The planet jupiter revolves around the sun in a period of about 12 years (3.79 * 108 seconds). what is its mean distance from the center of the sun? the mass of the sun is 1.99 * 1030 kilograms.

Question

Physics

Cloe Tran

21 December, 22:38

The planet jupiter revolves around the sun in a period of about 12 years (3.79 * 108 seconds). what is its mean distance from the center of the sun? the mass of the sun is 1.99 * 1030 kilograms.

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Answers (2)

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Savannah Mckenzie · Answer 1

Savannah Mckenzie 21 December, 23:53

0

7.8 * 1011 meters ...

Zaniyah Yates · Answer 2

F = m A

A = Ac = v^2/R

so m A = Mjupiter v^2/R (toward sun)

F = G Msun MJupiter / R^2 (toward sun)

so

G Msun/R^2 = v^2/R

G Msun = v^2 R

Time around = circumference / v

T = 2 pi R/v

so

v = 2 pi R/T

v^2 = (2pi) ^2 R^2/T^2

so

G Msun = (2 pi) ^2 R^3/T^2

(which by the way is Kepler's Third Law)

so

R^3 = G Msun T^2 / (2 pi) ^2

G is 6.67*10^-11

so

R^3 = 6.67*10^-11*1.99*10^30*14.36*10^16 / 39.48

R^3 = 4.828*10^35

=.4828 * 10^36

so

R =.784 * 10^12 = 7.84 * 10^11 meters