The space shuttle had a top orbital speed of 8000 m/s and orbited in a circular orbit approximately 320 km above the earth's surface. How long was one orbit in seconds?
Details and assumptions
The radius of the earth is 6370 km.
orbital radius = 6370+320=6690km
orbital circumference is thus 2pi*6690 = 42034km
divide that (in meters) by 800 m/s to get the period in seconds.
To find the time it takes for one orbit of the space shuttle, we can use the formula for the circumference of a circle:
Circumference = 2πr,
where r is the radius of the orbit. In this case, the radius of the orbit is the sum of the radius of the earth and the altitude of the shuttle:
Radius of orbit = radius of earth + altitude of shuttle.
Given that the radius of the earth is 6370 km and the altitude of the shuttle is 320 km, we can calculate the radius of the orbit:
Radius of orbit = 6370 km + 320 km = 6690 km.
Next, we need to calculate the circumference of the orbit using the formula:
Circumference = 2π × Radius of orbit.
Plugging in the value for the radius of the orbit, we have:
Circumference = 2π × 6690 km.
Now, we need to convert the units from kilometers to meters, since the velocity is given in meters per second:
Circumference = 2π × 6690 km × 1000 m/km.
Finally, we can calculate the time it takes for one orbit by dividing the circumference by the velocity:
Time for one orbit = Circumference / Velocity.
Plugging in the values for the circumference and the velocity, we have:
Time for one orbit = (2π × 6690 km × 1000 m/km) / 8000 m/s.
Evaluating the expression:
Time for one orbit ≈ 2π × 8370000 / 8000 s.
Calculating the result:
Time for one orbit ≈ 1047.2 s.
Therefore, the time it takes for one orbit of the space shuttle is approximately 1047.2 seconds.