1. Understand the Concepts

* Gravitational Force: The force of attraction between two objects with mass. It's calculated using Newton's Law of Universal Gravitation:

F = (G * m1 * m2) / r²

where:

* F = gravitational force

* G = gravitational constant (6.674 × 10⁻¹¹ N⋅m²/kg²)

* m1 = mass of the Earth (5.972 × 10²⁴ kg)

* m2 = mass of the satellite (124 kg)

* r = distance between the centers of the Earth and the satellite (radius of orbit)

2. Rearrange the Formula to Solve for Radius

We need to solve for 'r', so let's rearrange the formula:

* r² = (G * m1 * m2) / F

* r = √((G * m1 * m2) / F)

3. Plug in the Values

* G = 6.674 × 10⁻¹¹ N⋅m²/kg²

* m1 = 5.972 × 10²⁴ kg

* m2 = 124 kg

* F = 690 N

r = √((6.674 × 10⁻¹¹ N⋅m²/kg² * 5.972 × 10²⁴ kg * 124 kg) / 690 N)

4. Calculate the Radius

r ≈ 7.03 × 10⁶ meters

5. Convert to Kilometers

r ≈ 7.03 × 10⁶ meters * (1 kilometer / 1000 meters)

r ≈ 7030 kilometers

Therefore, the radius of the satellite's orbit is approximately 7030 kilometers.