You send a probe to orbit Mercury at 135 km above the surface. What orbital velocity (in km/s) is needed to keep it in orbit? (The mass of Mercury is 3.30 ✕ 1023 kg, and the radius of Mercury is 2.44 ✕ 103 km.) What is the ratio of the time it takes a signal from Earth to reach Mercury (d = 57.9 ✕ 106 km) to the time it would take to reach the Moon (d = 384,400 km)? If your signal is at 8 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.) The orbital velocity is just the circular velocity. vc = GM r, where the distance is the distance above the surface plus the radius of Mercury. vc =

You send a probe to orbit Mercury at 135 km above the surface. What orbital velocity (in km/s) is needed to keep it in orbit? (The mass of Mercury is 3.30 ✕ 1023 kg, and the radius of Mercury is 2.44 ✕ 103 km.) What is the ratio of the time it takes a signal from Earth to reach Mercury (d = 57.9 ✕ 106 km) to the time it would take to reach the Moon (d = 384,400 km)? If your signal is at 8 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.) The orbital velocity is just the circular velocity. vc = GM r, where the distance is the distance above the surface plus the radius of Mercury. vc =

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Question

You send a probe to orbit Mercury at 135 km above the surface. What orbital velocity (in km/s) is needed to keep it in orbit? (The mass of Mercury is 3.30 ✕ 10²³ kg, and the radius of Mercury is 2.44 ✕ 10³ km.)

What is the ratio of the time it takes a signal from Earth to reach Mercury (d = 57.9 ✕ 10⁶ km) to the time it would take to reach the Moon (d = 384,400 km)?

If your signal is at 8 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.)

The orbital velocity is just the circular velocity.

v_c =

where the distance is the distance above the surface plus the radius of Mercury.

v_c =

Expert Solution