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A satellite orbits at height $h$ from Earth's surface where $h \ll R$ ($R$ = Earth's radius). The minimum increase in speed for the satellite to escape Earth's gravitational field is:
For $h \ll R$, orbital radius $\approx R$:
Orbital speed: $v_o = \sqrt{gR}$
Escape speed from surface (approximately same radius): $v_e = \sqrt{2gR}$
Minimum increase: $\Delta v = v_e - v_o = \sqrt{2gR} - \sqrt{gR} = \sqrt{gR}(\sqrt{2}-1)$
Pakistan EPI Schedule (current):
| Age | Vaccines |
|---|---|
| Birth | BCG, OPV-0, Hepatitis B (birth dose) |
| 6 weeks | Pentavalent (DTP-HepB-Hib), OPV-1, PCV-1, Rotavirus-1, IPV-1 |
| 10 weeks | Pentavalent-2, OPV-2, PCV-2, Rotavirus-2 |
| 14 weeks | Pentavalent-3, OPV-3, PCV-3, IPV-2 |
| 9 months | Measles-1, Vitamin A (1st dose) |
| 15 months | Measles-2 (MMR) |
Pentavalent vaccine = 5-in-1 vaccine protecting against:
- Diphtheria
- Tetanus
- Pertussis (whooping cough)
- Hep B (Hepatitis B)
- Hib (Haemophilus influenzae type b)
Contraindications: Previous anaphylaxis to vaccine component, progressive neurological disorder (for pertussis component), severe febrile illness (defer, not contraindicate).
Cold chain: Pentavalent stored at \(2{-}8ยฐC\); never frozen (freeze-sensitive).
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