Class notes
ASTRO 101: dark stars
- Course
- ASTRO101 (ASTRA101)
- Institution
- University Of Alberta (UofA)
Understanding dark stars
[Show more]
Seller
Follow
Content preview
If I asked you who rst proposed the idea of a Blackhole, who would be your rst guess? PerhapsAlbert Einstein, Stephen Hawking or Karl Schwarzschild. While these scientists have had a huge
impact on black hole astrophysics, the idea of a strong gravitational eld altering light was rst
described by an often overlooked clergyman named John Michell. John Mitchell was the rst to
describe an object whose escape velocity exceeded the speed of light, which he called "Dark
Stars." The year was 1783, falling very close to the midpoint between Newton's theory of universal
gravitation and Einstein's theory of special relativity. John Michell, a retired professor of geology at
Cambridge was working as director of Thornhill in England, and he used his spare time to fuel his
scienti c curiosity, in particular, working with theories of light and gravity. John supposed that light
consisted of a particle, which was a topic of hot debate at the time, and that gravity acted upon the
particles of light in the same way that gravity acts on all objects. At the time, there was no
experimental evidence to think otherwise and Newton's gravity was considered a universal law.
i aid anatomies
Rector Michell reasoned that objects within a gravity well require a certain amount of speed to
reach in nity, the speed which we now call escape velocity. And that for particularly small and
dense objects, the escape velocity might exceed the speed of light. The French mathematician,
Pierre-Simon Laplace, came up with the same idea in 1796, which he referred to as an "invisible
body." Although Laplace rst wrote about invisible bodies in 1796, more than ten years after
Michell, this idea was probably developed independently since there was very little scienti c
communication between France and England in that period.
Let's have a look at the escape velocity equation again, but this time let's do something silly.
Instead of solving for the velocity, Ve, let's solve where the radius of an object with mass m whose
escape velocity is equal to the speed of light, just as rector Michell did.
2K
c FIRM i 2hpm r
We'll denote the speed of light as the letter c and use it to replace Ve. In order to solve for the radius
r, we need to rst square both sides of the equation so that C becomes C squared and the square
root sign on the right hand side goes away, and then we can multiply both sides of the equation by
a factor of r divided by C squared, leaving us with the solution in terms of the radius. A body of
mass M has an escape velocity equal to the speed of light when its radius r is equal to 2GM divided
by C squared. So what this means is that an object of mass M, we can calculate how small it would
need to be in order to have an escape velocity equal to the speed of light. Let's try Earth's mass for
fun. Inserting M equal to 5.972 times 10 to the 24 kilograms into the equation, yields a radius of a
puny 8.87 millimeters, like a tiny ball less than one centimetre on a side. So if a ball weighed the
same as the entire Earth, it would have an escape velocity equal to the speed of light at its surface.
fi fi
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller titaniayuki1. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for CA$4.43. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
51662 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 15 years now