The Ratio of a Radius?

[GeeKay]

I came upon this statement about gravity lensing the other day. It reads: "The ratio of a planet's radius squared to its mass lets us calculate the distance a spacecraft must reach to take advantage of gravity lensing." It's the first part of this statement that I can't understand - "The ratio of a planet's radius" especially. While I know the meaning of each individual word, I simply cannot string them together in any meaningful sense. Neither can Google apparently. Any suggestions?

[ajb]

Is it not just the ratio [math]R^2 / M[/math]?

[Strange]

It's the first part of this statement that I can't understand - "The ratio of a planet's radius" especially. While I know the meaning of each individual word, I simply cannot string them together in any meaningful sense. Neither can Google apparently. Any suggestions?

 

You are parsing it wrong. It is:

"The ratio of [a planet's radius squared] to [its mass] ..."

 

Or what ajb said

 

(Not "The [ratio of a planet's radius] squared to ..." which seems to be the interpretation your brain has got stuck on)

[GeeKay]

Thanks for unsticking my brain - and to ajb for supplying the correct formula.

Just one other point - well, two actually: I assume that kilometers and kilos respectively should be used as a metric when applying the above formula to a given celestial body. The second point is rather more complicated: how does one use the formula's solution as a means of calculating a celestial's body's focal sphere? As examples, a minimum of 550 AU is cited for the Sun, 15,300 AU for the Earth, and a focal sphere of just 10 million km for Sirius B, but I don't know how these figures are derived. (I'm afraid I only have an antique GCSE in Maths to assist me here).

 

Many thanks.

 

http://www.centauri-dreams.org/?p=35498

Correction: I meant 'focal distance' not 'focal sphere.'