If the earth suddenly became more massive while the satellite remains in the circular orbit at the same altitude, the orbital period will decrease.
The orbital time period of revolution of a satellite around a planet is given by,
T = 2π√(r³/GM)
Where,
T is the period of revolution,
r is the altitude of the satellite,
G is the universal gravitational constant,
M is the mass of the planet.
If the mass of the earth suddenly increased and the altitude of the circular orbit of the earth is kept same,
Then, we can write that the time period is proportional to the mass of the planet as,
T ∝ 1/√M
If the mass of the planet is increased, the orbital period will decrease.
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