Elizabeth asked in Science & MathematicsPhysics · 1 month ago

The International Space Station (ISS) orbits the Earth at an

altitude (distance above the surface of the Earth) of 408 km, conducting various experiments in a “weightless” environment.

a) The centripetal force is equal to the net inward force on an object.

Consider the other force(s) acting on the ISS and write an equation relating its

force(s). Air resistance is negligible.

b) Calculate the acceleration of the ISS.

c) Calculate the orbital period of the ISS. Answer in minutes.

d) Determine the speed that a rocket carrying supplies for the ISS would have to

achieve in order to enter orbit at the same altitude as the ISS. Assume air

resistance is negligible.

ty!!!

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Lv 7
1 month ago

a) The "other" force is gravity. Equating the gravitational force to the centripetal force we get

G*m*M / r² = mv²/r

where m is the mass of the ISS (which cancels)

and M is the mass of the Earth = 5.98e24 kg

and r is the orbit radius = (6.371e6 + 408e3) m = 6.779e6 m

and v is the orbit velocity

b) The acceleration is the weight divided by the mass:

a = GmM/r² / m = GM / r²

a = 6.674e−11N·m²/kg² * 5.98e24kg / (6.779e6m)²

a = 8.68 m/s²

c) a = v²/r = 8.68 m/s² / v² / 6.779e6m

v² = 5.89e7 m²/s²

v = 7.67e3 m/s

but also

v = 2πr / T

where T is the period

so

T = 2πr / v = 2π*6.779e6m / 7670m/s = 5.55e3 s

d) Horrible question. Rockets are powered. A velocity of 1 m/s would be sufficient if it was endured for long enough. The question wants to know the speed a PROJECTILE would require.

total mechanical energy = ½mv² - GmM/r

Ignoring the rotation of the Earth, the TME at launch would be

TME = 6.674e−11N·m²/kg² * m * 5.98e24kg / (6.371e6m)² + ½mV²

TME = m * [V²/2 - 6.26e7] J

for m in kg

At the ISS orbit,

TME' = m * [(7670m/s)²/2 - 6.674e−11N·m²/kg² * 5.98e24kg / 6.779e6m]

TME' = m * -2.946e7 J

Equate the two and solve for V. I get

V = 8141 m/s