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1 vote
A satellite in Earth orbit has a mass of 107 kg and is at an altitude of 2.08 × 10⁶ m. (Assume that u = 0 as r → [infinity].)

a) 9.8 m/s²
b) 9.8 N/kg
c) 0 m/s²
d) 0 N/kg

asked
User Rohrbs
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8.2k points

1 Answer

5 votes

Final answer:

The radius of the satellite's orbit is approximately 1.47 × 10⁷ m and the correct option for the acceleration due to gravity is 0 m/s².

Step-by-step explanation:

The radius of the satellite's orbit can be found by subtracting the radius of the Earth from the altitude of the satellite. The radius of the Earth is approximately 6371 km. Therefore, the radius of the satellite's orbit is 2.08 × 10⁶ m - 6371 km = 2.08 × 10⁶ m - 6.371 × 10⁶ m = 1.47 × 10⁷ m.

The acceleration due to gravity at the surface of the Earth is 9.8 m/s². However, at the altitude of the satellite, the acceleration due to gravity is significantly lower. It can be calculated using the formula:

g = (G * M) / r²

Where g is the acceleration due to gravity, G is the gravitational constant (approximately 6.67 × 10⁻¹¹ N m² / kg²), M is the mass of the Earth (approximately 5.97 × 10²⁴ kg), and r is the radius of the satellite's orbit.

By substituting the values into the formula, we can find the acceleration due to gravity at the altitude of the satellite:

g = (6.67 × 10⁻¹¹ N m² / kg² * 5.97 × 10²⁴ kg) / (1.47 × 10⁷ m)²

Simplifying the equation gives:

g ≈ 1.77 m/s²

Therefore, the correct option is 0 m/s² (c) as per the given choices.

answered
User Myanju
by
8.2k points
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