Chapter 10, Problem 64QAP

To determine

(a)

The time to make each orbit and gravitational force on the object

Answer to Problem 64QAP

Time taken for each orbital $=1.52hours$

Explanation of Solution

Given info:

Altitude = $345km$

Mass of the object = $10.0kg$

Formula used:

  $T^2=(\frac{4{\pi }^2}{GM}){(R+h)}^3$

  $T=$ Time

  $G=$ Gravitational constant

  $M=$ Mass of Earth

  $R=$ Radius of Earth

  $h=$ Altitude

  $F_g=\frac{GMm}{{(R+h)}^2}$

  $F=$ Gravitational force

  $m=$ Mass of the object

  $F=mg$

  $F=$ Force

  $m=$ Mass of the object

  $g=$ Acceleration

Calculation:

Time taken for each orbital,

  $\begin{array}{l}{T}^2=(\frac{4{\pi }^2}{GM}){(}^R\\ T=2\pi \sqrt{\frac{{(R+h)}^3}{GM}}=2\pi \sqrt{\frac{((6371+345)\times {10}^3){)}^3}{(6.67\times {10}^{-11}N{m}^2/k{g}^2)\times (6.0\times {10}^{24}kg)}}=5463.70s=1.52hours\end{array}$

Conclusion:

Time taken for each orbital $=1.52hours$

To determine

(b)

Gravitational force on the object

Answer to Problem 64QAP

Gravitational force $=88.73N$

Fraction $=\frac{88.73N}{98N}=0.91$

Explanation of Solution

Given info:

Altitude = $345km$

Mass of the object = $10.0kg$

Formula used:

  $T^2=(\frac{4{\pi }^2}{GM}){(R+h)}^3$

  $T=$ Time

  $G=$ Gravitational constant

  $M=$ Mass of Earth

  $R=$ Radius of Earth

  $h=$ Altitude

  $F_g=\frac{GMm}{{(R+h)}^2}$

  $F=$ Gravitational force

  $m=$ Mass of the object

  $F=mg$

  $F=$ Force

  $m=$ Mass of the object

  $g=$ Acceleration

Calculation:

Gravitational force,

  $F_g=\frac{GMm}{{(R+h)}^2}=\frac{(6.67\times {10}^{-11}N{m}^2/k{g}^2)\times (6.0*{10}^{24}kg)\times 10.0kg}{((6371+345)\times {10}^3){)}^2}=88.73N$

  $\begin{array}{l}F=mg=10.0kg\times 9.8m/s^2=98N\\ Fraction=\frac{F_g}{F}=\frac{88.73N}{98N}=0.91\end{array}$

Conclusion:

Gravitational force $=88.73N$

Fraction $=\frac{88.73N}{98N}=0.91$

To determine

(c)

How can an object be considered weightless in ISS?

According to the calculation comparatively to the weight on Earth, in the ISS weigh of the object is less.

Given info:

Altitude = $345km$

Mass of the object = $10.0kg$

Explanation:

Comparatively to the weight on Earth, in the ISS weigh of the object is less.

Conclusion:

Comparatively to the weight on Earth, in the ISS weigh of the object is less.

Answer to Problem 64QAP

According to the calculation comparatively to the weight on Earth, in the ISS weigh of the object is less.

Explanation of Solution

Given info:

Altitude = $345km$

Mass of the object = $10.0kg$

Comparatively to the weight on Earth, in the ISS weigh of the object is less.

Conclusion:

Comparatively to the weight on Earth, in the ISS weigh of the object is less.