This presentation presents the timeline of the evolution of human understanding and the development of the gravity model.

1. INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
History of Earth Gravity Model
Pawan Singh
Ph.D. (First Year)
CEN-514: Geodesy and GPS surveying

2. 2
CONTENT
• Pre-Satellite Era
• Basis of Model
• Sputnik Era
• Post Sputnik Era
• Apollo Era
• Post Apollo Era
• 21st Century
• Conclusion
• References

3. 3
Pre-Satellite Era
TIMELINE
• 130 BC
• 1686 AD
• 1740 AD
EVENTS
• Hipparchus suggested theory of precision with its
mathematical measurement 10 𝑝𝑒𝑟 𝑐𝑒𝑛𝑡𝑢𝑟𝑦.
• Newton proposed earth shape as oblate spheroid
with flattening of
1
230
.
• McLaurin experimentally proved earth gravity
changes with latitude.
Fig 1. Hipparchus
Statement from Newton Book
“the earth is higher under the
equator than at the poles, and that
by an excess of about 17 miles”
(Philosophiae Naturalis Principia
Mathematica, Book III, Proposition
XX)
Image courtesy: Wikipedia

4. 4
BASIS OF MODEL
𝑉(𝑟, ∅, 𝜆) =
𝐺𝑀
𝑅
𝑙 𝑚
(
𝑅
𝑟
)𝑙+1
𝑃𝑙𝑚 sin 𝜑 [𝐶𝑙𝑚 cos 𝑚𝜆 + 𝑆𝑙𝑚 sin 𝑚𝜆]
𝜑 = 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒
𝜆 = 𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒
𝑙 𝑎𝑛𝑑 𝑚 𝑎𝑟𝑒 𝑑𝑒𝑔𝑟𝑒𝑒 𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑜𝑓 𝑠𝑝ℎ𝑒𝑟𝑖𝑐𝑎𝑙 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐𝑠
𝑃𝑙𝑚 𝑙𝑒𝑔𝑒𝑛𝑑𝑟𝑒 𝑃𝑜𝑙𝑦𝑛𝑜𝑚𝑖𝑎𝑙
𝐶𝑙𝑚 𝑎𝑛𝑑 𝑆𝑙𝑚 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐶𝑜𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝑅 𝑖𝑠 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑒𝑎𝑟𝑡ℎ
𝑟 𝑖𝑠 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡 𝑓𝑟𝑜𝑚 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑜𝑓 𝑒𝑎𝑟𝑡ℎ
𝑀 𝑖𝑠 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑒𝑎𝑟𝑡ℎ
𝑚 = 0 𝑑𝑒𝑝𝑒𝑛𝑑 𝑜𝑛𝑙𝑦 𝑜𝑛 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒
𝑙 = 𝑚 𝑑𝑒𝑝𝑒𝑛𝑑 𝑜𝑛𝑙𝑦 𝑜𝑛 𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒
𝑙 ≠ 𝑚 𝑑𝑒𝑝𝑒𝑛𝑑 𝑜𝑛 𝑏𝑜𝑡ℎ

5. 5
𝒍 = 𝟗, 𝒎 = 𝟓 𝒎 = 𝟎 𝒍 = 𝒎
Courtesy: http://icgem.gfz-potsdam.de/vis3d/tutorial

6. 6
Sputnik Era
TIMELINE
• 1957
• 1958
EVENTS
• Sputnik was launched and stayed in space for 90
days and Month later Sputnik II was launched.
• Vanguard II ,Sputnik III and Explorer I were
launched. Few researchers from England and
Czechoslovakia observes the sputnik I orbit
Fig 2. Sputnik I
Image courtesy: https://www.popularmechanics.com/space/satellites/news/a28496/how-sputnik-worked/

7. 7
POST SPUTNIK ERA
TIMELINE
• 1960
• 1963
• 1965
EVENTS
• Transit Navy Navigational Satellite System
• ECHO satellite
• APL 1.0 model improvement program with degree
and order 8.
• APL 3.5 (most popular) order and degree 12
Fig 3. Working of TNNSS using Doppler frequency
Image courtesy: https://www.seaturtle.org/tracking/faq.shtml

8. 8
TIMELINE
• 1974
EVENTS
• APL 5.0 to degree and order of 15 and it was
predecessor to WGS-72 and accuracy of 5-10m
Fig 4. Tracking accuracy of geopotential
models obtained from the Transit system
over the 20 years of the Orbit Improvement
Program.
Image courtesy: Vetter(1994)

9. 9
APOLLO ERA
TIMELINE
• 1966
EVENTS
• Ist Model using Baker Nunn Camera 1966 achieved
order 8. They achieved order 16 using a combination of
Laser and Baker Nunn camera data in 1970.
Fig 5.(Left): Baker-Nunn Camera
Fig 6.(Right): Astronomical facility at
Nainital
Image courtesy: Wikipedia(L),https://media.arxiv-vanity.com/render-output/5214131/x1.png(R)

10. 10
TIMELINE
• 1972
• 1974
EVENTS
• NWL10E which became base of WGS-72, later updated in 1984
using GEOS-3 and RADAR sea Altimeter.
• WGS-72 was derived of 12 degree and order and WGS-66 was
completed to degree and order 24.
TABLE 1: Data types used in gravity model
developments. (ALT = altimeter; D = Doppler; L = laser;
MFA = mean free air anomaly; MGA = mean gravity
anomaly; MT = minitrack interferometer; O = optical; S =
SECOR; SST = satellite-to-satellite tracking; USB =
unified S-band.)
Image courtesy: Vetter(1994)

11. 11
POST APOLLO ERA
TIME
• 1972
• 1981
EVENTS
• Goddard Earth Model(GEM) was developed by Goddard space
flight center (GSFC) to degree and order of 12 using Baker Nunn
Camera.
• GEM-10 model includes satellite, RADAR altimetry, surface
gravity measurement to degree and order of 36.
Fig 7. RADAR Altimeter
Image courtesy:Barzaghi et al.,2015

12. 12
TIMELINE
• 1986
• 1992
• 1994
• 1996
EVENTS
• WGS-84 was launched.
• GEM-T3 till order and Degree of 50.
• JGM-2 model was complete to degree and order of
50. Data used to develop this model were TOPEX
satellite data, Doppler orthography Radio positioning
integrated by satellite(DORIS).
• EGM96S (only satellite) of degree and order 70. After
adjustment EGM96 was launched with degree and
order of 360.

13. 13
Image courtesy: Barzaghi et al.,2015

14. 14
20th CENTURY
• CHAMP (Challenging Minisatellite Payload)
• Launched in 2000 in low earth orbital(LEO)
• It has GPS antenna , accelerometer, Star camera, Satellite to Satellite
tracking, Laser measurement, Accelerometer.
• It has spatial resolution of 400km and degree and order of 50 after 72
months degree and order were improved to 150.
Fig 8. CHAMP
satellite
Image courtesy: eoportal

15. 15
GRACE
• Gravity Recovery and Climate experiment
• It’s an American and German mission designed by NASA and DLR launched in
2002.
• This consist of two satellite at low earth orbit (494km) separated by distance of
220km.
Fig 9. The GRACE
concept of satellite-to-
satellite (b) Artist’s
impression of the
GRACE satellites in
orbit
Image Courtesy: Rummel et al., 2002

16. 16
• GPS antenna, Electrostatic accelerometer, star camera, distance
meter(K-band) ,Satellite to satellite tracking, Gradiometer.
• Degree and order of 120 with spatial resolution of 170km and it
improves to 360.
• EGM2008 uses GRACE Data and launched with degree and order
of 2159.

17. 17
GOCE
• Gravity Field and Steady state ocean circulation explorer
• Mission by ESA launched in 2009 to LEO(250km).
• It has Xeon ion propulsion engine.
• It has high accurate accelerometer of preciseness of 10−12 𝑚𝑠−2.
• Spatial resolution of 100km
• Degree and order of 200, EGM 2020 will have its data and
expected to have Degree and order of 5399.

18. 18
Fig 10. Inner parts of GOCE
Image courtesy: eoportal

19. 19
Exploring GEOID
http://icgem.gfz-potsdam.de/vis3d/longtime

20. 20
WGS66 EGM2008

21. 21
CONCLUSION
• In pre-satellite era evolution of gravity model was slow due to no
technology advancement but after satellite and technology
advancement in sensors and computational power we achieved
pretty good earth gravity model. In the future we can achieve near
perfect model after getting more data and from innovative satellite
and more terrestrial survey that can overcome current issues.

22. 22
REFERENCES
• Vetter, J. R. (1994). The evolution of Earth gravitational models used in
astrodynamics. Johns Hopkins APL Technical Digest, 15(4), 319-335.
• Rapp, R. H. (1998). Past and future developments in geopotential
modeling. Geodesy on the Move, 58-78.
• Featherstone, W. (2010). Satellite and airborne gravimetry: their role in geoid
determination and some suggestions. In Airborne gravity 2010 (pp. 58-70).
Geoscience Australia.
• Barzaghi, R., Migliaccio, F., Reguzzoni, M., & Albertella, A. (2015). The Earth
gravity field in the time of satellites. Rendiconti Lincei, 26(1), 13-23.
• Nerem, R. S., Jekeli, C., & Kaula, W. M. (1995). Gravity field determination
and characteristics: retrospective and prospective. Journal of Geophysical
Research: Solid Earth, 100(B8), 15053-15074.

23. 23
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