Question

A satellite moves in a circular orbit around the earth at a speed of 5.7 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 1024 kg. The value of the universal gravitational constant is 6.67259 1011 n m2 /kg2 . Answer in units of km.

Answer 1

SOLUTION.

If a body a body revolve around earth in circular orbit than two force acting on it.

• Centrifugal Force ( Outwards)
• Gravitational pull by earth. (Inwards)

The radius of the circular orbit remains constant It means that both the forces balance each other.

• Centrifugal force = mv²/(R+h)

Where m is the mass of the body

R is the radius of the earth

h is the height from surface of earth.

• Gravitational attraction = GMm/(R+h) ²

Where M is the mass of earth

G is gravitation constant

From the above conversation we get.....

mv²/(R+h) = GMm/(R+h)²

v² = GM/(R+h)

R+h = GM/v²

h = (GM/v²) - R

h = (6.67 × 10^-11)×(5.98×10^24) / (5.7)² - 6370

h = 1.22 × 10^13 - 6370

h = 1.22 × 10^13 km

we can ignore 6370 as it is quite smaller than 1.22 × 10^13

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