suppose you observe a small star orbiting a much larger star. you observe that the small star is orbiting at a distance of 20 au (in terms of the semi-major axis of its orbit), and with an orbital period of 2 years. how massive is the large star? (hint: for this problem you can assume that the small star has a much smaller mass than the large star.)

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21-10-2022
Physics

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suppose you observe a small star orbiting a much larger star. you observe that the small star is orbiting at a distance of 20 au (in terms of the semi-major axis of its orbit), and with an orbital period of 2 years. how massive is the large star? (hint: for this problem you can assume that the small star has a much smaller mass than the large star.)

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aditmarkas98 aditmarkas98 · Answer 1 · 2022-10-25T08:57:03-04:00

The mass of the large star based on orbital period is 6912 x 10³⁰ kg.

We need to know about the orbital period to solve this problem. The orbital period depends on the semi-major axis, gravitational constant, and the mass of the massive object. It can be written as

T² = 4π².a³ / GM

where T is the orbital period, a is the semi-major axis, G is the gravitational constant and M is the mass.

From the question above, the given parameters are

a = 24 au = 24 . ³√(G.Msun yr²/ 4π²)

T = 2 years

Msun = 2 x 10³⁰ kg

By substituting the given parameters, we get

T² = 4π².a³ / GM

2² = 4π². (24 . ³√(G.Msun yr²/ 4π²))³ / GM

4 = 13824 Msun / M

M = 6912 x 10³⁰ kg

Find more on orbital period at: https://brainly.com/question/22247460

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