# In desperate need of some one who can help me.

1. Jun 25, 2011

### vibram82

My husband and I frequestly have arguements about physics when we are both intoxicated. Needless to say neither of us really have anything but a basic, basic, basic, understanding of physics much less astro-physics and the nature of the way things work.

That said, may I introduce my husband who has a question for any of those who choose to answer him/school him.

"How can we gauge the mass of a star when we we cannot get close enough to the star with out any matrials availble to man on earth obliterated by the star that is being studied."
-reinterpreted quote from wife, from husband.

Please for love of anything that is, please describe all and any technological advances that we have made over the past 400 years, up to any mathmatical equasions that will prove your point.

This has gone well beyond the scope of simple drunken physics arguements, and I seriously need everyones help to open his mind to the abilities of man and astrophysics.

2. Jun 25, 2011

### Janus

Staff Emeritus
The primary way of determining the mass of a star is when it is a member of a binary pair. When one star orbits another we can measure their distance apart and how fast they orbit. The period of the orbit is determined by the masses of the stars and their distance apart by the following equation:

$$P= 2 \pi \sqrt{\frac{D^3}{G(M_1+M_2}}$$

G is the universal gravitational constant.
D the distance between the stars
M1 and M2 the masses of the Star.

We know G and can measure P and D, which allows us to find M1+M2.
The star will orbit their common center of gravity. The relative distance of the stars from this point will give us the relative masses of the stars and thus the mass of each star.

Now, binary stars are quite common so we have a pretty good sampling of different types of stars.

By looking at the light from each star and looking at its spectrum ( the light from it broken up into its component colors), we can determine the Stars' "spectral class" and its surface temp. This can lead us to the stars luminosity or the measure of its brightness.

By comparing the luminosity and mass from stars who's mass we found by the binary method, we discovered the Mass/luminosity law; The brighter the star, the more massive it is. By applying this law to stars not part of binary pairs, but who's luminosity and spectrum we can measure, we can estimate the mass of these stars too.

3. Jun 25, 2011

### marcus

It is very beautiful that a married couple should frequently get drunk and argue about physics. It shows originality and a congenial sense of humor. I love it. So much better than arguing about money, or the in-laws, or extra-marital affairs, or whatever. I hope you realize how blessed you are.

Janus answered this totally, but in a kind of technical way.

The fact is, in astronomy we tell the masses of things by how fast stuff goes around them, at some given distance from center.

And then there are other ways of estimating mass that are CALIBRATED using that basic one. That takes care of cases where we can't observe anything going around the star.
Two normal routine stars with similar chemical make-up, if they have the same mass will have the same temperature. More mass normally makes more internal pressure and faster burning and hotter surface. So if we gauge the mass of one star by seeing how fast stuff orbits it, and then we find another star with similar spectral lines in its light and glowing with the same temperature, then we can infer it has the same mass.

As Janus' forumula shows, both masses enter into determining the orbit period but in some cases the mass of the satellite is small relative to the main body and can be neglected and in other cases you just have to go through more complicated steps of inference and do more comparisons. But let's assume that one of the bodies is small, like a small satellite, and not worry about that.

Last edited: Jun 25, 2011
4. Jun 25, 2011

### marcus

I looked up "geosynchronous" in Wikipedia and it said that if the orbital radius is 26,200 miles a satellite will take one day to orbit the earth.

That is not the ALTITUDE above sealevel. It is the radius of the orbit from the earth center. The altitude is more like 22,000 miles.

Anyway, that one-day orbit radius can be our handle on the mass of the earth.

If you saw another planet, with a satellite at the same (26,200 mile) distance taking FOUR days to go around it, then how massive is that planet?

Answer: half the earth's mass.

Just look at Janus' formula. The period goes as one over the square root of the mass.

If you see another planet with a satellite at 26,200 miles taking ONE QUARTER of a day, just 6 hours, to go around, then how massive is that planet?

Answer: twice the earth's mass.
==========================

And suppose the distance is different. Suppose you see a planet with a satellite at 4 times the distance from center----4x26,200 = 104,800 miles---that takes 8 days to go around. How massive is that planet?

Answer: the same mass as the earth***.
==========================

Suppose the satellite orbits at 104,800 miles and takes TWO days to go around. How massive is the planet?

Answer: twice the mass of the earth.

So from there, the next stop is to tell the mass of the sun, in earth mass units.
===========================

***Kepler on May 15 of the year 1618: the cube of the distance divided by the square of the period is proportional to the mass.

So if you muitiply the distance by 4 and the period goes up by a factor of 8, then the mass doesn't change.
43 = 82 = 64
and 64/64 = 1 therefore no change.

Yay Kepler!

5. Jun 25, 2011

### marcus

I hope you are not just kidding me, and that you and your husband really do get drunk and argue about physics.

6. Jun 27, 2011

### vibram82

My sincere thanks to both of you.

And I am am not kidding. We were debating for a half an hour before I whipped out my "Atlas of the Universe" in hopes of showing him that mass for ojects beyond our solar system can be measured, but he wasn't having any of it. So...on to the internet I went.

Again thank you both!

7. Jun 27, 2011

### vibram82

While we are at it, another topic that was raised the other night was whether the sun will super nova, or become a white dwarf.

8. Jun 27, 2011

### Janus

Staff Emeritus
White dwarf. A star has to be much larger than our sun to be able to produce a supernova.