A satellite orbits at a distance from the Earth's center of about 4.40 Earth radii and takes 13.0 hours to go around once. What distance (in meters) does the satellite travel in one day?
One day is 24/13 = 1.8462 revolutions.
Multiply that by 2 pi * R, where
R = 4.4 Earth radii.
The Earth's radius is about 6370 km. Look it up to make sure.
To calculate the distance the satellite travels in one day, we need to find its orbital circumference and then multiply it by the number of orbits the satellite completes in a day.
1. Find the orbital circumference:
The circumference of a circular orbit can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the orbit.
Given that the satellite orbits at a distance of 4.40 Earth radii from the Earth's center, we can calculate its orbital circumference as follows:
C = 2π(4.40 Earth radii)
2. Convert Earth radii to meters:
To find the distance in meters, we need to know the value of an Earth radius in meters. Let's assume the average radius of the Earth is approximately 6,371 kilometers or 6,371,000 meters.
3. Substitute the values and calculate the orbital circumference:
C = 2π(4.40)(6,371,000 meters)
4. Multiply the orbital circumference by the number of orbits in a day:
Since the satellite takes 13.0 hours to complete one orbit, it will complete approximately (24 hours / 13.0 hours) orbits in a day.
5. Substitute the values and calculate the distance traveled in one day:
Distance = (C x Number of orbits in a day)
Let's perform the calculation step by step:
1. Calculate the orbital circumference:
C = 2π(4.40)(6,371,000) meters
2. Find the number of orbits in a day:
Number of orbits in a day = 24 hours / 13.0 hours
3. Calculate the distance traveled in one day:
Distance = (C x Number of orbits in a day)
By following these steps and performing the calculations, you can determine the distance (in meters) the satellite travels in one day.