The international space station (ISS) orbits 400 km above Earth's surface at 7.66 km/s (17,100 mph). Suppose the ISS is moved to 400 km above Mars.1. To maintain its orbit above Mars, will the ISS have to move faster or slower that its orbital speed around Earth? Justify your answer.2. Will astronauts on the ISS feel lighter, heavier, or no change at all while in orbit around Mars. Explain your answer.

Orbital Velocity Orbital velocity is the velocity that is given to an artificial satellite a few hundred kilometers above a planet's surface. It is given by vo. Let m be the mass of the satellite and M be the mass of the planet around which it is rotating. Let R be the radius of the planet and h be the height above the surface in which the satellite is moving. To remain in the orbit, the centripetal force must balance the gravitational attraction between the planet and the satellite. This condition gives mvo2r=GMmr2⇒vo=GMR+h1) The mass of Mars M=6.39×1023 kg The radius of Mars R=3389.5 km=3389.5×103 m The height above the surface where the satellite is places h=400 km=400×103 m The universal gravitational constant G=6.67428×10-11 Nm2/kg2 Therefore the orbital velocity of ISS must be vo=GMR+h=6.67428×10-11×6.39×10233389.5×103+400×103=3354.76 m/s=3.354 km/s This velocity is less than that of what the ISS has to maintain at the same orbit around the Earth. 2) There will be no change in what weight the astronomers will feel than it was at an orbital velocity around the earth. This happens because to maintain the orbit, the ISS has to change its orbital velocity. The centripetal force acting on the ISS due to that velocity must be exactly equal to the gravitational force of attraction between the ISS and the planet. This causes both the force to cancel out and the astronauts in the ISS will always feel weightless whether it is on Earth or on Mars. Answer: 1) The orbital velocity of ISS around Mars must be less than that of the Earth. 2) There will be no change in the weight of the astronauts. The astronauts will always feel weightless.

Answered: 1. To maintain its orbit above Mars,…

1. To maintain its orbit above Mars, will the ISS have to move faster or slower that its orbital speed around Earth? Justify your answer. 2. Will astronauts on the ISS feel lighter, heavier, or no change at all while in orbit around Mars. Explain your answer.