Use the exact values you entered in previous answer(s) to make later calculation

Question

Use the exact values you entered in previous answer(s) to make later calculation(s).

The International Space Station orbits at an average height of 400 km above sea level.

C. period ___________s

(b) The Hubble Space Telescope orbits at 560 km. What is the telescope's orbital velocity and period?

A. orbital velocity __________m/s

B. period ___________s

C. period ___________s

(b) The Hubble Space Telescope orbits at 560 km. What is the telescope's orbital velocity and period?

A. orbital velocity __________m/s

B. period ___________s

Explanation / Answer

Acceleration is given by = GM/r²
where G = 6.674 * 10^-11 N·m²/kg²
M = mass of Earth = 5.97 * 10^24 Kg
r = radius of orbit = height + Re
where Re = radius of Earth = 6.37 * 10^3 Km
r = 400 + 6.37 * 10^3 Km
r = 6770 Km = 6770 * 10^3 m

a)
Acceleration a =( 6.674 * 10^-11 * 5.97 * 10^24 ) / (6770 * 10^3)^2
a = 8.69 m/s^2

Then the velocity can be found through
a = v² / r
v^2 = a*r
v = sqrt(a*r)
v = sqrt(8.69 * 6770 * 10^3)
v = 7670 m/s
Orbital velocity v = 7670 m/s


= ²r = (2/T)²r
T = 2/(sqrt(/r))
T = 2*3.14/ (sqrt(8.69 / (6770 * 10^3))
T = 5542 s

Please ask seperate questions in seperate post.

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