ESCAPE VELOCITY EXAMPLES

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Godfrey Dalton
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1 ESCAPE VELOCITY EXAMPLES 1. Escape velocity is the speed that an object needs to be taveling to beak fee of planet o moon's gavity and ente obit. Fo example, a spacecaft leaving the suface of Eath needs to be going 7 miles pe second, o nealy 5,000 miles pe hou, to ente obit. A Delta II ocket blasting off. A lage amount of enegy is needed to achieve escape velocity. Photo fom Jet Populsion Laboatoy's Planetay Missions & Instuments image galley Escape Velocity 00 Rev

Fo example, a spacecaft leaving the suface of Eath needs to be going 7 miles pe second, o nealy 5,000 miles pe hou, to ente obit.

2 . The ability to use and compute squae oots is often a necessay tool in physics. Fo example, squae oots ae used to compute the minimum velocity a spacecaft must have to escape the gavitational foce of a planet. The escape velocity, v, can be calculated using the following fomula: Escape Velocity In this fomula, G is a gavitational constant, M is the mass of the planet, and is the adius of the planet.. Since escape velocity depends on the mass of the planet o moon fom which a spacecaft is blasting, a spacecaft leaving the moon's suface could go slowe than one blasting off fom the Eath, because the moon has less gavity than the Eath. On the othe hand, the escape velocity fo Jupite would be many times that of Eath's because Jupite is so huge and has so much gavity. 4. Example: Compute the escape velocity fo Eath if its mass is 5.98 x 10 4 kg, its adius is.7 x 10 m, and G =.7 x N-m /Kg. The abbeviation N epesents Newton, a unit of foce in the metic 1kg m 1 N = system. Using these constaints, the answes will be in m/s. s (.7x10 (5.98x10.7x x x10 The escape velocity fo Eath is appoximately 1.1 x 10 4 m/s Point out that the gavitational constant is given in N-m /kg. The abbeviation N stands fo Newton. One Newton of foce acting on a mass of one kilogam causes acceleation of one mete pe second pe second (the thought pocess in this application is challenging. Exceptional students will have no poblem but it may be easie fo aveage students to accept this unit instead of deiving it. Escape Velocity 00 Rev

The escape velocity, v, can be calculated using the following fomula: Escape Velocity In this fomula, G is a gavitational constant, M is the mass of the planet, and is the adius of the planet.

3 . You may want to show students why the answe is labeled in m/s. Nm kg( m G is in with N in. (kg m Thus G is in. kg( s M is in kg. R is in m. Theefoe, And is in s m kg kg( s m m o o. m s s m m o. s s 7. Thought Povoke: Is it bette to launch a ship into obit fom nea o away fom the equato? (AWAY. The adius is geate at the equato than at the poles. This lowes the escape velocity. 8. Though Povoke: Why is mass impotant? (Mass is impotant because of two majo factos affecting how things move in space: inetia and gavity. The moe mass something has, the moe inetia and gavity affect it. That is why heavy things (things with a lot of mass ae had to move. When an object is sitting still, it esists moving, and the moe mass it has, the moe it esists. The amount of thust needed to move something and how fast it ends up moving ae both diectly tied to its mass. On the othe hand, once something massive stats moving, it is vey had to stop. This is also due to the elationship between mass and inetia. Gavity is also popotional to how much mass each thing has. The bigge an object is, the lage the gavitational pull it exets. Because of gavity and inetia, the moe massive something is, the hade it is to get into space, the hade it is to keep it thee, and the hade it is to move it whee you want it to go when it is thee. 9. Thought Povoke: Why is it difficult to plan inta-planet missions? (One eason that manned missions to othe planets ae difficult to plan is that a ship would have to take enough fuel into space to blast off of the othe planet when the astonauts wanted to go home. The weight of the fuel would make the spaceship so heavy it would be had to blast it off Eath. Escape Velocity 00 Rev

Though Povoke: Why is mass impotant? (Mass is impotant because of two majo factos affecting how things move in space: inetia and gavity.

4 Name: Date: Class: ESCAPE VELOCITY WORKSHEET Compute the escape velocity fo the indicated planet using the fomula below. Use G =.7 x N m. kg 1. Mas: mass.4 x 10 kg; adius.9 x 10 m. Mecuy: mass.5 x 10 kg; adius.44 x 10 m. Venus: mass 4.90 x 10 4 kg; adius.0 x 10 m Escape Velocity 00 Rev

4 x 10 kg; adius.9 x 10 m. Mecuy: mass.5 x 10 kg; adius.44 x 10 m. Venus: mass 4.

5 ESCAPE VELOCITY WORKSHEET KEY Compute the escape velocity fo the indicated planet using the fomula below. Use G =.7 x N m. kg 1. Mas: mass.4 x 10 kg; adius.9 x 10 m (.7x10 (.4x10.9x x10 The escape velocity fo Eath is appoximately 5.04 x 10 m/s.. Mecuy: mass.5 x 10 kg; adius.44 x 10 m (.7x10 (.5x10.44x x10 The escape velocity fo Eath is appoximately 4.8 x 10 m/s.. Venus: mass 4.90 x 10 4 kg; adius.0 x 10 m (.7x10 (4.90x10.0x x10 The escape velocity fo Eath is appoximately 1.04 x 10 4 m/s. Escape Velocity 00 Rev

44 x 10 m (.7x10 (.5x10.44x10 18151.9 4.8x10 The escape velocity fo Eath is appoximately 4.8 x 10 m/s.. Venus: mass 4.90 x 10 4 kg; adius.0 x 10 m (.

6 Student Name: Date: ESCAPE VELOCITY CHECKLIST 1. On question 1, did the student compute the escape velocity fo the indicated planet? a. Yes (5 points b. No, but only made mino mathematical eos (0 points c. No, used escape velocity fomula incoectly (15 points d. No, student could only set poblem up but could not solve (10 points. On question, did the student compute the escape velocity fo the indicated planet? a. Yes (5 points b. No, but only made mino mathematical eos (0 points c. No, used escape velocity fomula incoectly (15 points d. No, student could only set poblem up but could not solve (10 points. On question, did the student compute the escape velocity fo the indicated planet? a. Yes (5 points b. No, but only made mino mathematical eos (0 points c. No, used escape velocity fomula incoectly (15 points d. No, student could only set poblem up but could not solve (10 points Total Numbe of Points A B C D F 7 points and above 0 points and above 5 points and above 45 points and above 44 points and below Any scoe below C needs emediation! Escape Velocity 00 Rev

On question, did the student compute the escape velocity fo the indicated planet? a. Yes (5 points b. On question, did the student compute the escape velocity fo the indicated planet? a. Yes (5 points b. No, but only made mino mathematical eos (0 points c.

Gravitation. AP Physics C

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