The Weight of the Space Station The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 x 106 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 reduced at the height of the space station's orbit. Therefore, the weight of the space station will be smaller than that at the surface of the Earth. Categorize We model the space station as a particle in a gravitational field 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 = 9 = ]× 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: GME m/s? (RE + h)2 Use the particle in a field model again to find the space station's weight in orbit (in N): Fg = mg
The Weight of the Space Station The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 x 106 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 reduced at the height of the space station's orbit. Therefore, the weight of the space station will be smaller than that at the surface of the Earth. Categorize We model the space station as a particle in a gravitational field 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 = 9 = ]× 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: GME m/s? (RE + h)2 Use the particle in a field model again to find the space station's weight in orbit (in N): Fg = mg
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**The Weight of the Space Station**
The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 x 10^6 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 **reduced** at the height of the space station's orbit. Therefore, the weight of the space station will be **smaller** than that at the surface of the Earth.
**Categorize**
We model the space station as a particle in a gravitational **field**.
**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:
\[ m = \frac{F_g}{g} = \]
Use the equation for the free-fall acceleration with h = 350 km to find the magnitude of the gravitational field (in m/s²) at the orbital location:
\[ g = \frac{G M_E}{(R_E + h)^2} = \]
Use the particle in a field model again to find the space station's weight in orbit (in N):
\[ F_g = mg = \]
**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% **decrease** in the magnitude of the gravitational field.
---
**EXERCISE**
A planet has a gravitational acceleration on its surface of 0.9 times Earth's gravitational acceleration on its surface. The planet's radius is four times Earth’s radius.
What is the mass of the planet, in terms of Earth masses, \( M_E \)?
\[ M_E = \]
**Hint**: [Input box for hint]
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Transcribed Image Text:**The Weight of the Space Station**
The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 x 10^6 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 **reduced** at the height of the space station's orbit. Therefore, the weight of the space station will be **smaller** than that at the surface of the Earth.
**Categorize**
We model the space station as a particle in a gravitational **field**.
**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:
\[ m = \frac{F_g}{g} = \]
Use the equation for the free-fall acceleration with h = 350 km to find the magnitude of the gravitational field (in m/s²) at the orbital location:
\[ g = \frac{G M_E}{(R_E + h)^2} = \]
Use the particle in a field model again to find the space station's weight in orbit (in N):
\[ F_g = mg = \]
**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% **decrease** in the magnitude of the gravitational field.
---
**EXERCISE**
A planet has a gravitational acceleration on its surface of 0.9 times Earth's gravitational acceleration on its surface. The planet's radius is four times Earth’s radius.
What is the mass of the planet, in terms of Earth masses, \( M_E \)?
\[ M_E = \]
**Hint**: [Input box for hint]
**Need Help?** [Read it]
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