The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 x 10° N, measured at the Earth's surface, will have been lifted off the surface by various spacecraft during the construction process. What is the weight of the space station when in orbit? SOLUTION Conceptualize The mass of the space station is fixed; it is independent of its location. Based on the discussion in this section, we realize that the value of g will be --Select- v at the height of the space station's orbit. Therefore, the weight of the space station will be -Select V than that at the surface of the Earth. Categorize We model the space station as a particle in a gravitational --Select-- V Analyze From the particle in a field model, find the mass of the space station (in kg) from its weight at the surface of the Earth: kg Use the equation for the free-fall acceleration vwith h = 350 km to find the magnitude of the gravitational field (in m/s?) at the orbital location: GM- m/s2 (R + h)? Use the particle in a field model again to find the space station's weight in orbit (in N): F- mg = Finalize Notice that the weight of the Space Station is less when it is in orbit, as we expected. It has about 10% less weight than it has when on the Earth's surface, representing a 10% --Select-- V in the magnitude of the gravitational field.
The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 x 10° N, measured at the Earth's surface, will have been lifted off the surface by various spacecraft during the construction process. What is the weight of the space station when in orbit? SOLUTION Conceptualize The mass of the space station is fixed; it is independent of its location. Based on the discussion in this section, we realize that the value of g will be --Select- v at the height of the space station's orbit. Therefore, the weight of the space station will be -Select V than that at the surface of the Earth. Categorize We model the space station as a particle in a gravitational --Select-- V Analyze From the particle in a field model, find the mass of the space station (in kg) from its weight at the surface of the Earth: kg Use the equation for the free-fall acceleration vwith h = 350 km to find the magnitude of the gravitational field (in m/s?) at the orbital location: GM- m/s2 (R + h)? Use the particle in a field model again to find the space station's weight in orbit (in N): F- mg = Finalize Notice that the weight of the Space Station is less when it is in orbit, as we expected. It has about 10% less weight than it has when on the Earth's surface, representing a 10% --Select-- V in the magnitude of the gravitational field.
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Transcribed Image Text:The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 x 10° N, measured at the Earth's surface, will have been lifted off the surface by various spacecraft during the
construction process. What
the weight of the space station when in orbit?
SOLUTION
Conceptualize The mass of the space station is fixed; it is independent of its location. Based on the discussion in this section, we realize that the value of g will be ---Select-- v at the height of the space station's orbit. Therefore, the weight of the space
station will be -Select-- v than that at the surface of the Earth.
Categorize We model the space station as a particle in a gravitational -Select--- V
Analyze From the particle in a field model, find the mass of the space station (in kg) from its weight at the surface of the Earth:
m =
kg
Use the equation for the free-fall acceleration with h = 350 km to find the magnitude of the gravitational field (in m/s) at the orbital location:
GM
(R. + h)?
m/s?
Use the particle in a field model again to find the space station's weight in orbit (in N):
F.- mg =
Finalize Notice that the weight of the Space Station is less when it is in orbit, as we expected. It has about 10% less weight than it has when on the Earth's surface, representing a 10% ---Select--v in the magnitude of the gravitational field.
EXERCISE
A planet has a gravitational acceleration on its surface of 1.9 times Earth's gravitational acceleration on its surface. The planet's radius is three times Earth's radius.
What is the mass of the planet, in terms of Earth masses, M_?
Hint
ME
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