Calculate, using Newton\'s law of gravity, the size of the force of attraction b

Question

Calculate, using Newton's law of gravity, the size of the force of attraction between the earth and a mass of 2.0 kg on the earth. Data: Distance to the center of earth from the surface = 6370 km. Mass of earth = 5.98-10^24 kg. Gravitational G = 6.67 middot 10^-11 Nm^2/kg^2. 125 25*10^6 N The SI system of units uses meters as the unit of length. You must change the distance from km to m. How does your answer compare with just Mg? Calculate, using Newton's law of gravity, the size of the force of attraction between the moon and a mass of 2.0 kg on the earth's surface nearest the moon. Data: Distance to the moon from surface of the earth = 376,000 km. Mass of moon = 7.36 middot 10^27 kg. 6.945 times 10^-5 N Calculate, using Newton's law of gravity, the ratio of the strength of the force of attraction of a mass of 2.0 kg on the earth's surface by the sun to that by the moon. Additional Data: Mass of sun = 1.99 middot 10^30 kg Distance from the sun to the surface of earth = 1.50 middot 10^km. 1.699 times 10^2

Explanation / Answer

(1)

From newton's law of gravity,

F = G*M*m / r^2

F = 6.67*10^(-11)*5.98*10^24*2 / (6370*10^3)^2

F = 19.66 N

(2)

F = G*M*m / r^2

Fm = 6.67*10^(-11)*7.36*10^22*2 / (376000*10^3)^2

Fm = 6.94*10^(-5) N

(3)

Fs = G*M*m / r^2

Fs = 6.67*10^(-11)*1.99*10^30*2 / (1.5*10^11)^2

Fs = 0.0118 N

Fs / Fm = 0.0118 / 6.94*10^(-5)

Fs / Fm = 1.69*10^2

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