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cyt91

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## Homework Statement

The weight of a satellite in a circular orbit round the Earth is half of its weight on the surface of the Earth. If the mass of the satellite is 800kg, determine

(i)the altitude of the satellite

(ii)the speed of the satellite in the orbit

(iii)the minimum energy required to move the satellite from its orbit to outer space.

Radius of Earth = 6.4 x 10^6 m

Mass of Earth = 6.0 x10^24 kg

## Homework Equations

Gravitational force = -GMm/(r^2)

W=mg

Gravitational potential energy = -GMm/r

Kinetic energy of satellite = GMm/(2r)

## The Attempt at a Solution

(i) GMm/(r^2)=mg

GMm/(r'^2)=0.5mg

Solving, r'=(2^0.5)r

Altitude,h=r'-r

=(2^0.5-1)(6.4 x 10^6)

= 2.7 x 10^6 m

(ii) GMm/(r^2)= (mv^2)/r

v=(GM/(r)^0.5

Solving using r=2^0.5 x 6.4 x 10^6 m

v = 6.7 x 10^3 m/s

(iii) Total energy of satellite in orbit is

T=U+K

When removed to outer space,energy of satellite should be U=0 and K=0 since we want to find the minimum energy required.

Thus,

Energy required,E= 0 - (U+K)

E = 0 -(-GMm/r-GMm/(2r))

= GMm/(2r)

Solving using r= (2^0.5) x 6.4 x 10^6 m and m= 800kg

E=1.8 x 10^7 J

Please check my working,especially the third part of the question. When calculating Minimum energy required to remove the satellite to outer space, we should take into account the kinetic energy of the satellite shouldn't we?