Physics

Physics

Problem

A satellite is revolving in a circular orbit at a height ' hh ' from the earth's surface (radius of earth RR ; h≪Rh \ll R ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere.) [Main 2016] a. gR/2\sqrt{gR/2} b. gR(2−1)\sqrt{gR}(\sqrt{2}-1) c. 2gR\sqrt{2gR} d. gR\sqrt{gR}
Intuitive explanation

The key is recognizing that you're comparing two different orbital speeds at the same distance from Earth's center. First, find the circular orbital velocity at height hh, then find the escape velocity from that same point—the difference tells you how much speed boost is needed. Since h≪Rh \ll R, you can use approximations to simplify the algebra and see the clean relationship between these two velocities.

Intuitive explanation

The key is recognizing that you're comparing two different orbital speeds at the same distance from Earth's center. First, find the circular orbital velocity at height hh, then find the escape velocity from that same point—the difference tells you how much speed boost is needed. Since h≪Rh \ll R, you can use approximations to simplify the algebra and see the clean relationship between these two velocities.

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