Orbital Speeds

 

 Orbital Speeds                                    r_e = 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 + r_e = 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. T_m = 88642.66 r_m = 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, (r_m = 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.)