Question

Calculate the magnitude of the acceleration of gravity for an object that is (a) 0m, (b) 7550m, (c) 6.75×10⁵m, and (d) 7.47×10⁶m above the surface of the Earth. Take the radius of a spherical Earth to be R_E = 6.37×10⁶m and the mass of Earth to be M_E = 5.97×10²⁴kg.

Answer 1

here,

mass of earth , m = 5.98 * 10^24 kg

radius of earth , r = 6.37 * 10^6 m

a)

a = 0 m

the accelration due to gravity , g = G * M /( r + a)^2

g = 6.67 * 10^-11 * 5.98 * 10^24 /( 6.37 * 10^6 + 0)^2

g = 9.8 m/s^2

b)

a = 7550 m

the accelration due to gravity , g = G * M /( r + a)^2

g = 6.67 * 10^-11 * 5.98 * 10^24 /( 6.37 * 10^6 + 7550)^2

g = 9.8 m/s^2

c)

a = 6.75 * 10^5 m

the accelration due to gravity , g = G * M /( r + a)^2

g = 6.67 * 10^-11 * 5.98 * 10^24 /( 6.37 * 10^6 + 6.75 * 10^5)^2

g = 8.34 m/s^2

d)

a = 7.47 * 10^6 m

the accelration due to gravity , g = G * M /( r + a)^2

g = 6.67 * 10^-11 * 5.98 * 10^24 /( 6.37 * 10^6 + 7.47 * 10^6)^2

g = 2.08 m/s^2