Concept explainers
The oldest artificial satellite still in orbit is Vanguard I, launched March 3, 1958. It mass is 1.60 kg. Neglecting atmospheric drag, the satellite would still be in its initial orbit, with a minimum distance from the center of Earth of 7.02 Mm and a speed at this perigee point of 8.23 km/s. For this orbit, find (a) the total energy of the satellite–Earth system and (b) the magnitude of the
(a)
The total energy of the satellite earth system.
Answer to Problem 13.79CP
The total energy of the satellite earth system is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for total energy of the satellite earth system.
Here,
Substitute
Conclusion:
Therefore, the total energy of the satellite earth system is
(b)
The magnitude of angular momentum of the satellite.
Answer to Problem 13.79CP
The magnitude of angular momentum of the satellite is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for angular momentum.
Here,
Substitute
Conclusion:
Therefore, the magnitude of angular momentum of the satellite is
(c)
The satellite’s speed and it’s distanced from the centre of the earth at apogee.
Answer to Problem 13.79CP
The satellite’s speed is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for total energy at apogee.
Here,
Write the expression for angular momentum at apogee.
Rearrange the expression for distanced from the centre of the earth at apogee.
Substitute
Rearrange the above equation to get a quadratic equation of
Substitute
Find the smaller roots of the above equation.
Substitute
Conclusion:
Therefore, the satellite’s speed is
(d)
The semi major axis of its orbit.
Answer to Problem 13.79CP
The semi major axis of its orbit is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for length of major axis.
Substitute
Conclusion:
Therefore, the semi major axis of its orbit is
(e)
The period of the satellite.
Answer to Problem 13.79CP
The period of the satellite is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for time period.
Substitute
Conclusion:
Therefore, the period of the satellite is
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Chapter 13 Solutions
Physics for Scientists and Engineers, Volume 1
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