Exact Formula

At height h above Earth's surface, the orbital radius is r = R + h:

g'(h) = GM/(R + h)^{2} = $gR^{2}$/(R + h)^{2}

Approximate Formula (h ≪ R)

Using binomial expansion:

g'(h) ≈ g × (1 − 2h/R) valid only when h ≪ R

Critical Warning

The approximate formula FAILS for large h. Example: At h = R/2:

• Exact: g' = $gR^{2}$/(3R/2)^{2} = 4g/9 ≈ 0.44g
• Approximate: g' ≈ g(1−1) = 0 — WRONG

Always use the exact formula in NEET numericals unless explicitly told h ≪ R.

Key Values

Finding Height for g = g/n

From exact formula: h = R(√n − 1)

Examples:

• g/4: h = R(√4 − 1) = R
• g/9: h = R(√9 − 1) = 2R
• g/25: h = R(√25 − 1) = 4R