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ID: 2252793 • Letter: #
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The gravitational force on earth is only due to the mass M within earths orbit. If r is the radius of the orbit and let R be the radius of the new sun and Ms be its mass.
The mass within the orbit be M = (r/R)^3* Ms where r=1.5*10^11
after substituting M = (1.5*10^11/5.78*10^12)^3*1.99*10^30= 5.059*10^25 kg
The gravitational force on earth is given by GMm/r^2. Where m is the mass of the earth and G is the gravitational constant. Since centripetal acceleration is given by v^2/r where v is the speed of the earth
GMm/r^2= mv^2/r
v= (GM/r)^1/2= (6.67*10^-11*5.059*10^25/(1.5*10^11))^(1/2)= 1.49*10^2.
b) The ratio can be found as (1.49*10^2/2.98*10^4)=0.005
c)The period of revolution is
T= 2(pi)r/v= 2*3.14*1.5*10^11/(1.49*10^2)= 6.325*10^9 seconds= 200.56 years
The problem is similar to 37 th problem in the 45 th chapter of fundemental of physics by halliday 6th edition..... and its correct
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