an earth satellite in circular orbit 1250 kilometers high makes one complete revolution evry 90 min. What is it linear speed? use 6400 kilometers for the radius of the earth.
the diameter of the orbit is 1250+6400 km
the distance it goes in 90 minutes is therefore
pi*(1250+6400) km
the speed is distance over time
pi*(1250+6400)/90 km/hr
okay but don't you have to multiply the (1250+6400) by pi and 2 then divide that by 90? i got 534.07 as an answer
Yes, sorry, I left the 2 out. circumference = 2 pi R
thank you!
the radius at which it rotates = 6400+1250
circumference = 2pi(r)
= 2(6400+1250)pi = 15300pi
rate = distance/time
= 15300pi/1.5 km/h
= 32044 km/hr
To find the linear speed of the Earth satellite, we can use the formula for the circumference of a circle:
C = 2πr
where C is the circumference and r is the radius.
In this case, the radius of the Earth satellite's orbit is the sum of the radius of the Earth and the altitude of the satellite from the Earth's surface. So, the total radius would be:
R = 6400 km + 1250 km = 7650 km
To calculate the circumference, we substitute the radius into the formula:
C = 2π × 7650 km
Now we can calculate the linear speed of the satellite by dividing the distance it travels in one complete revolution by the time it takes:
Speed = Circumference / Time
Since the satellite makes one complete revolution every 90 minutes, we convert the time to hours:
Time = 90 min / 60 min/hour = 1.5 hours
Now we can calculate the linear speed:
Speed = (2π × 7650 km) / 1.5 hours
Calculating this equation will give us the linear speed of the Earth satellite.