Question

A geosynchronous orbit is an orbit in which the satellite
remains over the same spot on the planet as the planet turns.
This is accomplished by matching the velocity of the satellite to
the velocity of the turning planet. The orbital radius of the
geosynchronous satellite is 4.23 x 10^7m (measured from the
center of Earth). What is the speed of the satellite in orbit?

Answer 1

The speed of the satellite in orbit is 3069 m/s

Force on satellite

For the geosynchronous orbit, the gravitational force of attraction on the satellite, F equals the centripetal force on the satellite, F'

So, F = F'

GMm/R² = mv²/R where

• G = universal gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg²,
• M = mass of earth = 5.972 × 10²⁴ kg,
• m = mass of satellite,
• R = radius of geosynchronous orbit = 4.23 × 10⁷ m and
• v = speed of satellite in orbit

Speed of satellite in orbit

So, making v subject of the formula, we have

v = √(GM/R)

So, substituting the values of the variables into the equation, we have

v = √(GM/R)

v = √(6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg/4.23 × 10⁷ m)

v = √(39.83324 × 10¹³ Nm²/kg/4.23 × 10⁷ m)

v = √(9.4168 × 10⁶ Nm/kg)

v = 3.069 × 10³ m/s

v = 3069 m/s

So, the speed of the satellite in orbit is 3069 m/s

Learn more about speed of satellite in orbit here:

https://brainly.com/question/22247460