On July 15, 2004, NASA launched the Aura spacecraft to study the earth's climate and atmosphere. This satellite was injected into an orbit 705 km above the earth's surface, and we shall assume a circular orbit.
(a) How many hours does it take this satellite to make one orbit?

(b) How fast (in km/s) is the Aura spacecraft moving?

Question

On July 15, 2004, NASA launched the Aura spacecraft to study the earth's climate and atmosphere. This satellite was injected into an orbit 705 km above the earth's surface, and we shall assume a circular orbit.
(a) How many hours does it take this satellite to make one orbit?
  

(b) How fast (in km/s) is the Aura spacecraft moving?

anonymous · Answer

Hi. This one is easier done backwards.. i.e. do b) first.
Using equations for gravitational force, and centripetal force and equating them, you can rearrange to get$$v = \sqrt{\frac{ GM }{ r }}$$
G = 6.67E-11, M = 5.97E24 kg, r = radius of Earth + orbit height *in metres* 
[radius of Earth is 6371000m]. 
Once you have the speed, you can use speed = distance/time to get the time, using distance as the circumference of the orbit. you answer will be in seconds so you'll have to convert it to hours!