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The maximum distance from the Earth to the Sun (at aphelion) is 1.521 1011 m, and...

The maximum distance from the Earth to the Sun (at aphelion) is 1.521 1011 m, and the distance of closest approach (at perihelion) is 1.471 1011 m. The Earth's orbital speed at perihelion is 3.027 104 m/s. Ignore the effect of the Moon and other planets. (a) Determine the Earth's orbital speed at aphelion. m/s (b) Determine the kinetic and potential energies of the Earth

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The maximum distance from the Earth to the Sun (at our aphelion) is 1.521 1011 m and the distance of closest approach (at perihelion) is 1.471 1011 m. Assume the Earth's orbital speed at perihelion is 3.027 104 m/s. (Ignore the effect of the Moon and other planets.)

(a) Determine the Earth's orbital speed at aphelion

(b) Determine the kinetic and potential energies of the Earth-Sun system at perihelion

(c) Determine the kinetic and potential energies at aphelion

(d) Is the total energy constant? (Yes or No)

a) From conservation of angular momentum we have rp*vp = ra*va

va = vp*rp/ra = 3.027x10^4m/s*(1.471x10^11/1.521x10^11) = 2.927x10^4m/s

b) At perihelion K = 1/2*m*v^2 = 1/2*5.98x10^24*(3.027x10^4)^2 = 2.74x10^33J

U = -GMm/r = - 6.67x10^-11*1.99x10^30*5.98x10^24/1.471x... = -5.40x10^33J

c) At aphelion K = 1/2*m*v^2 = 1/2*5.98x10^24*(2.927x10^4)^2 = 2.56x10^33J

U = -GMm/r = - 6.67x10^-11*1.99x10^30*5.98x10^24/1.521x... = -5.22x10^33J

d) Yes

genius_generous answered 3 months ago
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