What is the orbital speed of the planet ? (G = 6.673 * 10 ^ - 11 * N * m ^ 2 / k * g ^ 2)

Question

whats the answer? help

Answer 1

For orbit of Earth around the Sun, establish:

Gravitational Constant G-------------------------------6.6725985E-11 N•m²/kg²

Solar Mass M_sun------------------------------------------1.991E30 kg

Earth Mass M_earth----------------------------------------5.98E24 kg

Earth's Solar Orbital Radius R_earth-------------------1.496E11 m

Earth's Period For 1 Solar Orbit T_earth---------------3.156E7 s

Orbital Speed Of The Planet (V_earth)-----------------To Be Determined

Earth's orbit around the Sun is extremely close to a circle, but note that the 

Sun is not at the dead center of this orbital path.

From the inverse-square law for circular orbits, equate the gravitational force by the Sun on Earth to the centripetal force required to maintain Earth's "circular" path around the star:

GM_sunM_earth/R_earth² = M_earthV_earth²/R_earth

Then V_earth is isolated as (GM_sun/R_earth)^0.5 which goes to 29800.07314 m/s.

Compare this last value to 2πR_earth/T_earth or 2π(1.496E11)/3.156E7 which gives 29783.41324 m/s.