AST 111 homework 8

The Earth has a diameter close to 1/100 of the Sun's diameter. When Earth goes in front of the Sun (as seen by distant aliens), what fraction of the Sun's light does Earth block?

0.01%

Jupiter has a diameter almost exactly 1/10 of the Sun's diameter. When Jupiter goes in front of the Sun (as seen by distant aliens), what fraction of the Sun's light does Jupiter block?

1%

What fraction of the solar radius is this?

1.12

What's the farthest away a planet can orbit from a star like the Sun and have a period of 2 years? Use Kepler's law!

1.56 AU

The Kepler telescope stared at stars in the constellation Cygnus just over 4 years. To officially detect a planet, a planet would have to transit its star 3 times. (1 times to notice there is a planet; 2 times to see if the same dip repeats itself after a time T; 3 times to make sure it repeats itself again after another wait of time T.) What's the maximum orbital period T a planet could have to be officially detected by Kepler? (Think carefully!)

2 years

As Jupiter orbits the Sun every 12 years, it pulls the Sun from one end of its little orbit to the other, about 1,000,000 km, in about 6 years. What's its average speed in m/s?

5 m/s

How many exoplanets are in the TRAPPIST-1 system?

7

The Sun has about 1000 times the mass of Jupiter. So the distance between the Sun's center and the center of mass between the Sun and Jupiter has to be about 1/1000 the Sun-Jupiter distance of 5.2 AU. How many kilometers is that?

7.8 x 10^5 km

What's the closest exoplanet?

Proxima b

Which would be the easiest type of planet to detect around a star like the Sun, using the radial velocity method?

a Jupiter-mass planet in a 4-day orbit