High School

A satellite in Earth orbit has a mass of 93 kg and is at an altitude of [tex]1.99 \times 10^6[/tex] m. (Assume that [tex]U = 0[/tex] as [tex]r \rightarrow \infty[/tex].) What is the potential energy of the satellite-Earth system?

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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