1. Make sure to show your work for all of the problems. F=Gm1m2/r^2 a. The mass

Question

1. Make sure to show your work for all of the problems.

F=Gm1m2/r^2

a. The mass of the sun is 333,000 times the mass of the earth. Is the force of the sun on the earth greater, less than, or equal to the force of the earth on the sun?

b. Lets say Earth was taken 5 times farther away than it currently is(This is about the distance to Jupiter). What is the ratio of the old force the sun exerted on the Earth to the new force the sun exerted on the Earth?(i.e. F new/F old)

c. Lets say we want to double the magnitude of the force exerted on the Earth by changing the mass of the sun. How would you do it?

d. Lets say we want to double the magnitude of the force exerted on the Earth by changing the distance of the earth to the sun. How would you do it?

Explanation / Answer

a) from newton's 3rd law,

force exterted by sun on earth is equal in magnitude the force extrted by earth on sun but in opposite direction.

Ans: equal

b) initial force: F = Gm1m2 / r^2

new r' = 5r

F' = Gm1m2 / (5r)^2 = Gm1m2 / 25r^2 = F/25

so force will be 1/25 th times as it was initially.

c) F = Gm1m2 /r ^2

Force is directly propotional to masse.

so we have double the mass of sun.

d) F is directly porpotional to 1/r^2 .

to double the force we have to change the r by 1/sqrt(2) = 0.707

so new r = 0.707 r   

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