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

Question

Calculate, using Newton's law of gravity, the of the force of attraction between the earth and a mats of 2.0 kg on the earth. Data: Distance to. the center of earth from the surface = 6370 km. Hass of earth = 5.98 middot 10^24 kg. Gravitational constant G = 6.67 middot 10^-11 Nm^2/kg^2. 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 10^22 kg. 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 10^8 km.

Explanation / Answer

Newton's law of gravitation F = G*m1*m2/r^2

(a)

m1 = mass of earth = 5.98*10^24 kg

r = 6730 km = 6730*10^3 m

m2 = 2 kg

F = 6.67*10^-11*5.98*10^24*2/(6730*10^3)^2

F = 17.61 N

=================

(b)

m1 = mass of moon = 7.36*10^22 kg

r = 376000 km = 376000*10^3 m

m2 = 2 kg

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

F = 6.94*10^-5 N

==================================

(c)

forc of attraction by sun F1 = 6.67*10^-11*1.99*10^30*2/(1.5*10^8*10^3)^2 = 0.0118 N

forc of attraction by moon F2 = 6.94*10^-5 N

ratio = F1/F2 = 0.0118/(6.94*10^-5)= 170

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