Determine the satellite’s altitude above the surface of the Earth.?
Determine the satellite’s altitude above the surface of the Earth.
A satellite moves in a circular orbit around
the Earth at a speed of 5.8 km/s.
Determine the satellite’s altitude above
the surface of the Earth. Assume the
Earth is a homogeneous sphere of radius
6370 km and mass 5.98 × 10^24 kg. The
value of the universal gravitational constant is
6.67259 × 10−11 N · m2/kg2. Answer in units
of km.
can anyone give me the answer and how they got it
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Verified answer
v = √(GM/R)
v = velocity
G = 6.673e-11 Nm²/kg²
M is mass of central body
R is radius of orbit
5800 = √(6.673e-11*5.98e24/R)
solve for R
3.364e7 = 6.673e-11*5.98e24/R
R = 6.673e-11*5.98e24 / 3.364e7 = 11860000 meters or 11860 km
radius of earth is 6370km, subtract that
orbit height above ground = 11860 - 6370 = 5490 km
.
.
The force F on the satellite in uniform circular motion is F = m*a, where F is the external force, m is the mass of the satellite, and a is the acceleration. But 'a' is the centripetal acceleration a = (v^2)/r. Plug this into F = m*a, and equate this to Newton's famous gravitational equation between two masses. The mass of the satellite will cancel out leaving only the radius. Since the question asked for the altitude, subtract this value from Earth's radius, and you'll get your answer.
Hope this helps.