SUMMARY
If the mass of Earth is multiplied by a factor of 4 while keeping the radius of a satellite's orbit unchanged, the period of the satellite will increase by a factor of 2. This conclusion is derived from applying Newton's Law of Gravity and Kepler's Third Law of Planetary Motion, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. Therefore, with the increased mass, the gravitational force acting on the satellite increases, resulting in a longer orbital period.
PREREQUISITES
- Newton's Law of Gravity
- Kepler's Third Law of Planetary Motion
- Understanding of orbital mechanics
- Basic algebra for manipulating equations
NEXT STEPS
- Study the implications of Kepler's Laws on satellite motion
- Explore the effects of varying mass on gravitational forces
- Learn about orbital period calculations in different gravitational fields
- Investigate the relationship between radius and orbital speed
USEFUL FOR
Students in physics, aerospace engineers, and anyone interested in orbital mechanics and gravitational effects on satellite motion.