Escape Velocities on Exoplanets

1. Fill out Mass and Radius columns below using above information.

Escape Velocities on Exoplanets

Are we alone? Is the solar system unique in the Universe? No. It is just difficult to find planets because they are so tiny and dark compared to stars. Maybe direct observation is impossible even if the planet is larger than Jupiter because of the brightness of stars. However, there are some indirect methods to find them, and so far about 2,000 planetary systems have been found. In 1992 for the first time, two planets circling around Pulsar PSR 1257+12 were founded by radio astronomers using the pulsar timing method. In 1995, a planet orbiting around a main sequence star like the sun, 51 Pegasi, was discovered using radial velocity method. After that, many extra solar planets (exoplanets) were discovered using numerous indirect methods. For more further information, you may visit the following websites:

http://exoplanetarchive.ipac.caltech.edu/ http://planetquest.jpl.nasa.gov/ http://planetquest.jpl.nasa.gov/news/239#

For this activity, we are going to calculate escape velocities for several exoplanets and compare them with our major planets. Escape velocity, Ve, is defined to be the minimum velocity an object must have in order to escape the gravitational field of the planet, that is, escape the planet without ever falling back. It can be evaluated by

where M is the mass of the planet, G is the gravitational constant, g is acceleration of gravity on the planet’s surface, and R is the radius of the planet.

The selected exoplanets with some physical properties are as follows.

Kepler- 452b is located about 1,400 light years away from earth. Its size is 1.6 times of Earth’s radius and it has 5 times Earth’s mass.

51 Pegasi b is about 41 light years from Earth. Its mass is about half of that of Jupiter. Its size is about twice of that of Jupiter. Jupiter’s mass is 318 times Earth’s mass and Jupiter’s size is about 11 times Earth’s size.

Kepler-78b is located about 400 light-years from Earth. Its mass is double of Earth’s mass and its size is 1.2 times of Earth’s radius.

The distance from “Super-Earth” exoplanet, OGLE-2005-BLG-390 Lb, is about 22,000 light years. Its size is about half of that of Earth. It is five times heavier than that of Earth.

The distance between WASP-18b and Earth is about 325 light years. The mass of WASP-18b is 10 times of Jupiter’s mass, that is, about 3,180 times the mass of Earth. Its size is 11 times bigger than that of Earth’s radius.

Look at the provided table below. The first column is the name of planet, the second column is the mass, the third column is the radius, the fourth column is the escape velocity, Ve, and the fifth column is gravitational acceleration, g. In order to find the escape velocities for the given exoplanets, enter the appropriate values of their masses and radii in unit of Earth’s mass and Earth’s radius in the table below. Then, the escape velocity and gravitational acceleration will be automatically calculated. In the case of our major planets, insert data from Table 10.1 on p. 199 in the textbook. Then, you will get them, too. After completing the table, answer the questions.

Microsoft excel software is required to use the table below for automated calculation. However, if you do not have this, you can use your own calculator. It should be no problem to answer the questions.

gR R GMve 2 2

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Exoplanet name Mass [ME] Radius [RE] Ve[km/s] g [m/s/s] 51 Pegasi b Kepler -78b Kepler-452b WASP-18b

OGLE-2005-BLG-390 Lb

Our Planets Mercury Venus Earth Mars Jupiter Saturn Uranus

Neptune

2.Which planet (including both exoplanets and our major planets) is the most difficult to escape?

3.Which planet (including both exoplanets and our major planets) has the largest gravitational field, and which planet has the smallest gravitational field?

4.Which exoplanet is most like the earth? Justify your answer. Your response should be at least 50 words in length.

5.Which factor affects the escape speed? Mass and/or radius? Your response should be at least 50 words in length.

6. If one of the planets becomes a black hole, what would the escape speed be? Your response should be at least 50 words in length.

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Escape Velocities on Exoplanets

Are we alone? Is the solar system unique in the Universe? No. It is just difficult to find planets because they are so tiny and dark compared to stars. Maybe direct observation is impossible even if the planet is larger than Jupiter because of the brightness of stars. However, there are some indirect methods to find them, and so far about 2,000 planetary systems have been found. In 1992 for the first time, two planets circling around Pulsar PSR 1257+12 were founded by radio astronomers using the pulsar timing method. In 1995, a planet orbiting around a main sequence star like the sun, 51 Pegasi, was discovered using radial velocity method. After that, many extra solar planets (exoplanets) were discovered using numerous indirect methods. For more further information, you may visit the following websites:

http://exoplanetarchive.ipac.caltech.edu/ http://planetquest.jpl.nasa.gov/ http://planetquest.jpl.nasa.gov/news/239#

For this activity, we are going to calculate escape velocities for several exoplanets and compare them with our major planets. Escape velocity, Ve, is defined to be the minimum velocity an object must have in order to escape the gravitational field of the planet, that is, escape the planet without ever falling back. It can be evaluated by

where M is the mass of the planet, G is the gravitational constant, g is acceleration of gravity on the planet’s surface, and R is the radius of the planet.

The selected exoplanets with some physical properties are as follows.

Kepler- 452b is located about 1,400 light years away from earth. Its size is 1.6 times of Earth’s radius and it has 5 times Earth’s mass.

51 Pegasi b is about 41 light years from Earth. Its mass is about half of that of Jupiter. Its size is about twice of that of Jupiter. Jupiter’s mass is 318 times Earth’s mass and Jupiter’s size is about 11 times Earth’s size.

Kepler-78b is located about 400 light-years from Earth. Its mass is double of Earth’s mass and its size is 1.2 times of Earth’s radius.

The distance from “Super-Earth” exoplanet, OGLE-2005-BLG-390 Lb, is about 22,000 light years. Its size is about half of that of Earth. It is five times heavier than that of Earth.

The distance between WASP-18b and Earth is about 325 light years. The mass of WASP-18b is 10 times of Jupiter’s mass, that is, about 3,180 times the mass of Earth. Its size is 11 times bigger than that of Earth’s radius.

Look at the provided table below. The first column is the name of planet, the second column is the mass, the third column is the radius, the fourth column is the escape velocity, Ve, and the fifth column is gravitational acceleration, g. In order to find the escape velocities for the given exoplanets, enter the appropriate values of their masses and radii in unit of Earth’s mass and Earth’s radius in the table below. Then, the escape velocity and gravitational acceleration will be automatically calculated. In the case of our major planets, insert data from Table 10.1 on p. 199 in the textbook. Then, you will get them, too. After completing the table, answer the questions.

Microsoft excel software is required to use the table below for automated calculation. However, if you do not have this, you can use your own calculator. It should be no problem to answer the questions.

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2.Which planet (including both exoplanets and our major planets) is the most difficult to escape?

3.Which planet (including both exoplanets and our major planets) has the largest gravitational field, and which planet has the smallest gravitational field?

4.Which exoplanet is most like the earth? Justify your answer. Your response should be at least 50 words in length.

5.Which factor affects the escape speed? Mass and/or radius? Your response should be at least 50 words in length.

6. If one of the planets becomes a black hole, what would the escape speed be? Your response should be at least 50 words in length.

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