Correction to: End-of-life geostationary satellite removal using realistic flat solar sails

Aerospace Systems (2021) 4:269–270 https://doi.org/10.1007/s42401-021-00094-x

C O R R E C T I O N

Correction to: End-of-life geostationary satellite removal using realistic flat solar sails

Hao Mei

¹·

Christopher J. Damaren

¹·

Xingqun Zhan

²

Published online: 14 June 2021

© Shanghai Jiao Tong University 2021

Correction to:

Aerospace Systems

https://doi.org/10.1007/s42401-021-00089-8

Due to an unfortunate oversight the Eq. (8), Tables 2 and 4 has been given erroneously. It should read (Tables

2

and

4)

d dt

⎛

⎜ ⎜

⎜ ⎜

⎜ ⎜

⎝

a e i ω θ

⎞

⎟ ⎟

⎟ ⎟

⎟ ⎟

⎠

x˙

=

⎛

⎜ ⎜

⎜ ⎜

⎜ ⎜

⎜ ⎜

⎜ ⎜

⎜ ⎜

⎝

2a²

√μa(1−e²)e

sin(θ)

√ ^2a2

μa(1−e²)(1+e

cos(θ)) 0

a(1−e²)

μ

sin(θ)

a(1−e²)

μ 2 cos(θ)+e(1+cos²(θ))

1+ecos(θ)

0

0 0

a(1−e²)

μ cos(ω+θ) 1+ecos(θ)

−

a(1−e²) μ cos(θ)

e

a(1−e²)

μ (2+ecos(θ))sin(θ) e(1+ecos(θ)) −

a(1−e²)

μ sin(ω+θ)

tan(i)(1+ecos(θ))

0 0

a(1−e²)

μ sin(ω+θ)

sin(i)(1+ecos(θ))

a(1−e²) μ cos(θ)

e −

a(1−e²)

μ (2+ecos(θ))sin(θ)

e(1+ecos(θ))

0

⎞

⎟ ⎟

⎟ ⎟

⎟ ⎟

⎟ ⎟

⎟ ⎟

⎟ ⎟

⎠

denote asP(x)

⎛

⎝

fr

f_θ fz

⎞

⎠

+

⎛

⎜ ⎜

⎜ ⎜

⎜ ⎜

⎜ ⎝

0 0 0 0 0

μ a³

(1√+ecos(θ))² (1−e²)³

⎞

⎟ ⎟

⎟ ⎟

⎟ ⎟

⎟ ⎠

denote asb(x)

(8)

The original article can be found online athttps://doi.org/10.1007/

s42401-021-00089-8.

B

^{Hao Mei}

hao.mei@mail.utoronto.ca Christopher J. Damaren damaren@utias.utoronto.ca Xingqun Zhan

xqzhan@sjtu.edu.cn

1 University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, ON M3H 5T6, Canada

2 Shanghai Jiaotong University School of Aeronautics and Astronautics, 800 Dongchuan Road, Shanghai 200240, China

123

270 Aerospace Systems (2021) 4:269–270

Table 2 The GEO graveyard

region Property Requirement

Perigee altitude A minimum increase of 235 km+(100·CR·A/m) 235 km : the sum of the upper altitude of the GEO

protected region (200 km) and the maximum descent due to luni-solar and geo-potential perturbations (35 km)

CR: the solar radiation pressure (SRP) coefficient A/m: the area to dry mass ratio

Eccentricity [0,0.003]

Table 4 Comparisons between the ideal solar sails and the realistic flat solar sails Solar sail thrust model

Ideal sail f_ideal=

2P·(A/m)·cos²α n

Realistic flat Sail f_real= f_n+f_t

f_n= P_m^A

(1+ ˜r s)cos²α+B_f(1−s)˜rcosα+(1− ˜r)^ξfB_ξf^f_+ξ^−ξb_b^Bbcosα n f_t=

P_m^A(1− ˜r s)cosαsinα t Control angle constraints

Ideal sail α∈ [0^◦,90^◦],δ∈ [0^◦,360^◦]

Realistic flat sail α∈ [0^◦,85^◦],δ∈ [0^◦,360^◦]

System dynamics

Ideal sail x˙(t)=P(x)·C_{O P}C_{P G}C_{G S}· f_ideal+b(x)

Realistic flat sail x˙(t)=P(x)·C_{O P}C_{P G}C_{G S}·(f_n+ f_t)+b(x)

The original article has been corrected.

123