Answer:(a) To find the height of the satellite's orbit if its total energy were 550 MJ greater, we can use the following equation:
K2 + U2 = K1 + U1 + 550 MJ
Since the satellite is in a circular orbit, its kinetic energy is given by:
K = (1/2)mv^2
where m is the mass of the satellite, and v is its velocity.
We can use the following equation to relate the height of the satellite's orbit to its velocity:
v = sqrt(GM/R)
where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth plus the height of the satellite's orbit.
Therefore, we can express the kinetic energy of the satellite in terms of its height:
K = (1/2)m(GM/R)
Using these equations, we can rewrite the conservation of energy equation as:
(1/2)m(GM/(R1+h1)) - GMm/(R1+h1) = (1/2)m(GM/(R2+h2)) - GMm/(R2+h2) + 550 MJ
where R1 is the radius of the Earth, and R2 is the radius of the Earth plus h2.
Simplifying and solving for h2, we get:
h2 = [(GMm/(R1+h1)) - (GMm/(R2+h2)) - 550 MJ/(GM/(R2+h2))]^(-1) - R2
Plugging in the given values, we get:
h2 = 931 km
Therefore, the height of the satellite's orbit would be 931 km if its total energy were 550 MJ greater.
(b) To find the difference in the system's kinetic energy, we can use the following equation:
Delta K = K2 - K1
Substituting the expressions for K1 and K2, we get:
Delta K = (1/2)m(GM/(R2+h2)) - (1/2)m(GM/(R1+h1))
Plugging in the given values, we get:
Delta K = -7.5 x 10^9 J
The negative sign indicates that the system's kinetic energy has decreased.
(c) To find the difference in the system's potential energy, we can use the following equation:
Delta U = U2 - U1
Substituting the expressions for U1 and U2, we get:
Delta U = -GMm/(R2+h2) + GMm/(R1+h1)
Plugging in the given values, we get:
Delta U = 5.9 x 10^9 J
The positive sign indicates that the system's potential energy has increased.
Explanation: