Orbital Speed of Planet

📌 CONCEPT: The orbital speed of a planet or spacecraft is the speed at which it moves around a celestial body in a stable circular orbit.

📐 RULE / FORMULA: The orbital speed (v) of a planet or spacecraft can be calculated using the formula v = √(G · M / r), where G is the gravitational constant, M is the mass of the celestial body, and r is the radius of the orbit.

💡 WORKED EXAMPLE: To calculate the orbital speed of the spacecraft, we can use the given values: G = 6.67 x 10^-11 N m^2 kg^-2, M = 5.98 x 10^24 kg, and r = 6.38 x 10^6 m. Plugging these values into the formula, we get v = √(6.67 x 10^-11 N m^2 kg^-2 x 5.98 x 10^24 kg / 6.38 x 10^6 m) = 7.73 km/s.

⚠️ COMMON MISTAKE: Students often forget to use the correct values for the gravitational constant (G) and the mass of the Earth (M), or they may incorrectly plug in the values into the formula.