In the spacecraft, the instruments noted a 2-fold decrease in the acceleration of gravity.

| May 7, 2021 | education

In the spacecraft, the instruments noted a 2-fold decrease in the acceleration of gravity. To what height from the surface of the Earth did the spaceship rise?

To find the height of the specified spacecraft above the Earth’s surface, we use the equality: g / 2 = gk and G * Ms / 2Rs2 = G * Ms / (h + Rs) 2, whence we express: 2Rs ^ 2 = (h + Rs) ^ 2 = h ^ 2 + 2h * Rz + Rz ^ 2 and h ^ 2 + 2h * Rz – Rz ^ 2 = 0.

Constants: Rz – the average radius of the Earth (Rz = 6371 km).

Let’s make a calculation: h ^ 2 + 2h * 6371 – 63712 = 0.

h2 + 12742h – 40589641 = 0.

D = 127422 – 4 * 1 * (-40589641) = 324717128.

Height above the Earth: h1 = (-12742 + √ (324717128)) / 2 = 2639 km (correct); h2 = (-12742 – √ (811792820)) / 2 = -153817 km (wrong).

Answer: Above the surface of the Earth, the indicated ship ascended 2639 km.



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