Earthed - What is the gravitational force between the Earth and the Sun in pounds?

What is the gravitational force between the Earth and the Sun in pounds?

What is the gravitational force between the Earth and the Sun in pounds? If you want the ten points, show how you did the calculations or post a link to where you found the answer.

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The gravitational force acting on two massive bodies is given by the equation:

F = G M m / r^2

where F is the force of gravity, G is the gravitational constant, M is the mass of one body, m is the mass of the other body, and r is the distance between their centers of mass.

We can look up the values of G, M (mass of sun), m (mass of Earth). On the other hand, we have to approximate r, since the distance between the Earth and the sun is not exactly constant. We'll approximate this distance as 1 AU, meaning r is equal to 1 AU plus the equatorial radius of the Earth, plus the equatorial radius of the sun:

r = (1 AU)(149598000000 m / AU) + (6378100 m) + (6.955 x 10^8 m) = 1.503 x 10^11 m

G = 6.674 x 10^-11 m^3 / kg s^2

M = 1.9891 x 10^30 kg

m = 5.9736 x 10^24 kg

Finally, we plug in these values and calculate the magnitude of F:

F = G M m / r^2

F = (6.674 x 10^-11 m^3 / kg s^2)(1.9891 x 10^30 kg)(5.9736 x 10^24 kg) / (1.503 x 10^11 m)^2

F = 3.510 x 10^22 N

The problem statement asks for the force in units of pounds, so we convert:

F = (3.510 x 10^22 N)(0.224808943 lbs / N)

F = 7.892 x 10^21 lbs

My sources for the numbers used in the calculation are given below.
As I remember

Orbital velocity of Earth V

V = 30000 m/sec

Density of Earth ro

ro = 5000 kg/m^3

Radius of Earth r

r = 6000000 m

Distance from Earth to Sun R

R = 150000000000 m

So, force F

F = M * V^2 / R

Here M is mass of the Earth

M= ro * pi * r^3

pi=3 (if you wish it is 3.14)

F= ro * pi * r^3 * V^2 / R =

= 10^22 kg*m/sec^2

its about 5*10^21 pounds