The Earth’s radius is about 6380 km. The space shuttle is orbiting about 275.0 km above Earth’s surface.
If the average speed of the space shuttle is 23500 km/h, find the time required for it to circle Earth.
To find the time required for the space shuttle to circle Earth, we need to calculate the circumference of the Earth's orbit at an altitude of 275.0 km.
The total distance that the space shuttle needs to travel is equal to the circumference of the Earth's orbit, which can be calculated using the formula:
Circumference = 2 * π * r
where r is the radius of the Earth's orbit (Earth's radius + altitude of the shuttle).
Plugging in the values:
r = Earth's radius + altitude of the shuttle
= 6380 km + 275.0 km
= 6655.0 km
Circumference = 2 * π * 6655.0 km
Next, we need to calculate the time required to travel the total distance. The average speed of the space shuttle is given as 23500 km/h.
Time = Distance / Speed
Plugging in the values:
Time = Circumference / Speed
= (2 * π * 6655.0 km) / 23500 km/h
To determine the time required, we will calculate this expression.
To find the time required for the space shuttle to circle Earth, we need to calculate the distance it travels in one complete orbit.
The distance traveled in one complete orbit can be calculated by adding the radius of Earth (6380 km) to the altitude of the space shuttle (275.0 km). So, the total distance traveled in one orbit is:
Distance = Radius of Earth + Altitude of space shuttle
Distance = 6380 km + 275.0 km
Distance = 6655.0 km
Next, we can calculate the time required to travel this distance by dividing the total distance by the average speed of the space shuttle:
Time = Distance / Speed
Time = 6655.0 km / 23500 km/h
To simplify the calculation, we need to ensure that the units are consistent. Since the speed is given in kilometers per hour, we can convert the distance to kilometers as well:
Time = (6655.0 km / 1) / (23500 km/h / 1)
Time = 6655.0 km / 23500 km/h
Now, we can divide the distance by the speed to get the time required:
Time ≈ 0.2834043 hours
So, it takes approximately 0.2834043 hours for the space shuttle to circle Earth.
time=distance/velocity
=(6380+275)km*2PI/(23500km/hr)= about 1.8 hours