Use the universal law of gravitation to solve the following problem. Hint: mass of the Earth is = 5.97 x 1024 kg

A scientific satellite of mass 1300 kg orbits Earth 200 km above its surface. If Earth has a radius of 6378 km, what is the force of gravity acting on the scientific satellite?

a. Write out the formula for this problem.

b. Plug in the values from this problem into the formula.

c. Solve the problem, writing out each step.

d. Correct answer

11963.43 N

Explanation:

From the question given above, the following data were obtained:

Mass of the earth (Mₑ) = 5.97x10²⁴ Kg

Mass of satellite (Mₛ) = 1300 Kg

Radius of the earth (R) = 6378 km

Distance between the earth and satellite (r) = R + 200 Km = 6378 + 200 = 6578 Km

Force of gravity (F) =?

Next, we shall convert 6578 Km to m. This can be obtained as follow:

1 Km = 1000 m

Therefore,

6578 Km = 6578 Km × 1000 m / 1 Km

6578 Km = 6578000 m

Finally, we shall determine the force of gravity. This can be obtained as follow:

Mass of the earth (Mₑ) = 5.97x10²⁴ Kg

Mass of satellite (Mₛ) = 1300 Kg

Distance apart (r) = 6578000 m

Gravitational constant (G) = 6.67×10¯¹¹ Nm²/Kg²

Force of gravity (F) =?

F = GMₑMₛ / r²

F = (6.67×10¯¹¹ × 5.97x10²⁴ × 1300) / (6578000)²

F = 11963.43 N

Therefore, the force of gravity on the scientific satellite 11963.43 N

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.