What is the proportionality constant for the Sun's gravitational force?

[moonman239]

This book that I'm reading mentions something where the gravitational pull of the Sun is proportional to that planet's mass/its orbital radius. What is this proportionality constant?

 

[mgb_phys]

Not quite , for an object in orbit the centrifugal force throwing it outwards is equal to the gravitational force pulling it into the object in the centre.

 

[moonman239]

Oh, okay. So really, F=(4pi^2mr)/T2 should be used.

 

[Janus]

This book that I'm reading mentions something where the gravitational pull of the Sun is proportional to that planet's mass/its orbital radius. What is this proportionality constant?

The gravitational pull on any planet by the Sun is proportional to that planet's mass divided by the square of its orbital radius. The actual formula is

$$F_g = G\frac{M_{sun}M_{planet}}{r_{orbit}^2}$$

where G is the gravitational constant and is equal to 6.673e-11 when M is measured in Kg and r in meters.

 

[sardar]

The proportionality constant mentioned in your book is known as the gravitational constant, denoted by the symbol G. It is a fundamental physical constant that appears in the law of universal gravitation, which describes the gravitational force between two objects with mass. The value of G is approximately 6.674 x 10^-11 m^3 kg^-1 s^-2. This means that for any two objects with masses m1 and m2 separated by a distance r, the force of gravity between them can be calculated using the equation F = G (m1m2)/r^2. This relationship holds true for the gravitational force between the Sun and any planet in its orbit, as well as between any two objects in the universe.