The orbital period of the spacecraft is about 5.9 × 10³ s ≈ 99 minutes
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Further explanation
Let's recall Centripetal Force formula as follows:
[tex]\boxed{F = m \frac{v^2}{R}}[/tex]
where:
F = Centripetal Force ( Newton )
m = mass of object ( kg )
v = speed of object ( m/s )
R = radius ( m )
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Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:
[tex]\boxed {F = G \frac{m_1 ~ m_2}{R^2}}[/tex]
where:
F = Gravitational Force ( Newton )
G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )
m = Object's Mass ( kg )
R = Distance Between Objects ( m )
Let us now tackle the problem !
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Given:
free-fall acceleration = g = 3.8 m/s²
radius of Mars = R = 3.37 × 10⁶ m
Asked:
orbital period = T = ?
Solution:
[tex]\Sigma F = ma[/tex]
[tex]G \frac{ M m} { R^2 } = m \omega^2 R[/tex]
[tex]G \frac{ M } { R^2 } = \omega^2 R[/tex]
[tex]g = \omega^2 R[/tex]
[tex]\omega^2 = g \div R[/tex]
[tex]\omega = \sqrt { g \div R }[/tex]
[tex]2 \pi \div T = \sqrt { g \div R }[/tex]
[tex]T = 2 \pi \div \sqrt { g \div R [/tex]
[tex]T = 2 \pi \sqrt{ R \div g}[/tex]
[tex]T = 2 \pi \sqrt{ 3.37 \times 10^6 \div 3.8 }[/tex]
[tex]\boxed{T \approx 5.9 \times 10^3 \texttt{ s}}[/tex]
[tex]\boxed{T \approx 99 \texttt{ minutes}}[/tex]
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Learn more
- Impacts of Gravity : https://brainly.com/question/5330244
- Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
- The Acceleration Due To Gravity : https://brainly.com/question/4189441
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Answer details
Grade: High School
Subject: Physics
Chapter: Gravitational Fields
