Question

The image below shows the average altitude of the International Space Station in 2020. Posigrade burns are done to avoid orbital debris and as a result of orbit decay (decay rate varies with solar cycle), or to accommodate vehicle docking phase angle requirements. Retrograde burns may also be done to accommodate the phase angle requirement for docking vehicles - may have been the case for the April and early July orbit adjustments - or when the orbit is too high. A lower orbit is better for crew radiation protection and for better orbital debris protection (debris in lower orbits encounter more drag and decays faster to burn up in the atmosphere). The max altitudes in this table are all less than the upper limit of 460 km altitude. Referencing the diagram, consider the burn in mid-April to transition from the initial higher orbit to the lower orbit. Assume the initial orbit is circular and estimate altitude from the image. Assume the lower orbit is elliptical after a single burn, with the initial altitude as it's apogee. Estimate the final average orbit from the image. Calculate the required delta V. Include a sketch with the intial and final orbits; identify and label the burn location. G =6.67300 * $10^{-11}$m$^3$kg$^{-1}$s$^{-2}$ Avergae radius of Earth = 6371 km Mass of Earth = 5.974 x$10^{24}$ kg $\mu_{earth}$ = 3.98600 * $10^5$km$^3$/sec$^2$

          The image below shows the average altitude of the International Space Station in 2020.
Posigrade burns are done to avoid orbital debris and as a result of orbit decay (decay rate varies with
solar cycle), or to accommodate vehicle docking phase angle requirements. Retrograde burns may
also be done to accommodate the phase angle requirement for docking vehicles - may have been
the case for the April and early July orbit adjustments - or when the orbit is too high. A lower orbit
is better for crew radiation protection and for better orbital debris protection (debris in lower orbits
encounter more drag and decays faster to burn up in the atmosphere). The max altitudes in this
table are all less than the upper limit of 460 km altitude. 
Referencing the diagram, consider the burn in mid-April to transition from the initial higher orbit
to the lower orbit. Assume the initial orbit is circular and estimate altitude from the image. Assume
the lower orbit is elliptical after a single burn, with the initial altitude as it's apogee. Estimate the
final average orbit from the image. Calculate the required delta V. Include a sketch with the
intial and final orbits; identify and label the burn location.
G =6.67300 * $10^{-11}$m$^3$kg$^{-1}$s$^{-2}$
Avergae radius of Earth = 6371 km
Mass of Earth = 5.974 x$10^{24}$ kg
$\mu_{earth}$ = 3.98600 * $10^5$km$^3$/sec$^2$

The image below shows the average altitude of the International Space Station in 2020.
Posigrade burns are done to avoid orbital debris and as a result of orbit decay (decay rate varies with
solar cycle), or to accommodate vehicle docking phase angle requirements. Retrograde burns may
also be done to accommodate the phase angle requirement for docking vehicles - may have been
the case for the April and early July orbit adjustments - or when the orbit is too high. A lower orbit
is better for crew radiation protection and for better orbital debris protection (debris in lower orbits
encounter more drag and decays faster to burn up in the atmosphere). The max altitudes in this
table are all less than the upper limit of 460 km altitude.
Referencing the diagram, consider the burn in mid-April to transition from the initial higher orbit
to the lower orbit. Assume the initial orbit is circular and estimate altitude from the image. Assume
the lower orbit is elliptical after a single burn, with the initial altitude as it's apogee. Estimate the
final average orbit from the image. Calculate the required delta V. Include a sketch with the
intial and final orbits; identify and label the burn location.
G =6.67300 * 10^-11m^3kg^-1s^-2
Avergae radius of Earth = 6371 km
Mass of Earth = 5.974 x10^24 kg
μearth = 3.98600 * 10^5km^3/sec^2

Added by Carolina V.

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