Astro 210 Homework 7 Solutions - Astronomy 210 Spring 2011...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Astronomy 210 Spring 2011 Homework Set #7: Solutions 1. A Transiting Exoplanet . (a) [5 points] Since a 3 = GMP 2 / (4 2 ), we have a = parenleftbigg GM 4 2 parenrightbigg 1 / 3 P 2 / 3 (1) It is fine to just use this formula, being careful with units. A shortcut is to divide this result by the value for the earth a = parenleftbigg GM 4 2 parenrightbigg 1 / 3 P 2 / 3 (2) where of course P = 1 year and a = 1 AU. Dividing, we get a 1AU = parenleftbigg M M parenrightbigg 1 / 3 parenleftbigg P 1yr parenrightbigg 2 / 3 (3) and thus for M = 1 . 35 M and P = 4 . 89 day = 0 . 0134 yr, we get a = 0 . 062 AU, in good agreement with the professional value. (b) [5 points] We want the stars speed v about the center of mass. Since both the star and the planet move about the center of mass with period P and angular speed = 2 /P , the stars speed is v = r (4) where r s tar is the stars distance from the center of mass, which we need to find. We have r + r p = a (5) and m r = m p r p (6) Since we want r , we eliminate r p : m r = m p ( a r ) (7) ( m + m p ) r = m p a (8) r = m p m + m p a (9) and thus we have v = m p m + m p 2 a P = m p m + m p v (10) where v is the speed of the planet relative to the star ....
View Full Document

Page1 / 3

Astro 210 Homework 7 Solutions - Astronomy 210 Spring 2011...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online