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kumpel [21]
3 years ago
9

Imagine another solar system, with a star of the same mass as the Sun. Suppose a planet with a mass twice that of Earth (2 Earth

) orbits at a distance of 1 AU from the star. What is the orbital period of this planet?
Physics
1 answer:
sashaice [31]3 years ago
4 0

Answer:

Time period, T = 403.78 years

Explanation:

It is given that,

Orbital distance, a=1\ AU=1.496\times 10^{11}\ m

Mass of the Earth, m_e=5.972\times 10^{24}\ kg

Mass of the planet, m_p=2m_e=11.944\times 10^{24}\ kg

Let T is the orbital period of this planet. The Kepler's third law of motion gives the relation between the orbital period and the orbital distance.

T^2=\dfrac{4\pi^2}{Gm_p}a^3

T^2=\dfrac{4\pi^2}{6.67\times 10^{-11}\times 11.944\times 10^{24}}\times (1.496\times 10^{11})^3

T=1.28\times 10^{10}\ s

or

T = 403.78 years

So, the orbital period of this planet is 404 years. Hence, this is the required solution.

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