Gravitational potential energy: Sputnik I was launched into orbit around Earth in 1957. It had a perigee (the closest approach to Earth, measured from Earth's center) of 6.81 × 10⁶ m and an apogee (the furthest point from Earth's center) of 7.53 × 10⁶ m. What was its speed when it was at its perigee? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 × 10^-11 N ∙ m²/kg². A) 7180 m/s B) 7840 m/s C) 8230 m/s D) 11,000 m/s E) 13,400 m/s

Question

Quizplus · Accepted Answer

To find the speed of Sputnik I at its perigee, we can use the formula for the orbital speed of a satellite: $v = \sqrt{\frac{GM}{r}}$, where $v$ is the orbital speed, $G$ is the gravitational constant, $M$ is the mass of the Earth, and $r$ is the distance from the center of the Earth to the satellite at perigee. Plugging in the given values: $G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2$, $M = 5.97 \times 10^{24} \, \text{kg}$, and $r = 6.81 \times 10^6 \, \text{m}$, we can calculate the speed. This calculation yields a value close to the option B, 7840 m/s, indicating that at its closest approach to Earth, Sputnik I was traveling at this speed.

Gravitational Potential Energy: Sputnik I Was Launched into Orbit Around