a 500 kg satellite experiences a gravitational force of 3000 N, while moving in a circular orbit around the earth.
a) find the radius of the circular orbit
b) find the speed of the satellite
c) find the period of the orbit
a) find the radius of the circular orbit
b) find the speed of the satellite
c) find the period of the orbit
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a)
Using the gravitational force equation .. F = G.Ms.Me / R²
3000N = (6.67^-11)(500kg)(5.97^24kg) / R²
3000 = 1.99^17 / R² .. .. R² = 1.99^17 / 3000 = 6.63^3 (m²) .. .. .. ►R = 8.14^6 m
b)
Centripetal force = 3000N = Ms.v² / R
v² = 3000.R / Ms .. .. 3000 x 8.14^6m / 500kg
v² = 4.89^7(m/s)² .. .. .. ►v= 6.99^3 m/s .. (7000 m/s)
c)
Period time .. T = circumference (2πR) / v
T = (2π x 8.14^6m) / 7.0^3m/s .. .. .. ►T = 7.31^3 s .. ( ≈ 2.0hr)
Using the gravitational force equation .. F = G.Ms.Me / R²
3000N = (6.67^-11)(500kg)(5.97^24kg) / R²
3000 = 1.99^17 / R² .. .. R² = 1.99^17 / 3000 = 6.63^3 (m²) .. .. .. ►R = 8.14^6 m
b)
Centripetal force = 3000N = Ms.v² / R
v² = 3000.R / Ms .. .. 3000 x 8.14^6m / 500kg
v² = 4.89^7(m/s)² .. .. .. ►v= 6.99^3 m/s .. (7000 m/s)
c)
Period time .. T = circumference (2πR) / v
T = (2π x 8.14^6m) / 7.0^3m/s .. .. .. ►T = 7.31^3 s .. ( ≈ 2.0hr)