Question

An artificial satellite circling the Earth completes each orbit in 107 minutes. What is the value of g at the location of this satellite? The mass of the earth is 5.98 × 1024 kg and the universal gravitational constant is 6.67259 × 10−11 N · m2 /kg2 . Answer in units of m/s 2 .

Answer 1

Answer:

6,208 m/s2

Explanation:

*Angular velocity:

w= 2π/T

T= 119 minutes *60= 7140 s

w=2π/ (7140s )

w= 0:00087999 rad/s

*According to Newton's Universal Law of Gravitation:

Fc = m*r*w^2 = (G M(earth) *m )/r2

then:

r =  (G Mearth  /w^2 )^(1/3 )

r= ((6,67259 x10-11 N m2/kg2) /(0:00087999^2)) ^(1/3)

= 8,017x 10^6 m

that´s the radius of the satellite's orbit.

*And at this  distance from the Earth,...

F = (G*Mearth*m) /r2 = mg

then

g = (G* Mearth) /r^2

g=((6,67259 x10^11 N m2/kg2) * (5,98 x1024 kg) )/(8:017x 10^6 m)2

finally

g= 6:20832 m/s 2