Answer :
The Gravitational Potential Energy of the System ≈ [tex]-5.430 * 10^8[/tex]J
The potential energy of the satellite-Earth system can be calculated using the formula for gravitational potential energy:
PE = -GMm / r
where PE is the gravitational potential energy,
G is the gravitational constant (approx [tex]6.67430 * 10^{-11} N(m/kg)^2[/tex])
M is the mass of the Earth (approx [tex]5.972 * 10^{24}kg[/tex]),
m is the mass of the satellite (93 kg), and
r is the distance between the satellite and the center of the Earth
(altitude + radius of the Earth)
Given:
Mass of the satellite, m = 93 kg
Altitude, h = [tex]1.99 * 10^6 m[/tex]
Radius of the Earth, R = [tex]6.371 * 10^6 m[/tex]
First, we need to calculate the distance between the satellite and the center of the Earth (r). It is the sum of the altitude and the radius of the Earth:
r = h + R
Substituting the values:
r = [tex]1.99 * 10^6 + 6.371 * 10^6[/tex]
r ≈ [tex]8.361 * 10^6 m[/tex]
Now, we can calculate the gravitational potential energy using the formula:
PE = -GMm / r
Substituting the known values:
PE = [tex]-(6.67430 * 10^{-11} N(m/kg)^2)*(5.972 * 10^{24} kg)*(93 kg) / (8.361 * 10^6 m)[/tex]
PE ≈ [tex]-5.430 * 10^8 J[/tex]
Therefore, the potential energy of the satellite-Earth system is approximately -5.430 × 10^8 Joules.
The negative sign indicates that the gravitational potential energy is negative, indicating a bound system.
You can learn more about gravitational potential energy here:
https://brainly.com/question/19768887
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