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Saturday, November 21, 2020

Orbital Speeds

 

 Orbital Speeds                                    re = 6371 km

 

1.    Geostationary satellites are used for telecommunications. They appear not to move in the sky. However they do orbit the Earth with a period of 1 sidereal day. (23 hours 56m). There are two other conditions for the satellite to remain above one point on Earth. Over the equator, East à West,

Geostationary satellites orbit the earth at an altitude of 35 786km. Calculate their speed.

T = (23 x 60) + 56 min) = 1436 min x 60 sec =86160 s

r = height + re = 6371 +35786= 42157 x1000 m = 4.22 x107m

 = (2 x 3.142 x 4.22 x107) / 86160 = 3074 ms-1

Similar satellites orbit Mars at an altitude of 17 031 km.  The length of a Martian day is similar to that of the Earth, why are the altitudes so different? .

Mars has less mass than the Earth

Calculate the speed of an Arestationary satellite. Tm = 88642.66 rm = 3396.2 km. 1448 ms-1

 

2.    GPS satellites orbit at a height of 20 200km. Their orbital period is 11h 58min earth time (– their time is about 20 microseconds faster due to the relativistic effects of their motion and the Earth’s mass bending space-time). Calculate their orbital speed. 3900 ms-1

 

3.    NASA’s Mercury messenger probe orbited the planet at an altitude of 201 km, (rm = 2.44 x 106m) with a period of 5.75 x 103 s Calculate its speed. 2900 ms-1

 

 

 

4.    Complete this table

Distance from Sun (106 km)

Orbital Period (days)

T (Years)

Orbital Speed m/s

MERCURY

57.9

88

0.241096

48 000

VENUS

108.2

224.7

0.615616

35 000

EARTH

149.6

365.2

1.000548

30 000

MARS

227.9

687

1.882192

24 000

JUPITER

778.6

4331

11.86575

13 000

SATURN

1433.5

10747

29.44384

9700

URANUS

2872.5

30589

83.80548

6800

NEPTUNE

4495.1

59800

163.8356

5500

PLUTO

5870

90588

248.1863

4700

 

5.    There are 5 planets orbiting the star tau Ceti (12 light years away and similar to our sun although it’s slightly cooler, 5344K compared to 5778K ) The planets are called a,b,c,d e&f.

Tau Cati F orbits at 1.35 AU from the star. (1AU = 150 million km) with a period of 1.76yrs. Calculate its orbital speed. 22 000 ms-1

(Assuming that Tau Ceti f is a terrestrial planet, it would likely be at least 2.3 times larger in size than the Earth. With an Earth-like atmosphere, the surface temperature would be approximately −40°C (233 K). With a denser atmosphere able to produce a stronger greenhouse effect it could have a much higher temperature, between 0°C and 50°C, enough for complex life to exist.)

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