of California, Berkeley.
- Spring '06