Kepler’s law – problems and solutions

1. The Earth’s distance from the Sun is 149.6 x 106 km and period of Earth’s revolution is 1 year. Calculate T2 / r3

Known :

T = 1 year, r = 149.6 x 106 km

Wanted : T2 / r3 = … ?

Solution :

k = T2 / r3 = 12 / (149.6 x 106)3 = 1 / (3348071.9 x 1018) = 2.98 x 10-25 year2/km3

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2. Universal constant (G) = 6.67 x 10-11 N.m2/kg2 and Sun’s 1.99 x 1030 kg.

Kepler's law – problems and solutions 1

Kepler's law – problems and solutions 2

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3. The mean distance of Earth from the Sun is 149.6 x 106 km and the mean distance of Mercury from the Sun is 57.9 x 106 km. The period of Earth’s revolutions is 1 year, what is the period of Mercury’s revolution?

Known :

r of Earth = 149.6 x 106 km

r of mercury = 57.9 x 106 km

T of Earth = 1 year

Wanted: T of mercury?

Solution :

Kepler's law – problems and solutions 3

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  1. Newton’s law of universal gravitation problems and solutions
  2. Gravitational force, weight problems, and solutions
  3. Acceleration due to gravity problems and solutions
  4. Geosynchronous satellite problems and solutions
  5. Kepler’s law problems and solutions problems and solutions

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