Time Period of a Satellite Experiment – For Schools, Teachers, and Students
Definition
The time period of a satellite is the time taken to complete one revolution around a celestial body. This is a fundamental concept in orbital mechanics and depends on the altitude of the satellite and the gravitational properties of the celestial body.
This concept is demonstrated in Dencity – Online Science Lab and Simulations to enhance interactive learning.
Theory
1. Kepler’s Third Law and Time Period Formula
The time period of a satellite is derived using Kepler’s Third Law, which states:
T = 2π √(r³ / GM)
where:
- T = Time period of the satellite (seconds)
- r = Orbital radius (r = R + h, where R is the planet’s radius and h is the satellite’s altitude)
- G = Gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²)
- M = Mass of the celestial body
2. Derivation of Time Period
The gravitational force (F_g) provides the necessary centripetal force (F_c) for circular motion:
F_g = F_c
GMm / r² = mv² / r
Solving for orbital velocity (v):
v = √(GM / r)
Substituting this into the velocity relation v = 2πr / T, we derive:
T = 2π √(r³ / GM)
Applications of Satellite Time Period
- Communication satellites require precise time periods to maintain synchronization with Earth’s rotation (e.g., geostationary satellites).
- GPS and Weather satellites rely on accurate orbital timing to provide real-time data.
- Astronomical satellites use precise time period calculations for deep-space observations.
Real-World Uses of Time Period Calculations
- Geostationary satellites have a time period of 24 hours, allowing them to stay fixed relative to the Earth.
- Low Earth Orbit (LEO) satellites, such as Starlink, complete multiple orbits daily due to their shorter time periods.
- Orbital timing ensures precise navigation systems like GPS, Galileo, and GLONASS.
- Online Science Lab: Students can simulate satellite motion to explore orbital mechanics.
Observations and Key Learnings
- As altitude increases, the satellite’s time period increases.
- Lower altitude satellites complete more orbits in a given time than higher altitude satellites.
- For a fixed celestial body, the time period follows the cube root relationship with the orbital radius.
This science practical simulator provides an interactive way to understand the relationship between a satellite’s altitude and its time period using Kepler’s Third Law. By adjusting orbital parameters, students can observe how changes affect satellite motion, reinforcing theoretical concepts through hands-on experimentation.
Dencity’s Experiment App allows learners to explore real-world applications, such as geostationary satellites, GPS systems, and astronomical observations. Through this Science Lab, students can develop a deeper understanding of orbital mechanics, making complex space science concepts accessible and engaging.
