Question

fill in the blank question
the higher a spacecraft’s orbit, the
the magnitude of free - fall acceleration, because of the
square relationship between ( r_e ) and ( r ).
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Explanation:

Step1: Recall free-fall acceleration formula

Free-fall acceleration \( g \) at orbit radius \( r \) is \( g = \frac{GM}{r^2} \), where \( GM \) is constant.

Step2: Analyze relationship with orbit height

Higher orbit means larger \( r \). Since \( g \propto \frac{1}{r^2} \), \( g \) decreases as \( r \) increases.

Step3: Identify the relationship type

The formula shows an inverse square relationship between \( g \) and \( r \).

Answer:

smaller; inverse