Question

Id the radius of earths orbit around the sun is r and time is t,the mass of sun is

Answer 1

Answer:M=(4π^2/G)*(R^3/t^2)

Step-by-step explanation:   π

Let mass of Sun be M and mass of earth be m

and radius of orbit is R

Since we are considering circular motion where earth is orbit at time t

therefore angular velocity omega ϖ=2π/t

we know that

ϖR=v

v=2πR/t

Newton says that gravitational force between earth(m) and sun(M) if

Fg=GMm/R^2

since earth is orbiting its faces centrifugal force Fc=mv^2/R

Fg=Fc

GMm/R^2=m*(4π^2*R^2)/R*t^2

GM/R^2=4π^2^R/t^2

M=4π^2*R^3/t^2*G

there fore

M=(4π^2/G)*(R^3/t^2)