Lecture 04_ Newton's Laws and Lab 03

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Santa Barbara City College *

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101

Subject

Astronomy

Date

Apr 3, 2024

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docx

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Uploaded by ChancellorKnowledge13606

LAB 03A Your weight is the product of your mass and the acceleration of gravity , which we call “g.” Newton showed us that the force of gravity – that is, the gravitational attraction between any two bodies - is proportional to the product of their two masses (the planet or star and a smaller body) and inversely proportional to the distances between the centers of each body. When you weigh your mass by standing on a scale, you are measuring the force of gravitational attraction between your mass and the Earth. This equation says it all: W = weight (in a unit called Newtons) G = Newton’s universal gravitational constant = 6.67 x 10 -11 kg-m/sec 2 M = mass of planet, in kg m = mass of small body, in kg R = distance between the center of the planet and the center of the small body In this activity you will get a feeling for how much any hypothetical being of your choice would weigh on the surface of other planets, and from this you can calculate the acceleration of gravity, g, on each planet. 1. Go to this url: https://www.exploratorium.edu/ronh/weight/ 2. Make up a hypothetical being (an avatar) and give them a weight, in pounds: Name of avatar: Emma Weight of avatar in pounds: 150 3. Calculate the mass of your avatar in kg using this formula: 68.03 and enter this value in the box on the website that says “ENTER YOUR WEIGHT HERE.” Although the website says you can enter weight in any units you wish, we are going to use kilograms because the meter- kilogram-second unit system is what we universally use in science. 4. Then click on the box that says “Calculate.” Voila! You can see how much your avatar would weigh in kg on each planet and moon listed, and also three representative stars. Write your answers in the following table (next page): Your avatar’s weight on other worlds: Mercur y 25.7 Venus 61.7 The Moon 11.3 Mars 25.7 Jupiter 172 Saturn 72.4 Uranus 60.5 Neptune 76.6 Pluto 4.6 Io 12.5 Europa 9.1 Ganymede 9.8 Callisto 8.6 The Sun 1841.9 A White Dwarf 88450512.2 A Neutron Star 95254397700 00 5. Finding the acceleration of gravity on the surface of each planet: The average acceleration of gravity on the surface of the Earth is 9.8 m/sec 2 . To find the acceleration of gravity on the surface of each planet, do the following calculation, which you can do on your calculator, the calculator function of your cell phone, or in Excel if you are comfortable using it. where W p is your weight on each planet which the website calculated for you, W E is the weight, in kg, of your avatar on Earth (which you calculated in step 2), and g p is the acceleration of gravity on the surface of each planet. Write your answers in the following table.

Acceleration due to gravity on other worlds, in meters/sec 2 Mercur y Venus The Moon Mars Jupiter Saturn Uranus Neptune Pluto Io Europa Ganymede Callisto The Sun A White Dwarf A Neutron Star Finally, answer the discussion questions on the next page. 6. Discussion questions: Density is mass / volume. A good way to visualize density is to think of a 1cm 3 cube made of different substances. A sugar cube is approximately 1 cubic centimeter (1 cm 3 ). The density of sugar is 1.5 grams/cm 3 and a typical sugar cube has a volume of 1 cm 3 . Now imagine a sugar cube-sized chunk of lead. The density of lead is 11.3 gr/cm 3 . Imagine holding the cube of white sugar and the same size cube of lead in your hand. They are both the same volume (size in 3 dimensions), but the lead is 7.5 times DENSER than the sugar. So, which one will have more mass (feel heavier)? a) Thought experiment: Imagine a hypothetical planet made completely of white sugar, and another made completely of lead. Both planets are the same volume . Sugar planet. Density = 1.5 gr/cm 3 Lead planet. Density = 11.3 gr/cm 3 Which planet will have a greater mass, considering that they are the same size?_____________ Which planet will have a greater acceleration of gravity at its surface?____________________ On which planet would you weigh more?_______________________________ b) Notice from your table that Mercury and Mars have approximately the same value of g at their surfaces. However, Mercury has a radius of around 2400 km while Mars has a radius of around 3400 km. Which planet must be denser, Mercury or Mars? c) The website also calculated your weight on the Sun, a white dwarf, and a neutron star. The radius of the Sun is around 6.96 x 10 5 km, the radius of a white dwarf that started out as a star like the Sun is around 7,000 km, while the radius of a typical neutron star is around 10 km. Here is a schematic representation. The white dwarf is shown next to the Earth for comparison. Look back at your table of your weight on other worlds. Compare your weight on the Sun, a white dwarf, and a neutron star. On which would you weigh most? ___________________________________ On which would you weigh least? ___________________________________ From the above picture, rank the Sun, a white dwarf, and a neutron star in terms of their radius, from least to greatest: ____________________________________________________________ From your calculations of “g” for the Sun, a white dwarf, and a neutron star, rank the Sun, a white dwarf, and a neutron star in terms of “g” at their surface, from least to greatest: _______________________________________________________________________________ Based on all the above information, rank the Sun, a white dwarf, and a neutron star in terms of their density, from least dense to most dense: Keep these concepts in mind as we study planets, stars, and how stars evolve.

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