A satellite orbits at a distance from the Earth's center of abut 3.00 earth radii and takes 7.30 hours to go around once. What distance (in meters) does the satellite travel in one day? And, what is the orbital velocity (in m/s)? I'm completely lost. I haven't gotten even close with several practice questions. Does anyone have any guidance? Thank you.
figure the radius R of the orbit
The distance traveled in one orbit is thus 2πR
Now just figure how many orbits it makes in 24 hours. That will give the total distance traveled.
Then just divide that by the time (86400 s) to get the speed.
Thanks, Steve. Still get the wrong answer. I don't know what I'm doing wrong. One of the practice problems is 5.80 radii and 19.6 hours. It gives the answers as 284,000,000 and 3287. I get how they got the velocity, but not the distance. Since I haven't been able to determine the distance on any of the problems, velocity determination is also incorrect. I appreciate your help.
(2)(3.14)(3.00)(6.4 x 10^6)(3.288) = 396,453,888 m
24/7.3 = 3.288
396,453,888 / 86,400 = 4,589
Hmmm. your math looks good. Using the 5.8R and 19.6 I get
(2)(3.14)(5.8)(6.4 * 10^6)(1.22) = 284,398,592
which agrees with their rounded answer for distance. Divide that by 86400 seconds and it gives a speed of 3291 m/s, which is pretty close.
Is your answer anywhere near theirs?
yes, it is. Got both answers correct. 396,453,888 and 4589. I needed to multiply by the partial day 24/7.3. Then, it worked. That was the missing piece. Thanks again!
To find the distance the satellite travels in one day, we need to calculate the circumference of its circular orbit. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius of the orbit is 3.00 earth radii.
To convert the radius from earth radii to meters, we need to know the value of 1 earth radius in meters. The average radius of the Earth is about 6,371 kilometers, which is equivalent to 6,371,000 meters. So, 1 earth radius is equal to 6,371,000 meters.
Now, we can calculate the distance traveled in one day. Since the satellite takes 7.30 hours to go around once, we can determine how many times it goes around the Earth in one day by dividing 24 hours by 7.30 hours. Let's call this value n.
n = 24 hours / 7.30 hours
Next, we can calculate the distance traveled in one day by multiplying the circumference of the orbit by n:
Distance traveled in one day = C * n = 2πr * n
Now, let's plug in the values:
C = 2π * 3.00 earth radii = 2π * 3.00 * 6,371,000 meters
n = 24 hours / 7.30 hours
Finally, multiply C by n to find the distance traveled in one day.
As for the orbital velocity, we can calculate it using the formula v = d/t, where v is the velocity, d is the distance traveled in one orbit, and t is the time taken for one orbit.
For the orbital velocity, we want to calculate the velocity for one full orbit, so we can use the given time period of 7.30 hours.
v = d / t = (2πr) / t
Let's substitute the values:
r = 3.00 * 6,371,000 meters
t = 7.30 hours
Now, we can plug these values into the formula to find the orbital velocity.
I hope this helps! Let me know if you need any further assistance.