perplexus.info :: Science : Distant Solar System

Distant Solar System (Posted on 2003-09-18)

A solar system with a star like your own sun and a planet like Jupiter has been discovered 90 light years from us. If the star is just as bright as our sun, how does it compare in brightness to the other stars in our night sky?

Background information: Light from the sun takes 8 minutes to reach the earth. The magnitude system for stars and other astronomical objects in our sky is designed so that a difference of 5 magnitudes represents a factor of 100 in brightness, with the larger numbered magnitudes being the dimmest. The dimmest stars seen with the unaided eye in a dark sky are about magnitude 6; the brightest stars (other than the sun) about 0. The planet Venus at times is magnitude -4, the full moon -14 and the sun -27.

Submitted by Charlie

Rating: 2.6000 (5 votes)

Solution: (Hide)

There are 1440 x 365.25 = 525,960 minutes in a year, so the star in question is 90 x 525,960 / 8 = 5,917,050 times as far away as the sun. As the brightness of light obeys an inverse square law, its brightness is 1/35011480702500 that of the sun as seen from earth (recognizing of course that the precision implied is way too high, but we'll carry it through until the end). That a factor of 100 in brightness implies a difference of magnitude of 5 means that you can take the common logarithm of the ratio of brightnesses and multiply by 2.5 to get the magnitude difference (as log(100) = 2, you need the factor 2.5 to stretch it to 5).
log(35011480702500) is approximately 13.54.
Multiplied by 2.5, it is 33.9. Add that to the sun's -27 to get 6.9. The star would not quite be visible to the unaided eye.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	CodyDunning	2024-04-29 08:39:52
Distant Solar System	CodyDunning	2024-04-17 06:28:18
Distant Solar System	CodyDunning	2024-02-06 07:51:00
re: Correct me if I'm wrong	JamesYawn	2023-12-17 12:02:57
re: solution?!?	JamesYawn	2022-12-27 09:14:02
No Subject	Dej Mar	2012-05-27 16:21:05
Some thoughts	K Sengupta	2007-05-04 12:51:14
agree	ofnoconcern	2004-11-28 15:43:20
duh!	no	2004-05-19 16:02:28
re(2): solution?!?	SilverKnight	2003-09-18 15:28:07
re: solution?!?	Charlie	2003-09-18 15:26:44
re(2): Correct me if I'm wrong	Brian Wainscott	2003-09-18 15:20:43
re: Correct me if I'm wrong	SilverKnight	2003-09-18 15:19:04
Correct me if I'm wrong	Brian Wainscott	2003-09-18 15:14:02
solution?!?	SilverKnight	2003-09-18 15:13:48

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