Physics help please?!?
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.
- NCSLv 72 months agoFavourite answer
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
v = 2πr / T
where T is the period
T = 2πr / v = 2π*6.779e6m / 7670m/s = 5.55e3 s
(about 1½ hours)
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
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