SUMMARY
The orbital speed of the space shuttle in a 290-mile-high orbit is calculated using the formula v=√(GM/(R+h)). With the Earth’s mass (Me) at 5.98x10^24 kg and the gravitational constant (G) at 6.67x10^-11 N m²/kg², the shuttle's speed is determined to be approximately 7639.54 m/s. The calculations also yield an orbital period (T) of 5622.8 seconds. The initial attempt at solving the problem involved incorrect values and assumptions, which were clarified through subsequent calculations.
PREREQUISITES
- Understanding of gravitational physics and orbital mechanics
- Familiarity with the formula v=√(GM/(R+h))
- Knowledge of the Earth's mass and radius
- Basic algebra and unit conversions (miles to meters)
NEXT STEPS
- Study the derivation of orbital mechanics equations
- Learn about the implications of varying orbital altitudes on speed
- Explore the effects of gravitational forces on satellite motion
- Investigate real-world applications of orbital speed calculations in aerospace engineering
USEFUL FOR
Aerospace engineers, physics students, and anyone interested in understanding the dynamics of satellite motion and orbital mechanics.