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Monday, 1 July 2013

Answers to Orbital Speeds worksheet


 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 m/s

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 m/s

 

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 m/s

 

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 m/s

 

 

 

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 m/s

(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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