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A satellite is to travel from the Earth to Mars using a Hohmann transfer. 1. Calculate the semi-major axis of the transfer orbit. Using the Vis-Viva equation compute the heliocentric velocity of the satellite as it reaches Mars. 2. The spacecraft is adjusted so that it will pass within $300$ $km$ of the surface of Mars just behind of it in its orbit. Calculate the eccentricity of the hyperbolic passage and hence the half turn angle $\delta$. **[20 points]** 3. The approach of the spacecraft is on the sunward side of Mars. Compute the heliocentric velocity of the spacecraft when it exits Mars' sphere of influence. 4. A Hohmann transfer requires a long transfer time. Propose a method to reduce the transfer time to reach Mars and outline the procedure that you would use to compute the radial and transverse velocity at Mars arrival. Relevant Data Sun gravitational parameter us = 1.327×10¹¹ km³ s¯ -2 = Mars gravitational parameter μM Mars orbital radius r = 2.279×108 km Radius of Mars RM - 3390 km = = 4.2828×104 km³s-2 Earth orbital radius TE = = 1.496×108 km

A satellite is to travel from the Earth to Mars using a Hohmann transfer. 1. Calculate the semi-major axis of the transfer orbit. Using the Vis-Viva equation compute the heliocentric velocity of the satellite as it reaches Mars. 2. The spacecraft is adjusted so that it will pass within $300$ $km$ of the surface of Mars just behind of it in its orbit. Calculate the eccentricity of the hyperbolic passage and hence the half turn angle $\delta$. **[20 points]** 3. The approach of the spacecraft is on the sunward side of Mars. Compute the heliocentric velocity of the spacecraft when it exits Mars' sphere of influence. 4. A Hohmann transfer requires a long transfer time. Propose a method to reduce the transfer time to reach Mars and outline the procedure that you would use to compute the radial and transverse velocity at Mars arrival. Relevant Data Sun gravitational parameter us = 1.327×10¹¹ km³ s¯ -2 = Mars gravitational parameter μM Mars orbital radius r = 2.279×108 km Radius of Mars RM - 3390 km = = 4.2828×104 km³s-2 Earth orbital radius TE = = 1.496×108 km

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A satellite is to travel from the Earth to Mars using a Hohmann transfer. 1. Calculate the semi-major axis of the transfer orbit. Using the Vis-Viva equation compute the heliocentric velocity of the satellite as it reaches Mars. 2. The spacecraft is adjusted so that it will pass within $300$ $km$ of the surface of Mars just behind of it in its orbit. Calculate the eccentricity of the hyperbolic passage and hence the half turn angle $\delta$. **[20 points]** 3. The approach of the spacecraft is on the sunward side of Mars. Compute the heliocentric velocity of the spacecraft when it exits Mars' sphere of influence. 4. A Hohmann transfer requires a long transfer time. Propose a method to reduce the transfer time to reach Mars and outline the procedure that you would use to compute the radial and transverse velocity at Mars arrival. Relevant Data Sun gravitational parameter us = 1.327×10¹¹ km³ s¯ -2 = Mars gravitational parameter μM Mars orbital radius r = 2.279×108 km Radius of Mars RM - 3390 km = = 4.2828×104 km³s-2 Earth orbital radius TE = = 1.496×108 km
Transcribed Image Text:A satellite is to travel from the Earth to Mars using a Hohmann transfer. 1. Calculate the semi-major axis of the transfer orbit. Using the Vis-Viva equation compute the heliocentric velocity of the satellite as it reaches Mars. 2. The spacecraft is adjusted so that it will pass within $300$ $km$ of the surface of Mars just behind of it in its orbit. Calculate the eccentricity of the hyperbolic passage and hence the half turn angle $\delta$. **[20 points]** 3. The approach of the spacecraft is on the sunward side of Mars. Compute the heliocentric velocity of the spacecraft when it exits Mars' sphere of influence. 4. A Hohmann transfer requires a long transfer time. Propose a method to reduce the transfer time to reach Mars and outline the procedure that you would use to compute the radial and transverse velocity at Mars arrival. Relevant Data Sun gravitational parameter us = 1.327×10¹¹ km³ s¯ -2 = Mars gravitational parameter μM Mars orbital radius r = 2.279×108 km Radius of Mars RM - 3390 km = = 4.2828×104 km³s-2 Earth orbital radius TE = = 1.496×108 km
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