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The specific angular momentum of a spacecraft in circular Earth orbit is 48,000 km2 /s. Determine the period of the orbit.

User Slindenau
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2 Answers

3 votes

Final answer:

The period of a spacecraft's orbit, given its specific angular momentum, can be calculated using the spacecraft's orbital velocity and the circumference of the orbit. However, the highly unrealistic period of about 50 billion years indicates a mistake in the provided calculation.

Step-by-step explanation:

The question involves calculating the orbital period of a spacecraft given its specific angular momentum. The specific angular momentum provided is 48,000 km2/s. To find the period of a circular orbit, we can use the equation T = 2πr/Vorbit, where T is the orbital period, r is the radius of the orbit, and Vorbit is the orbital velocity. Given that the orbital velocity is 47 km/s, we can solve for T.

However, the period provided seems to be incorrect as it indicates about 50 billion years, which is unrealistic for an Earth-orbiting spacecraft. The correct calculation would be to find the circumference of the orbit using the radius and divide it by the given orbital velocity to determine the period.

User Danpe
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5.5k points
1 vote

Answer:

T = 5325 s

Step-by-step explanation:

Given:

- Specific angular momentum h = 48,000 km^2 /s

- Radius of earth r_e = 6.3781 *10^3 km

Find:

The period of orbit

The relationship between Specific angular momentum h and period of orbit is as follows:

h = 2*pi*r_e^2 / T

T = 2*pi*r_e^2 / h

Hence, Plug the values

T = 2*pi*(6.3781 *10^3)^2 / 48,000

T = 5325 s = 1.48 h

User Despatcher
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5.0k points