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LAB 2 HOMEWORK: ENTRY, DESCENT AND LANDING YOUR MISSION: I. Learn some of the physics (potential energy, kinetic energy, velocity, and gravity)

that will affect the success of your spacecraft. II. Explore differences in gravity on other planetary bodies. III. Design a planetary landing vehicle that will successfully reach the target and land

safely (without breaking the egg). IV. Work as a team to create a prototype using the least amount of materials. V. Test the prototype by dropping at increasing heights. RECENT LANDINGS ON MARS, VENUS, TITAN AND ASTEROIDS: Mars Science Laboratory and the Curiosity Rover NASA launched the Mars Science Laboratory (MSL) on November 26, 2011, which landed the rover Curiosity on the surface of Mars on August 6th, 2012. The Entry, Descent, and Landing event took place in four stages including a guided entry, a parachute descent, a powered descent, and a sky crane landing. The guided entry allowed MSL to be steered to its landing site. The parachute descent stage involved the release of a large parachute to slow the spacecraft down to about 100 meters per second. During the powered descent, a platform with eight rocket thrusters slowed the descent even more. The sky crane landing involved the rover being lowered down with a 7.6 meter tether to the Martian surface.

The Curiosity rover and parachute imaged by the Mars Reconnaissance Orbiter (MRO) on August 6th, 2012.

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Soviet Venera 13 The Venera 13 spacecraft was launched on October 30th, 1981 and traveled for about four months to Venus. A descent vehicle separated and descended into Venus’ atmosphere. A parachute was then released and air breaking was used to descend Venera 13 to the surface. The harsh temperature of 457° C (855° F) and atmospheric pressure of 92 Earth atmospheres allowed the lander to only survive for ~127 minutes on Venus’ surface.

This is a picture taken by Venera 13 of its landing site on Venus. Part of Venera 13 can

be seen in the lower left corner of the image.

The Huygens Probe The Cassini-Huygens spacecraft was launched on October 15, 1997. The Huygens probe was released from the Cassini spacecraft, and landed on Saturn’s moon Titan on January 14, 2005. The Huygens probe gathered data for about 90 minutes after it touched down on the surface of Titan. An image taken by the Huygens probe on Titan’s surface.

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NEAR Shoemaker Probe NASA’s NEAR Shoemaker Probe landed on the asteroid 433 Eros (34.4 km in its longest measurement) on February 12, 2001. The NEAR Shoemaker probe was not designed as a lander (see the picture to the right), but near completion of its mission the team decided to land it on Eros. Its impact velocity was 1.5-1.8 m/s.

The NEAR Shoemaker probe that now resides on 433 Eros. Hayabusa The Japanese spacecraft Hayabusa landed on the asteroid 25142 Itokawa (630 m in its longest measurement) on November 21, 2005 for 30 minutes, and collected a sample that it returned to earth on June 13, 2010. The gravity of Itokawa is so small that as the Hayabusa spacecraft flew towards it, approaching at 12 cm/s (0.27 miles per hour) the spacecraft incrementally decreased its velocity to zero, 17 meters above the surface and fell the rest of the way to a soft landing on the surface. However, in its fall it was not primarily accelerated toward the asteroid by Itokawa’s very weak gravity (6x10-9 m/s2) but by the stronger, but still weak, pressure of solar radiation (1x10-7 m/s2), Hayabusa took these photographs during its slow descent to Itokawa.

Photograph: Japanese Aerospace Exploration Agency (JAXA), 2008.

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Some of the Physics Behind Descent & Landing In the Impact Cratering lab, you learned that when a projectile hits another body it

releases all of its kinetic energy. If it is massive and has a high velocity, it will excavate a crater and may explode. When you build a spacecraft (with an egg as your payload) next week, you do not want it to! There are two main strategies (that can be combined) for a successful descent and landing:

1) Design features to reduce velocity before impact (ex. a parachute) 2) Design features that will absorb the energy at impact (ex. cushioning)

Learning about basic physics will help you design your spacecraft and better understand the space missions discussed in this lab. According to the First Law of Thermodynamics, energy cannot be created or destroyed: it just changes form. The greater potential energy an object has before release, the greater the kinetic energy it will have upon impact. Potential energy (PE) is related to the mass of the object (m), gravity (g), and the height of the object above the surface (h), by the equation PE = mgh. Kinetic energy (KE) is related to the mass of the object (m) and the velocity of the object (v), by the equation KE = (1/2)*mv². The higher the drop height is, the greater the velocity is at impact because as the object falls, its potential energy is converted to kinetic energy. The SI unit of energy is the Joule (J):

1 J = 1 kg(m/s)2 We have the equations and units for energy, but we also want to understand the relationship between velocity and height, which can be found by reconfiguring the PE and KE formulas. We have the equations and units for energy, but we also want to understand the relationship between velocity and height, which can be found by reconfiguring the PE and KE formulas. PE=KE therefore KE = (1/2)*mv² = PE = mgh which we can simply to: (1/2)*mv² = mgh Mass (m) can be canceled out (1/2)*mv² = mgh Relationship between height & gravity (1/2)*v² = gh Re-arranged to more convenient forms:

€

v = 2gh

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h =v 2

2g

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Name: Lab Instructor: Lab Section: In the lab, you will drop your spacecraft from two heights: (1) 5.9 m (2) 10.5 m The mass of an egg is approximately 0.050 kg. Use this information to calculate the impact energy (PE=KE, choose which one you prefer) and the velocity at impact for your egg, without a spacecraft. (For these calculations, we are ignoring drag.)

Planetary Body

Acceleration of Gravity

(m/s2)

Drop Height 1: Energy at Impact (J)

Drop Height 2: Energy at Impact (J)

Drop Height 1: Velocity at

Impact (m/s)

Drop Height 2: Velocity at

Impact (m/s)

Earth 9.81

Venus 8.87

Mars 3.71

Titan 1.35

(433) Eros* 0.0059

(25143) Itokawa** 1.06x10-7

* 433 Eros is elongate not spherical so its gravity is varies significantly across its surface. This value is its mean gravity. **This is the amount the Hayabusa spacecraft was accelerated toward 25143 Itokawa. Itokawa’s gravity is only 1.06x10-7 m/s2. To learn more re-read the paragraph about Hayabusa.

Show your work for one of your calculations: Energy at Impact: Velocity at Impact:

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Without a spacecraft, do you think the egg would survive landing on any of these bodies? If so, which ones? Since energy cannot be lost, where does the energy go if you reduce your spacecraft’s velocity before landing (and by association reduce its KE)?