PS 5.3 | Universal Gravitation

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Problems

1 Consider a 70.0 kg human standing on the surface of Earth

• a. Calculate the force of attraction between the two masses
• b. Calculate the resulting acceleration of the human toward Earth
• c. Calculate the resulting acceleration of the Earth toward the human

• 2. Consider a 70.0 kg human standing on the surface of Earth’s moon, Luna

• a. Calculate the force of attraction between the two masses
• b. Calculate the resulting acceleration of the human toward Luna
• c. Calculate the resulting acceleration of Luna toward the human.

3. Calculate the weight of a 45.5 kg person in the following locations:

• a. On the surface of Earth
• b. 1.0x103 km above Earth
• c. On the “surface” of Saturn (there may well be no such thing)
• d. Compare your values for part (a) and (c ) above. Explain mathematically why they are so similar. Hint: masses, radii
• e. 1.0x103 km above Saturn
• f. Compare your value for part (b) and (e) above. Explain mathematically why they are so dissimilar.

4. A spacecraft of mass 1850 kg holds a roughly circular orbit 2.00 radii above Earth’s surface.

• a. Calculate the force of gravity experienced by the spacecraft
• b. Determine the centripetal acceleration experienced by the spacecraft
• c. Determine the velocity of the spacecraft

5. Suppose it is the year 1798 and the value of G has just been determined experimentally. Approximate the mass of Earth to three significant figures.

6. A hypothetical planet has a radius of 2.0 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

7. A 958 kg lander probe touched down on the surface Europa (one of the moons of Jupiter) contains an accelerometer reading 1.98 m/s2. If the mass of Europa is 4.9 x 1022 kg:

1. Determine the force of attraction from Europa’s gravity
2. Calculate the circumference of the moon (in km)

8. Jupiter and Saturn are an average of 646,270,000 km apart. Calculate the (average) attractive force between the two bodies.

Answers

1. (a) $685 \,N$
   (b) $9.79 \,m/s^2$
   (c) $1.15 x 10^{-22} \, \frac{m}{s^2}$
2. (a) $113 \,N$
   (b) $1.61 \frac{m}{s^2}$
   (c) $1.5 x 10{-21} \,m/s^2$
3. (a) $446 \,N$
   (b) $333 \,N$
   (c) $475 \,N$
   (e) $475 \,N$
4. (a) $1 900 \,N $
   (b) $1.09 \,m/s^2 $
   (c) $4 560 \,m/s $
5. $5.98 x 10^{24} \,kg$
6. $2.45 \,m/s2 $
7. (a) $1\,910 \, N$
   (b) $8.07 x 10^3 \,km$
8. $1.72 x 1020 \, N$