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 = 5.98·1024kg. Gravitational constant G = 6.67·10-11 Nm2/kg2.

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 = 7.36·1022 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 =1.99·1030 kg Distance from the sun to the surface of earth = 1.50·108 km.

Explanation / Answer

Me = mass of earth = 5.98 x 1024 kg

m = given mass = 2 kg

R = distance between center of earth and given mass = 6370 km = 6.37 x 106 m

force of attraction between the earth and a mass is given as

Fattaraction = G Me m/R2

Fattaraction = (6.67 x 10-11) (5.98 x 1024) (2) /(6.37 x 106)2

Fattaraction = 19.7 N

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 = 7.36·1022 kg.

Mm = mass of moon = 7.36 x 1022 kg

m = given mass = 2 kg

r = distance between surface of earth and moon = 376,000 km = 3.76 x 108 m

force of attraction between the moon and mass is given as

F'attaraction = G Mm m/r2

F'attaraction = (6.67 x 10-11) (7.36 x 1022) (2) /(3.76 x 108)2

F'attaraction = 6.94 x 10-5 N

Ms = mass of sun = 1.99 x 1030 kg

m = given mass = 2 kg

r = distance between surface of earth and sun = 1.5 x 108 km = 1.5 x 1011 m

force of attraction between the sun and mass is given as

F''attaraction = G Ms m/r2

F''attaraction = (6.67 x 10-11) (1.99 x 1030) (2) /(1.5 x 1011)2

F''attaraction = 1.18 x 10-2 N

Ratio = F''attaraction /F'attaraction = (1.18 x 10-2 )/(6.94 x 10-5 ) = 170.03

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