warfreak131
Oct8-09, 02:00 PM
1. The problem statement, all variables and given/known data
A shuttle is in orbit 400km above the Earths surface, and circles it every 90 minutes. Find the centrip. acceleration and find it in terms of g. (He says for sake of ease, assume gravity = 10 m/s^2)
Earth radius = 6400 km
2. Relevant equations
a_{c}=\frac{v^2}{r}, v=\frac{2{\pi}r}{t}
3. The attempt at a solution
First I converted everything to meters and seconds:
6400 km = 6400000m, 90 minutes = 5400 seconds
v=\frac{2{\pi}r}{t}
v=\frac{2{\pi}(6400000+400000)}{5400}
v=7900\frac{m}{s}
a_{c}=\frac{v^2}{r}
a_{c}=\frac{7900^2}{6800000}
a_{c}=\frac{6.3{\cdot}10^7}{6800000}
a_{c}=9.2\frac{m}{s^2}
= .92g's
A shuttle is in orbit 400km above the Earths surface, and circles it every 90 minutes. Find the centrip. acceleration and find it in terms of g. (He says for sake of ease, assume gravity = 10 m/s^2)
Earth radius = 6400 km
2. Relevant equations
a_{c}=\frac{v^2}{r}, v=\frac{2{\pi}r}{t}
3. The attempt at a solution
First I converted everything to meters and seconds:
6400 km = 6400000m, 90 minutes = 5400 seconds
v=\frac{2{\pi}r}{t}
v=\frac{2{\pi}(6400000+400000)}{5400}
v=7900\frac{m}{s}
a_{c}=\frac{v^2}{r}
a_{c}=\frac{7900^2}{6800000}
a_{c}=\frac{6.3{\cdot}10^7}{6800000}
a_{c}=9.2\frac{m}{s^2}
= .92g's