
(a)
The radius of the orbit of Mars Global Surveyor spacecraft given that, the orbital period of the Mars Global Surveyor spacecraft is
(a)

Answer to Problem 40Q
Solution:
Explanation of Solution
Given data:
The orbital periodic time for Mars Global Surveyor spacecraft is
Mass of Mars is
Formula used:
Write the expression for Newton’s form of Kepler’s third law,
Here,
Explanation:
The spacecraft’s orbital periodic time
Recall the expression for Newton’s form of Kepler’s third law,
Substitute
Here, M is the mass of Mars.
Substitute
Conclusion:
Hence, the radius of Mars Global Surveyor spacecraft is
(b)
The average altitude of Mars Global Surveyor spacecraft above the surface of Mars given that, it was in the orbit of Mars for
(b)

Answer to Problem 40Q
Solution:
Explanation of Solution
Given data:
The orbital periodic time for Mars Global Surveyor spacecraft is
Formula used:
Write the relation between the radius and the diameter of Mars,
Here,
Explanation:
Recall the expression for the radius of the orbit,
Substitute
From part (a), radius of Mars is 3770 km.
The radius of orbit of Mars Global Surveyor spacecraft above the surface is
Conclusion:
Hence, the average altitude of Mars Global Surveyor spacecraft is more than the radius of Mars by 373 km.
(c)
The reason for the possibility of observing the entire surface of the planet from the orbit of the Mars Global Surveyor spacecraft passing through the poles of Mars.
(c)

Answer to Problem 40Q
Solution:
The orbital plane of Mars Global Surveyor spacecraft remains fixed whereas, Mars rotates continuously on its orbit. This makes it possible for the spacecraft to observe the entire surface of Mars.
Explanation of Solution
Introduction:
Polar orbits are those orbits, in which when an object (usually satellites) orbits those objects (satellites) that are able to pass through both the poles of the object (usually planets) that is being orbited.
Explanation:
Satellites in polar orbits are able to observe the entire surface of the planet as the orbital plane in which the motion of the satellite is fixed, remains the same. Therefore, while Mars is rotating about its axis, spacecrafts at the polar orbit like Mars Global Surveyor are able to observe the entire surface of the planet, Mars in this case.
Conclusion:
The orbital plane of the Mars Global Surveyor spacecraft is fixed with respect to the orbital plane of Mars, so, it is possible for it to observe the entire surface of Mars.
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