Question

A satellite with a mass of 5.6 E 5 kg is orbiting the Earth in a circular path. Determine the satellite's velocity if it is orbiting at a distance of 6.8 E 5 m above the Earth's surface. Earth's mass = 5.98 E 24 kg; Earth's radius = 6.357 E 6 m.

A) 6,800 m/s
B) 7,200 m/s
C) 7,500 m/s
D) 7,900 m/s

Answer 1

C) 7,500 m/s

Step-by-step explanation:

The satellite's acceleration due to gravity equals its centripetal acceleration.

v² / r = GM / r²

Solving for velocity:

v² = GM / r

v = √(GM / r)

Given:

G = 6.67×10⁻¹¹ m³/kg/s²

M = 5.98×10²⁴ kg

r = 6.357×10⁶ m + 6.8×10⁵ m = 7.037×10⁶ m

Substituting the values:

v = √(6.67×10⁻¹¹ × 5.98×10²⁴ / 7.037×10⁶)

v = √(5.67×10⁷)

v = 7500 m/s