Question

What speed should a satellite with a mass of 1500 kg at 8,500 km above the center of the earth be traveling at in order to stay in orbit (remember the mass of the earth is 5.97×10 to the 24th kg ) (in m/s , G= 6.67×10 to the -11 n (m/kg) ^2)

Answer 1

6.8 × 10³ m/s

Step-by-step explanation:

for those using CK12, the answer, (6.78 × 10³ m/s), rounds to 6.8 × 10³ m/s

Answer 2

6844.5 m/s.

Step-by-step explanation:

To get the speed of the satellite, the centripetal force on it must be enough to change its direction. This therefore means that the centripetal force must be equal to the gravitational force.

Formula for centripetal force is;

F_c = mv²/r

Formula for gravitational force is:

F_g = GmM/r²

Thus;

mv²/r = GmM/r²

m is the mass of the satellite and M is mass of the earth.

Making v the subject, we have;

v = √(GM/r)

We are given;

G = 6.67 × 10^(-11) m/kg²

M = 5.97 × 10^(24) kg

r = 8500 km = 8500000

Thus;

v = √((6.67 × 10^(-11) × (5.97 × 10^(24)) /8500000) = 6844.5 m/s.