Response:
83%
Clarification:
At the surface, the weight can be expressed as:
W = GMm / R²
where G denotes the gravitational constant, M represents the Earth's mass, m signifies the shuttle's mass, and R is the Earth's radius.
When in orbit, the weight is given by:
w = GMm / (R+h)²
where h indicates the shuttle's altitude above Earth's surface.
The weight ratio is as follows:
w/W = R² / (R+h)²
w/W = (R / (R+h))²
For R = 6.4×10⁶ m and h = 6.3×10⁵ m:
w/W = (6.4×10⁶ / 7.03×10⁶)²
w/W = 0.83
Thus, the shuttle maintains 83% of its weight as it orbits.
U = 1794.005 × 10⁶ J. Explanation: Information provided indicates that the capacitance of the original capacitor is C = 1.27 F, and the potential difference applied to it is V = 59.9 kV, or 59.9 × 10³ V. The potential energy (U) for the capacitor is determined by the formula: U = (1/2) × C × V². Substituting the respective values, we find U = (1/2) × 1.27 × (59.9 × 10³)², resulting in U = 1794.005 × 10⁶ J.
