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GPE-1 The planet Mars has a mass of 6.39×1023 kilograms (kg) and a radius of 3390 kilometers (km). A satellite is in orbit around Mars, at a height of 4250 km above the surface. You are on the surface of Mars, and you want to deliver a package to the satellite. What is the minimum initial speed (v) the package needs to be launched upwards in order to make it to the satellite? Assume that mechanical energy is conserved. Give your answer in units of km/s. The universal gravitational constant is 6.67×10-11 N m²/kg².

GPE-1 The planet Mars has a mass of 6.39×1023 kilograms (kg) and a radius of 3390 kilometers (km). A satellite is in orbit around Mars, at a height of 4250 km above the surface. You are on the surface of Mars, and you want to deliver a package to the satellite. What is the minimum initial speed (v) the package needs to be launched upwards in order to make it to the satellite? Assume that mechanical energy is conserved. Give your answer in units of km/s. The universal gravitational constant is 6.67×10-11 N m²/kg².

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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GPE-1 The planet Mars has a mass of 6.39×1023 kilograms (kg) and a radius of 3390 kilometers (km). A satellite is in orbit around Mars, at a height of 4250 km above the surface. You are on the surface of Mars, and you want to deliver a package to the satellite. What is the minimum initial speed (v) the package needs to be launched upwards in order to make it to the satellite? Assume that mechanical energy is conserved. Give your answer in units of km/s. The universal gravitational constant is 6.67×10-11 N m²/kg². GPE-2 Calculate the escape velocity of Mars using the data above. GPE-3 Consider a 1550 kg satellite in circular orbit around Mars with an altitude of 105 km. You want to move the satellite to a circular orbit with an altitude of 905 km. How much work must be done on the satellite (in units of Joules) in order to achieve this? 4250 km V = ?
Transcribed Image Text:GPE-1 The planet Mars has a mass of 6.39×1023 kilograms (kg) and a radius of 3390 kilometers (km). A satellite is in orbit around Mars, at a height of 4250 km above the surface. You are on the surface of Mars, and you want to deliver a package to the satellite. What is the minimum initial speed (v) the package needs to be launched upwards in order to make it to the satellite? Assume that mechanical energy is conserved. Give your answer in units of km/s. The universal gravitational constant is 6.67×10-11 N m²/kg². GPE-2 Calculate the escape velocity of Mars using the data above. GPE-3 Consider a 1550 kg satellite in circular orbit around Mars with an altitude of 105 km. You want to move the satellite to a circular orbit with an altitude of 905 km. How much work must be done on the satellite (in units of Joules) in order to achieve this? 4250 km V = ?
Expert Solution
Step 1

GPE-(1):

Let us assume the minimum initial speed requirement for the the package is v.

Now the gravitational potential energy of the object at the mars' surface is

EP=-GMmRm where G is the universal gravitational constant, M is the mass of the Mars, m is the mass of the package and Rm is the radius of the planet.

The expression for the initial kinetic energy of the package is given by

Ek=12mv2

Now the formula to calculate the total energy of the package at the surface of the Mars is given by

Ei=EP+Ek

Substitute the values into the formula to obtain the initial total energy of the package.

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