You send a probe to orbit Mercury at 123 km above the surface. What orbital velocity (in km/s) is needed to keep it in orbit? (The mass of Mercury is 3.30 x 1023 kg, and the radius of Mercury is 2.44 x 10³ km.) What is the ratio of the time it takes a signal from Earth to reach Mercury (d = 57.9 x 106 km) to the time it would take to reach the Moon (d = 384,400 km)? If your signal is at 9 cm, what is the wavelength shift (in cm) at this orbital velocity? (Assume the probe is at a point in its orbit in which it is moving directly away from the Earth.)
You send a probe to orbit Mercury at 123 km above the surface. What orbital velocity (in km/s) is needed to keep it in orbit? (The mass of Mercury is 3.30 x 1023 kg, and the radius of Mercury is 2.44 x 10³ km.) What is the ratio of the time it takes a signal from Earth to reach Mercury (d = 57.9 x 106 km) to the time it would take to reach the Moon (d = 384,400 km)? If your signal is at 9 cm, what is the wavelength shift (in cm) at this orbital velocity? (Assume the probe is at a point in its orbit in which it is moving directly away from the Earth.)
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Transcribed Image Text:You send a probe to orbit Mercury at 123 km above the surface. What orbital velocity (in km/s) is needed to keep it in orbit? (The mass of Mercury is 3.30 x 1023 kg, and the radius of Mercury
is 2.44 x 10³ km.)
What is the ratio of the time it takes a signal from Earth to reach Mercury (d = 57.9 x 106 km) to the time it would take to reach the Moon (d = 384,400 km)?
If your signal is at 9 cm, what is the wavelength shift (in cm) at this orbital velocity? (Assume the probe is at a point in its orbit in which it is moving directly away from the Earth.)
Part 1 of 4
The orbital velocity is just the circular velocity.
where the distance is the distance above the surface plus the radius of Mercury.
GM Mercury-kg
x
How high above the surface is the probe? Make sure you enter your distance in meters. m
km/s
Vc =
GM
Vc =
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