Orbital period and speed of a space shuttle in flight

[kevnm67]

Homework Statement

The space shuttle is in a 290-mile-high orbit. What is the shuttles orbital speed?

Homework Equations

v=√GM/R+h

The Attempt at a Solution

Period:
Me= 5.98x10^24kg
Re= 6.38x10^6m
H= 290miles * 1609m = 466610m

v= √(6.67x10^-11 N)(5.98x10^24 kg)/ (6.38x10^6 m)+ 466610 m

I didn't get the correct answer and would like some help working through this problem.

 

[willem2]

try


$$v = \sqrt {\frac{ G M } {R+h}}$$

 

[kevnm67]

That's the equation I used above

 

[kevnm67]

i don't know if this is correct but here are my recent calculations:

v=2pi r/T ---> 42955687.5/T
G*M/r^2 = 8.5368*r= 58362553.54 ->v=sqrt(58362553.54)= 7639.54
T=2pi r/v = 5622.8

 

[rwisz]

To calculate the orbital speed of the space shuttle, we can use the equation v=√GM/R+h, where G is the gravitational constant, M is the mass of the Earth, R is the distance from the center of the Earth to the object's orbit, and h is the height of the orbit.

In this case, we can assume that the shuttle's orbit is circular, so R is equal to the sum of the radius of the Earth (Re) and the height of the orbit (h). Plugging in the values, we get:

v=√(6.67x10^-11 N)(5.98x10^24 kg)/ (6.38x10^6 m + 466610 m)

= 7.68 km/s

Therefore, the orbital speed of the space shuttle in this scenario is approximately 7.68 km/s. It is important to note that this is an average speed and the actual speed may vary slightly due to factors such as atmospheric drag and changes in the shuttle's altitude.