If the radius of a satellite’s circular orbit is doubled, how does this affect the satellite’s orbital speed?

Question

BlackTom AI · Accepted Answer

Question: If the radius of a satellite’s circular orbit is doubled, how does this affect the satellite’s orbital speed?

Option a: The speed stays the same. This is incorrect because in a circular orbit, the speed depends on the radius; increasing the radius changes the required centripetal force, so the speed cannot remain unchanged.

Option b: The speed becomes four times greater. This is not physically plausible for a satellite in a stable circular orbit around a central body. Increasing the orbit radius does not cause the speed to increase; in fact, it tends to decrease the needed speed.

Option c: The speed is reduced. This is true in general terms, but more precisely the speed decreases by a specific factor (see below). Doubling the radius reduces the orbital speed because v ∝ 1/√r for a gravitationally bound circular orbit, so the speed decreases, not stays the same or increases.

Option d: The speed is doubled. This contradicts the relationship v ∝ 1/√r; increasing r would not cause the speed to double. It would require a much smaller radius to reach a higher speed, not the same or a doubled value.

In summary, the correct qualitative statement is that the speed is reduced when the radius is doubled. The more precise relation is v2 = v1 / √2, since v ∝ 1/√r for a circular orbit, so doubling r lowers the speed by a factor of √2 (approximately 0.707 times the original speed).

If the radius of a satellite’s circular orbit is doubled, how does this affect the satellite’s orbital speed?单项选择题

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