How can you calculate the orbital speed of a planet?

The orbital speed of a planet can be calculated using the formula: v = √(GM/r).

To calculate the orbital speed of a planet, you need to understand the principles of gravitational force and circular motion. The formula v = √(GM/r) is derived from these principles. In this formula, 'v' represents the orbital speed, 'G' is the gravitational constant, 'M' is the mass of the central body (for example, the sun in our solar system), and 'r' is the distance from the centre of the central body to the orbiting planet.

The gravitational constant (G) is a fixed value, approximately 6.67 x 10^-11 N(m/kg)^2. The mass of the central body (M) and the distance to the orbiting planet (r) will vary depending on the specific scenario. For example, if you're calculating the orbital speed of Earth around the Sun, you would use the mass of the Sun and the average distance from the Sun to the Earth.

To use the formula, you simply substitute the known values into the equation and solve for 'v'. The result will give you the orbital speed of the planet, usually in metres per second (m/s). This is the speed at which the planet needs to travel in order to maintain its orbit around the central body without being pulled in by gravity or flung out into space.

Remember, this formula assumes a circular orbit and doesn't account for elliptical orbits which are more common in reality. However, it provides a good approximation for most purposes at the IGCSE level.