Trying to find orbital velocity based off of height

[kasra12321]

Homework Statement

A Titan IV rocket has put your spacecraft in circular orbit around Earth at an altitude of 397 km. What is your orbital velocity? Give your answer in m/s.

Homework Equations

http://as370.socialhwk.com/engr370i/ch04/ch4_3/IMG00015.GIF
http://as370.socialhwk.com/engr370i/ch04/ch4_3/IMG00016.GIF

The Attempt at a Solution

I have been attempting to take the online midterm for the class but I have been having issues. Every answer I have inputed for the first question comes out as incorrect.
When using this formula and substituting 500km for 397km for the midterm I get: 7688.328079. I have tried inputing this in as many variations as possible but am told it is incorrect every time.


I have also tried using an online orbital velocity calculator to confirm my math and I receive the answer 7673.24507 which also does not work.

I'm completely stuck and cannot progress with the test. I was wondering if there was something I was doing wrong or if there was an issue with the midterm.
also if it helps, the professor has included a midterm review which he has posted a similar problem with the answer, but not how he got the answer:

A Titan IV rocket has put your spacecraft in circular orbit around Earth at an altitude of 350 km. What is your orbital velocity? Give your answer in m/s.

Answer: V = 7697.5 m/s

 

[SteamKing]

Try using GM = 398600 km^3/s^2 for Earth to calculate orbital velocity.

V will have units of km/s, so convert to m/s

 

[kasra12321]

Try using GM = 398600 km^3/s^2 for Earth to calculate orbital velocity.

V will have units of km/s, so convert to m/s

if i did it right, i got 7.674861 km/s or 7674.861 m/s, however, it is telling me it is also wrong...

 

[haruspex]

Looks to me that you're just a bit inaccurate somewhere. Using GM = 3.98E14 I get:
397km: 7673 m/s
500km: 7615m/s
350km: 7700m/s

 

[kasra12321]

Hmm, but what i don't understand is, you got 7700 m/s for 350 and for the example problem, it says 7697.5. Is the teacher doing something differently?

 

[haruspex]

Hmm, but what i don't understand is, you got 7700 m/s for 350 and for the example problem, it says 7697.5. Is the teacher doing something differently?

That's only a 0.03% difference (2.5km). The radius of the Earth is not that precisely definable - it varies by 30km. I would argue that 7697.5 is wrong in that it overstates the precision.

 

[kasra12321]

Yea i understand what you mean, but the problem is that the test is online and unless I get the precise answer, I can't move on to the next question. which is a terrible system. I guess I need to find out what constants the professor used to reach that number in the example problem.

 

[kasra12321]

i ended up solving backwards for the constant he used and got 6,400^3. I used that in the problem and got the right answer. Thanks for the help though.