Question

(Please help if you can, I need this last answer done by tonight.)

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

Answer 1

11963.43 N

Step-by-step 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