Exploring Planet Nine: Orbits, Mass, and Kepler's Law

Astronomers speculate about Planet Nine, a massive body in the distant Solar System. Calculations are made about its orbit period, potential interactions with a black hole, and changes in period if it were more massive than the Sun. Utilizing Newton's version of Kepler's Law, astronomers delve into the dynamics of this hypothetical celestial body.

• Astronomy
• Planet Nine
• Solar System
• Orbits
• Keplers Law

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Uploaded on Sep 15, 2024 | 0 Views

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1. Some helpful numbers and formulae

2. Group 1 Pluto and its moon, Charon, taken by New Horizons in 2015 There is some evidence from distant Solar System objects of a large massive body very far from the Sun, often referred to as Planet Nine. Astronomers predict that, if this body were to exist, Planet Nine would be on a moderately elliptical orbit; additionally, it would be 4 times more massive than the Earth. Astronomers also predict a semi-major axis of 600 AU and a semi-minor axis of 500 AU. (a) What would the period of Planet Nine s orbit be? (b) Let s imagine replacing the Sun with a black hole of the same mass as the sun. How does this change the orbit of Planet Nine? (c) Now imagine that Planet Nine were 4 times more massive than the Sun. Using Newton s version of Kepler s Law, calculate the new period of Planet Nine assuming the semi-major and semi-minor axes.

3. Group 2 Pluto and its moon, Charon, taken by New Horizons in 2015 There is some evidence from distant Solar System objects of a large massive body very far from the Sun, often referred to as Planet Nine. Astronomers predict that, if this body were to exist, Planet Nine would be on a moderately elliptical orbit; additionally, it would be 4 times more massive than the Earth. Astronomers also predict a semi-major axis of 600 AU and a semi-minor axis of 500 AU. (a) What would the period of Planet Nine s orbit be? (b) Let s imagine replacing the Sun with a black hole of the same mass as the sun. How does this change the orbit of Planet Nine? (c) Now imagine that Planet Nine were 4 times more massive than the Sun. Using Newton s version of Kepler s Law, calculate the new period of Planet Nine assuming the semi-major and semi-minor axes.

4. Group 3 Pluto and its moon, Charon, taken by New Horizons in 2015 There is some evidence from distant Solar System objects of a large massive body very far from the Sun, often referred to as Planet Nine. Astronomers predict that, if this body were to exist, Planet Nine would be on a moderately elliptical orbit; additionally, it would be 4 times more massive than the Earth. Astronomers also predict a semi-major axis of 600 AU and a semi-minor axis of 500 AU. (a) What would the period of Planet Nine s orbit be? (b) Let s imagine replacing the Sun with a black hole of the same mass as the sun. How does this change the orbit of Planet Nine? (c) Now imagine that Planet Nine were 4 times more massive than the Sun. Using Newton s version of Kepler s Law, calculate the new period of Planet Nine assuming the semi-major and semi-minor axes.

5. Group 4 Pluto and its moon, Charon, taken by New Horizons in 2015 There is some evidence from distant Solar System objects of a large massive body very far from the Sun, often referred to as Planet Nine. Astronomers predict that, if this body were to exist, Planet Nine would be on a moderately elliptical orbit; additionally, it would be 4 times more massive than the Earth. Astronomers also predict a semi-major axis of 600 AU and a semi-minor axis of 500 AU. (a) What would the period of Planet Nine s orbit be? (b) Let s imagine replacing the Sun with a black hole of the same mass as the sun. How does this change the orbit of Planet Nine? (c) Now imagine that Planet Nine were 4 times more massive than the Sun. Using Newton s version of Kepler s Law, calculate the new period of Planet Nine assuming the semi-major and semi-minor axes.

6. Group 5 Pluto and its moon, Charon, taken by New Horizons in 2015 There is some evidence from distant Solar System objects of a large massive body very far from the Sun, often referred to as Planet Nine. Astronomers predict that, if this body were to exist, Planet Nine would be on a moderately elliptical orbit; additionally, it would be 4 times more massive than the Earth. Astronomers also predict a semi-major axis of 600 AU and a semi-minor axis of 500 AU. (a) What would the period of Planet Nine s orbit be? (b) Let s imagine replacing the Sun with a black hole of the same mass as the sun. How does this change the orbit of Planet Nine? (c) Now imagine that Planet Nine were 4 times more massive than the Sun. Using Newton s version of Kepler s Law, calculate the new period of Planet Nine assuming the semi-major and semi-minor axes.

7. Group 6 Pluto and its moon, Charon, taken by New Horizons in 2015 There is some evidence from distant Solar System objects of a large massive body very far from the Sun, often referred to as Planet Nine. Astronomers predict that, if this body were to exist, Planet Nine would be on a moderately elliptical orbit; additionally, it would be 4 times more massive than the Earth. Astronomers also predict a semi-major axis of 600 AU and a semi-minor axis of 500 AU. (a) What would the period of Planet Nine s orbit be? (b) Let s imagine replacing the Sun with a black hole of the same mass as the sun. How does this change the orbit of Planet Nine? (c) Now imagine that Planet Nine were 4 times more massive than the Sun. Using Newton s version of Kepler s Law, calculate the new period of Planet Nine assuming the semi-major and semi-minor axes.