Physics

Problem

Two satellites are in circular orbits around the Earth. Both satellites have the same mass and satellite

X

is closer to Earth than satellite

Y

. What is correct for the orbital periods of

X

and

Y

and the total energies of

X

and

Y

? A. Orbital periods:

X

greater than

Y

; Total energies:

X

greater than

Y

B. Orbital periods:

X

greater than

Y

; Total energies:

Y

greater than

X

C. Orbital periods:

Y

greater than

X

; Total energies:

X

greater than

Y

D. Orbital periods:

Y

greater than

X

; Total energies:

Y

greater than

X

Intuitive explanation

The key is Kepler's third law: orbital period depends only on orbital radius, not mass. Since $X$ is closer to Earth, it orbits faster and has a shorter period than $Y$ . For total energy, remember that orbital energy is negative and becomes more negative (lower) at smaller radii—so $X$ , being closer in, has less total energy than $Y$ . The closer orbit is tighter and more bound.

Intuitive explanation

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