# Orbit and Gravity Questions

**Orbit and Gravity Questions**

Directions: Show the solutions (i.e. your work) to these on a separate sheet of paper.

30. m/s/s2.1 “g”s

6.6 m/s / -3. An amusement park ride has a radius of 4.5 m and is going 11.7 m/s at the top of its vertical circle. What is the centripetal acceleration at the top, and what g-force do the riders feel at the top? What is the minimum speed the ride could go at the top for people to not fall out?

26 m/s/s

10. m/s / -2. The loop of a roller coaster is 3.8 m in radius. You read 1.7 “g” s at the top of the loop. What is your centripetal acceleration at the top? What is your velocity at the top?

10.9 m/s/s

-5.28 N @ top

+97.1 N @ bottom / -1. Thor twirls a 4.68 kg hammer precisely at 3.50 m/s in a 1.12 m radius vertical circle. What is the centripetal acceleration of the hammer head? What is the force on the 4.68 kg hammer head at the top of the circle? What is the force exerted on the hammer head at the bottom?

6.66 m/s/s

Top: 5.51 N up

Bot: 28.8 N up / 0. A 1.75 kg mass moves in a vertical circle on the end of a 35.0 cm rod. The mass completes one rotation in 1.44 seconds. What is the centripetal acceleration of the mass? What force and in what direction does the rod exert on the mass at the top and the bottom of the circle?

8.17x10-10 N / 1.What is the force of gravity between the two 4.2 Kg bowling balls whose centers are 1.2 m distant?

1.99 x 1020 N

2.8x10-3 m/s/s

2.3x106 s or 27 days / 2. What is the force of gravity between the earth and the moon? What acceleration does the moon undergo? (use F=ma) What is its period of motion? (Use a centripetal acceleration equation)

10.9 N / 3. What is the force of gravity on a 10 Kg object twice earth's radius above the earth?

3.1 x 107 m / 4. What distance from the center of the moon is the attraction between a 500. kg object and the moon itself equal to 2.5 N?

880 hours

4.2x10-6 m/s / 5. A flea is in orbit 2.1 m from the center of a .545 kg baseball. What is the period of orbit? What is the orbital velocity? (the flea and baseball are in deep space)

6970 m/s or 15,600 mph / 6. What velocity do you need to orbit 8.20 x 106 m from the center of the earth?

1470 m/s

9620 s / 7. What velocity do you need to orbit 5.20 x 105 m from the surface of the moon? What would be your period of orbit?

537 m/s

1.01 x1023 kg / 8. Fred the alien orbits the planet Zirkon, completing an orbit with a radius of 23.4 x 106 m every 3.17 earth days. What is his velocity, and what is the mass of the planet he is orbiting?

4.22 x 107 m

6.61 Re / 9. What is the radius of a geosynchronous orbit? (Around earth, T = 23 hrs, 56 min, 4 sec - but convert it to seconds) How many earth radii is this?

365 days

(31556425.51 s) / 10. What is the period of an orbit 149.6x109 m from the center of the sun (in earth days)?

9.55x106 m / 11. At what distance from the surface of the earth is the orbital velocity 5000. m/s?

1480 m/s

365 s / 12. A 4090 kg spacecraft is approaching the moon at 6839 m/s, and wants to orbit 510. km above its surface. What is the speed of orbit at this elevation? They aim 510 km to the side of the moon, but for what time do they need to burn their main engine (that generates 60,123 N of thrust) to reduce their speed to the proper orbital speed?

Useful things to know:

Mass of the Earth / 5.97x1024 kg / Radius of the Moon / 1.738x106 mMass of the Moon / 7.36x1022 kg / Radius of the Earth / 6.38x106 m

Mass of the Sun / 1.99x1030 kg / Earth-Moon Distance / 3.84x108 m

Earth-Sun Distance / 1.496x1011 m