Gravity and Space Mechanics
Learning Objectives
- Students will be able to calculate orbital velocity and escape velocity
- Students will be able to understand weightlessness and orbital mechanics
- Students will be able to explain satellite motion and types of orbits
Core Concepts
- Orbital velocity
- Escape velocity
- Weightlessness
- Kepler's laws
Formulas
$$F = \frac{Gm_1 m_2}{r^2}$$
Newton's law of universal gravitation
$$v_{orbit} = \sqrt{\frac{GM}{r}}$$
Orbital velocity for circular orbits
$$v_{escape} = \sqrt{\frac{2GM}{r}}$$
Escape velocity from a celestial body
Units
| Kilometer per second | km/s |
Interesting Fact
Escape velocity from Earth is about 11.2 km/s; no slower object can escape Earth's gravity
Key Scientist
Johannes Kepler
Discovered the laws of planetary motion
Modern Research
Space missions exploit orbital mechanics and gravity assists, while dark matter research reveals that visible gravity accounts for only 5% of mass.
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