The gravitational force is defined as F = Gm_1m_2/r^2 The mass of the sun is 333

Question

The gravitational force is defined as F = Gm_1m_2/r^2 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? 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).?. Let's 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? Let's 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)

the force of thesun on the earth is equal to the force of the earth on the sun

thgravitational force between any two objects is the force of attraction exerted by one on the other

b)

the force is inversly proportional to the square of the distance so

Fnew / Fold = (rold)^2/(rnew)^2

rnew = 5 * rold

Fnew / Fold = 1/25

c)

To double the force the mass should be doubled

d)

we have F1 / F2 = r2^2 / r1^2

F2 = F1 * (r1^2 / r2^2)

to double the force

r2 = r1 / sqrt(2)

so the distance should be reduced by sqrt(2) times

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