You want to put a 128 kg mass inorbit around the sun. Assuming a circular orbit,

Question

You want to put a 128 kg mass inorbit around the sun. Assuming a circular orbit, how far from thecenter of the sun would you have to place it for it to have thesame orbital speed as Mercury?
I do not understand what equation to use because the onlygiven i know is the mass of the object which does not affect theanswer at all You want to put a 128 kg mass inorbit around the sun. Assuming a circular orbit, how far from thecenter of the sun would you have to place it for it to have thesame orbital speed as Mercury?
I do not understand what equation to use because the onlygiven i know is the mass of the object which does not affect theanswer at all

Explanation / Answer

         Mass of Sun, M1 =2 X 10 30 kg          Mass of mercury,M2 = 3.2 X 10 23 kg          Distance from thecenter of sun , R1 = ?          Radius of mercury,R2 = 2.4 X 10 6 m         Orbital speed, Vo = ( G M / r )         Orbital speed aroundsun, V1 = ( G M1 / R1 )         Orbital speed aroundmercury, V2 = ( G M2 / R2 )          By equating V1 andV2         ( G M1 / R1 ) = ( G M2 / R2 )     ( G M1 / R1 ) = ( G M2 / R2 )       R1 = M1 * ( R2 / M2 )            = 2 X10 30 * ( 2.4 X 10 6 / 3.2 X 10 23)            = 1.5X 10 13 m

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