To calculate the magnitude of the gravitational force exerted on the satellite by the earth, we can use the formula F = G(m1m2)/r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
In this case, m1 is the mass of the earth and m2 is the mass of the satellite. We know the mass of the satellite is 8410kg, and we can find the mass of the earth to be approximately 5.97 x 10^24 kg.
To find the distance between the two objects, we need to use the fact that the satellite is in orbit around the earth. We know that the time it takes for the satellite to make one revolution around the earth is 927 minutes. Using this information, we can find the radius of the satellite's orbit using the formula r = (GmT^2/4π^2)^(1/3), where m is the mass of the earth, T is the period of the orbit (in seconds), and G is the gravitational constant.
Plugging in the values, we get:
r = ((6.67 x 10^-11 Nm^2/kg^2)(5.97 x 10^24 kg)(927 x 60 s)^2/(4π^2))^(1/3)
r = 7.15 x 10^6 m
Now we can plug in all the values into the formula for gravitational force:
F = (6.67 x 10^-11 Nm^2/kg^2)(5.97 x 10^24 kg)(8410 kg)/(7.15 x 10^6 m)^2
F = 3.53 x 10^4 N
Therefore, the magnitude of the gravitational force exerted on the satellite by the earth is 3.53 x 10^4 N.