A satellite is in a circular orbit around the Earth. If the radius of the orbit
Practice Questions
Q1
A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the gravitational acceleration is 9.8 m/s², what is the speed of the satellite?
5.5 km/s
7.9 km/s
9.8 km/s
11.2 km/s
Questions & Step-by-Step Solutions
A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the gravitational acceleration is 9.8 m/s², what is the speed of the satellite?
Step 1: Understand that the satellite is in a circular orbit around the Earth.
Step 2: Identify the radius of the orbit, which is given as 7000 km.
Step 3: Convert the radius from kilometers to meters because the gravitational acceleration is in meters per second squared. 7000 km = 7000 * 1000 m = 7,000,000 m.
Step 4: Note the gravitational acceleration (g) is given as 9.8 m/s².
Step 5: Use the formula for the speed (v) of a satellite in orbit: v = √(g * r).
Step 6: Substitute the values into the formula: v = √(9.8 m/s² * 7,000,000 m).
Step 7: Calculate the product inside the square root: 9.8 * 7,000,000 = 68,600,000.
Step 8: Take the square root of 68,600,000 to find the speed: √(68,600,000) ≈ 8,287.5 m/s.
Step 9: Convert the speed from meters per second to kilometers per second: 8,287.5 m/s = 8.3 km/s.
Circular Orbit Dynamics – Understanding the relationship between gravitational acceleration, radius of orbit, and orbital speed.
Units Conversion – Converting kilometers to meters to ensure consistency in calculations.
