Answer to Question #216298 in Physics for ran li

Question

1.Mars has an orbital radius of 1.524 AU. Using Kepler’s constant of 1a²/Au³ you can determine it’s orbital period is ___ years. (Give your answer with 4 sig digs and do not include units).

2.Neptune has 3 moons, Proteus, Triton and Nereid. Proteus has an orbital radius of 117600 km and an orbital period of 1.12 days. Triton has an orbital radius of 354800 km. The orbital period of Triton is ___days. (Give your answer with the correct number of sig digs and do not include units)

3.The earth’s orbital radius is 1.49x10¹¹m and its period of revolution around the sun is 1.00 years. If Mercury has an orbital radius around the sun of 5.79x10¹⁰m, its period of revolution is _____years. (Give your answer with the correct number of sig digs and do not include units).

4.The earth’s orbital radius is 1.49x10¹¹m and its period of revolution around the sun is 1.00 years. If Venus has an orbital period of 224.7 days its orbital radius is _____x10¹¹m.

Answer 1

1)

$$T^2=1.524^3\\T=1.881\ years$$

2)

$$\frac{(354800)^3}{(117600)^3}=\frac{T_t^2}{1.12^2}\\T_t=5.87\ days$$

3)

$$\frac{(5.79\cdot10^{10})^3}{(1.49\cdot10^{11})^3}=\frac{T_m^2}{1.^2}\\T_m=0.242\ years$$

4)

$$\frac{r_V^3}{(1.49\cdot10^{11})^3}=\frac{224.7^2}{365^2}\\r_V=1.08\cdot10^{11}m$$