Question answers 1-3 Background:Newton formulated the Universal Law of Gravitation: F =R2GmMwhere,Fthe gravitational force between two masses.the gravitational constant, G = 6.67 x 101" N- m/kg?the mass of one objectmass of other objectdistance between the center of the objects%3DG =mM =R =Also, we learned that weight, w=mg. Equating weight with Newton's Law of GravitationGmMwe get: mg =R2or canceling m:GMg =R2This can be used to calculate the acceleration of gravity on any planet/object/body.Objective:Investigate several phenomena using Newton's Universal Law of Gravitation. Understandthe difference between accuracy and precision.Procedure:Perform the indicated calculations. The following information can be used for thecalculations.Mass of SunMass of Earth1.99 x 1030 kg5.98 x 1024 kg7.36 x 1022 kg2 x 1030 kg1.90 x 1027 kgEarth-Sun distance1.50 x 10" m6.38 x 10° m1.74 x 10 mRadius of EarthMass of MoonRadius of MoonMass of neutron starRadius of neutron starMass of JupiterEarth-Jupiter distance (in-line)12,000 m6.3 x 10" mError and Uncertainty:All measurements contain error and thus uncertainty. We can calculate errors depending onthe nature of the experiment. We define two main types of uncertainty:Precision is how well independent measurements (E, and E2) match. Precision can bequantified using the formula: Percent Difference = -E, - E-x100(E, + E)/2Percent difference is used when there is not an accepted value; it is used to compare twoindependent quantities.Accuracy is how close a measurement (E) is to an accepted value (A). Accuracy can bequantified using the formula: Percent Error =|A-E/Ax100Percent error is used to compare a quantity/measurement to an accepted value. 1. Calculate the acceleration of gravity on A) the Earth. B) the Moon. C) a neutron star.2. Forces cause accelerations, and thus velocity. Using Newton's Law of Gravitation, theGMorbital velocity (speed) of an object can be shown to be: v =RWhere M is themass of the body being orbited and R is the average distance from the body. A) CalculateEarth's orbital velocity around the Sun. B) How fast is Earth traveling in m.p.h.? C)Calculate Earth's orbital velocity using a second method. (Hint: The Earth orbits theSun in approximately a circle every 365 days. Speed = Distance/Time. Distance = thecircumference of Earth's orbit = 2rR and Time is number of seconds in a year.) D)Compare the orbital velocities (speeds) from Parts A and C by calculating the percentdifference of the two velocities and comment (are they about the same?).EarthM (Sun)3. Astrologers claim that when Jupiter is 'lined-up' with the Earth and Sun, its gravitationalpull on humans is significant, and thus affects our life. A) Calculate the gravitational pullfrom Jupiter on a human (m=70 kg) when Jupiter is 'in-line' with the Earth and Sun. B)Calculate the gravitational pull from a skyscraper on a human walking through anydowntown, or city center (ASsume a skyscraper has a mass of 1.2 x 10° kg, and thedistance between the center of masses is 175 m). C) Calculate the pull from a large cliff(M=8.8 x 107 kg and R=14 m). D) How many times bigger are the answers in B and cthan the answer in part A? Comment on these results.m = 70 kgA)M (Jupiter)m = 70 kgB)RM (skyscraper)m = 70 kgC)M (cliff)

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Question answers 1-3 Background:Newton formulated the Universal Law of Gravitation: F =R2GmMwhere,Fthe gravitational force between two masses.the gravitational constant, G = 6.67 x 101&#34; N- m/kg?the mass of one objectmass of other objectdistance between the center of the objects%3DG =mM =R =Also, we learned that weight, w=mg. Equating weight with Newton's Law of GravitationGmMwe get: mg =R2or canceling m:GMg =R2This can be used to calculate the acceleration of gravity on any planet/object/body.Objective:Investigate several phenomena using Newton's Universal Law of Gravitation. Understandthe difference between accuracy and precision.Procedure:Perform the indicated calculations. The following information can be used for thecalculations.Mass of SunMass of Earth1.99 x 1030 kg5.98 x 1024 kg7.36 x 1022 kg2 x 1030 kg1.90 x 1027 kgEarth-Sun distance1.50 x 10&#34; m6.38 x 10° m1.74 x 10 mRadius of EarthMass of MoonRadius of MoonMass of neutron starRadius of neutron starMass of JupiterEarth-Jupiter distance (in-line)12,000 m6.3 x 10&#34; mError and Uncertainty:All measurements contain error and thus uncertainty. We can calculate errors depending onthe nature of the experiment. We define two main types of uncertainty:Precision is how well independent measurements (E, and E2) match. Precision can bequantified using the formula: Percent Difference = -E, - E-x100(E, + E)/2Percent difference is used when there is not an accepted value; it is used to compare twoindependent quantities.Accuracy is how close a measurement (E) is to an accepted value (A). Accuracy can bequantified using the formula: Percent Error =|A-E/Ax100Percent error is used to compare a quantity/measurement to an accepted value. 1. Calculate the acceleration of gravity on A) the Earth. B) the Moon. C) a neutron star.2. Forces cause accelerations, and thus velocity. Using Newton's Law of Gravitation, theGMorbital velocity (speed) of an object can be shown to be: v =RWhere M is themass of the body being orbited and R is the average distance from the body. A) CalculateEarth's orbital velocity around the Sun. B) How fast is Earth traveling in m.p.h.? C)Calculate Earth's orbital velocity using a second method. (Hint: The Earth orbits theSun in approximately a circle every 365 days. Speed = Distance/Time. Distance = thecircumference of Earth's orbit = 2rR and Time is number of seconds in a year.) D)Compare the orbital velocities (speeds) from Parts A and C by calculating the percentdifference of the two velocities and comment (are they about the same?).EarthM (Sun)3. Astrologers claim that when Jupiter is 'lined-up' with the Earth and Sun, its gravitationalpull on humans is significant, and thus affects our life. A) Calculate the gravitational pullfrom Jupiter on a human (m=70 kg) when Jupiter is 'in-line' with the Earth and Sun. B)Calculate the gravitational pull from a skyscraper on a human walking through anydowntown, or city center (ASsume a skyscraper has a mass of 1.2 x 10° kg, and thedistance between the center of masses is 175 m). C) Calculate the pull from a large cliff(M=8.8 x 107 kg and R=14 m). D) How many times bigger are the answers in B and cthan the answer in part A? Comment on these results.m = 70 kgA)M (Jupiter)m = 70 kgB)RM (skyscraper)m = 70 kgC)M (cliff)

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