Answer:
The mass of the sun is [tex]m_s = 5.568 *10^{30} \ kg[/tex]
Explanation:
From the question we are told that
The mass of the planet is [tex]M = 7 *10^{24} \ kg[/tex]
The period of the planet is [tex]T = 1 \ Earth \ year = 365 * 24 * 3600 = 3.15 *10^{7} \ s[/tex]
The speed of the planet is [tex]v = 42000 \ m/s[/tex]
Generally the radius at which the planet orbits the sun is mathematically represented as
[tex]r = \frac{Gm_s }{v^2 }[/tex]
Where [tex]G[/tex] is the gravitational constant with value [tex]G = 6.67 *10^{-11} \ m^3 \cdot kg^{-1} \cdot s^{-2}[/tex]
and [tex]m_s[/tex] is the mass of the sun
Generally the period of planet is mathematically represented as
[tex]T = \frac{2 \pi r}{v}[/tex]
=> [tex]T = \frac{2 \pi}{v} * \frac{G * m_s}{v^2}[/tex]
=> [tex]m_s = \frac{T * v^3}{2* \pi * G}[/tex]
substituting values
[tex]m_s = \frac{ 3.15 *10^{7} * (42000)^3}{2* 3.142 * 6.67 *10^{-11}}[/tex]
[tex]m_s = 5.568 *10^{30} \ kg[/tex]
The mass of the sun will be "5.568 × 10³⁰ kg".
According to the question,
Planet's mass, M = 7 × 10²⁴ kg
Planet's period, T = 1 Earth year
= 365 × 24 × 3600
= 3.15 × 10⁷ s
Planet's speed, v = 4200 m/s
Gravitational constant, G = 6.67 × 10⁻¹¹ m³.kg⁻¹.s⁻²
We know the relation,
T = [tex]\frac{2 \pi r}{v}[/tex]
or,
= [tex]\frac{2 \pi}{v}\times \frac{G\times m_s}{v^2}[/tex]
hence,
The sun's mass be:
[tex]m_s[/tex] = [tex]\frac{T\times v^3}{2\times \pi\times G }[/tex]
By substituting the values,
= [tex]\frac{3.15\times 10^7\times (42000)^3}{2\times 3.142\times 6.67\times 10^{-11}}[/tex]
= 5.568 × 10³⁰ kg
Thus the response above is correct.
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